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Muhammad Muazu Bala, Shailender Singh, Dhruba Kumar Gautam, Stochastic frontier approach to efficiency analysis of health facilities in providing services for non-communicable diseases in eight LMICs, International Health, Volume 15, Issue 5, September 2023, Pages 512–525, https://doi.org/10.1093/inthealth/ihac080
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Abstract
The rising burden of non-communicable diseases presents an increasing public health challenge to many low- and middle-income countries. This problem may be compounded in health systems with lower levels of technical efficiency (TE).
This study used recent Service Provision Assessments data to estimate the level of TEs of health facilities in eight countries. Initially, the general and disease-specific service readiness indexes are estimated. Finally, the production function is estimated using the exposures and the outcomes of the model.
Evidence shows that the general and disease-specific service readiness indexes are significantly associated with an increase in the number of outpatient visits. Outpatient visits may increase by 14% with an increase in health worker density. Similarly, outpatient visits may increase by 0.3% with a unit increase in the general and diabetes service readiness indexes. Furthermore, outpatient visits may increase by 0.4% and 0.8% with an increase in services readiness for cardiovascular and respiratory diseases. respectively. Overall, the level of TE score suggests the need for improvement.
Facility-level service readiness for chronic diseases is quite low. Therefore, improving health outcomes related to chronic diseases requires urgent investment in high-quality health systems in these countries.
Introduction
Non-communicable diseases (NCDs) constitute the largest portion of the global burden of morbidity and mortality. These conditions include cardiovascular diseases, cancer, respiratory diseases and diabetes, which affect individuals across ages, countries and economic conditions.1 More than 80% of NCD burden occurs in low- and middle-income countries (LMICs).2 Globally, from the 53 million annual mortality estimates, 35 million are attributed to NCDs and more than three-quarters of these occurred in LMICs.3 Worldwide, NCDs account for 44% of premature mortality. The death toll attributed to these conditions has roughly doubled the mortality rates from infectious diseases, maternal and perinatal conditions and nutritional defects.1 The burden of NCDs is only projected to increase and available estimates suggest an increase in the NCD burden in LMICs by almost 17%, and up to 27% in some regions of the world, including Africa.4
Importantly, NCDs cause the greatest burden of inequitable disability and mortality within LMICs. In India, NCD prevalence is higher among people of higher socio-economic status and lower among the poor, which implies that the poor have little or no access to diagnostic services.5 In LMICs, NCD risk factors include excessive smoking and low levels of fruit and vegetable consumption, which were significantly prevalent among poor and disadvantaged groups.6 Across income groups in LMICs, wealth and educational disparities are negatively associated with angina, asthma, depression, arthritis and comorbidity. The prevalence of diabetes is positively associated with wealth and, to a lesser degree, with education.6
Furthermore, the growing burden of NCDs and their associated worse health status may be related to the lower level of technical efficiency (TE) of health production functions.7 The level of TE of the health system of a country measures the highest unit of health that can be attained, using the available inputs, with the existing resource constraints.8 The mean estimates of TE can be of crucial importance for planning, monitoring and controlling the performance of the health system over time.9
The objective of this article is to measure the level of TE of health facilities in providing general and chronic disease–specific health services in Afghanistan, Bangladesh, Democratic Republic of the Congo, Haiti, Malawi, Nepal, Senegal and Tanzania using the stochastic frontier model.
Methods
Technically, the production process describes the transformation of inputs into outputs using the existing technology. Thus a maximum output level could be achieved if the production function is utilized at its full potential. It is possible to determine the effects of varying input combinations in the production function that results in an optimum level of output that is consistent with either cost minimization or maximization of health outcomes. In this case, health facilities are assumed to be the production units that process health inputs into health output.10 In much health-related applied research, the commonly used input indicators are health worker density, health expenditure and the level of supply of medical resources.11 Similarly, in the available literature, different indicators are used as health system outputs. For instance, inpatient and outpatient visits have been used as health outcomes.12 The analysis of TE is one of the techniques employed to evaluate the strength of health facilities in health production.13,14
Data envelopment analysis (DEA) and stochastic frontier analysis (SFA) are the techniques applied to the evaluation of TE of health facilities in health production.15–17 However, the DEA approach uses input and output combinations to establish efficient production frontiers of health facilities that perform the best. Of note, any deviation from the efficient production frontier is ascribed to technical inefficiency (indicated as ui).18 That is, the DEA approach does not fully account for the randomness in the stochastic error term ui which may lead to deviation from the efficient production frontier.16
This article applied the econometric approach of SFA to investigate the levels of TE of health facilities in the countries of the study. The SFA method employed allows for the estimation of efficient production frontiers from the available input and output volumes, thereby obtaining estimates for the technical inefficiency term and the stochastic error term.15 Moreover, the SFA technique allows for the analysis of facility-level heterogeneity in the production function of the current model (indicated as zij).8,19 Therefore the health production function is specified in line with the SFA approach of Aigner et al.,20 which can be given as:
where yi measures the productive capacity of health facility i, xij indicates the health inputs j supplied to health facility I, |$\beta $| indicates a (KX1) vector of some parameters, e denotes the natural log of the continuous variable in the model, vi denotes the stochastic error term and ui measures the levels of technical inefficiency in the model.
The TE of the health facility as the unit of analysis can be expressed as:
where 0 < TEi ≤ 1. Thus, if the coefficient of TE is quite low or near zero, it indicates a higher level of technical inefficiency in health production. However, a TE coefficient closer to unity shows a greater level of efficiency of health facilities in the delivery of health services. The parameters of equation (1) can be estimated using the maximum likelihood approach and the estimates of technical inefficiency are obtained following the Jondrow method.8
Importantly, estimating the parameters of equation (1) requires a proper econometric functional form that accounts for the distribution of the technical inefficiency term. In line with the extant literature, this article follows Coelli et al.15 and Hamidi21 and specifies the Cobb–Douglass (CD) and the translog (TL) specifications in the SFA analysis. Initially the analysis applied the generalized maximum likelihood ratio test to choose the right functional form for the model.22 Similarly, half-normal (HN), exponential and truncated distributions are applied to choose the appropriate model regarding the distribution of ui.19 Lastly, the information criterion is also used to select the best model.
The model
The Cobb–Douglass specification of the stochastic frontier model can be given as:
Thus the translog representation of the stochastic frontier model is given as:
where yi denotes health output, xij indicates health inputs and zij is the covariates of the model.
Definition of the variables of the model
The empirical model of this study has three components: the input, the covariates and the output. Detailed description of the variables are presented in Table 1. Further details regarding selection of the variables included in this model can be found elsewhere.14
Indicator . | Definition . | Total . |
---|---|---|
Health outcome (mean±SD) | ||
Output | Total number of outpatient visits in the last full month | 7605±1552 |
Input variables (mean±SD) | ||
Density of health workers | Total number of health workers across health facilities | 7552±14 |
SRIs | Represents the percentage of list of various items that are consider essential for providing general health services, diseases specific health services in health facilities. The scores can be interpreted as lowest or highest, i.e. 0–100. | GSRI 54.96 (10.87) |
DSRI 35.86 (20.21) | ||
CDSRI 36.49 (25.23) | ||
RDSRI 25.23 (10.12) | ||
Covariates | ||
Factype | Type of health facility reported by the survey | |
= 1 for national/regional hospitals | 132 (1.76%) | |
= 2 for provincial hospital | 739 (9.84%) | |
= 3 for special hospital | 655 (8.73%) | |
= 4 for private hospital | 809 (10.78%) | |
= 5 for private clinic | 1549 (20.63%) | |
= 6 for health centres | 1072 (14.20%) | |
= 7 for dispensary | 646 (8.61%) | |
= 8 for primary health centres | 1440 (19.18%) | |
Facloc | Location of health facility reported by the survey | |
= 1 for urban area | 2236 (34.17%) | |
= 2 for rural area | 4308 (65.83%) | |
Facmagt | Management authority of the health facility | |
= 1 for public or government owned facilities | 4830 (64.34%) | |
= 2 for private-not-for profit facilities | 681 (9.07%) | |
= 3 for private-for-profit facilities | 1212 (16.14%) | |
= 4 for mission or faith-based facilities | 660 (8.79%) | |
= 5 for others | 124 (1.66%) |
Indicator . | Definition . | Total . |
---|---|---|
Health outcome (mean±SD) | ||
Output | Total number of outpatient visits in the last full month | 7605±1552 |
Input variables (mean±SD) | ||
Density of health workers | Total number of health workers across health facilities | 7552±14 |
SRIs | Represents the percentage of list of various items that are consider essential for providing general health services, diseases specific health services in health facilities. The scores can be interpreted as lowest or highest, i.e. 0–100. | GSRI 54.96 (10.87) |
DSRI 35.86 (20.21) | ||
CDSRI 36.49 (25.23) | ||
RDSRI 25.23 (10.12) | ||
Covariates | ||
Factype | Type of health facility reported by the survey | |
= 1 for national/regional hospitals | 132 (1.76%) | |
= 2 for provincial hospital | 739 (9.84%) | |
= 3 for special hospital | 655 (8.73%) | |
= 4 for private hospital | 809 (10.78%) | |
= 5 for private clinic | 1549 (20.63%) | |
= 6 for health centres | 1072 (14.20%) | |
= 7 for dispensary | 646 (8.61%) | |
= 8 for primary health centres | 1440 (19.18%) | |
Facloc | Location of health facility reported by the survey | |
= 1 for urban area | 2236 (34.17%) | |
= 2 for rural area | 4308 (65.83%) | |
Facmagt | Management authority of the health facility | |
= 1 for public or government owned facilities | 4830 (64.34%) | |
= 2 for private-not-for profit facilities | 681 (9.07%) | |
= 3 for private-for-profit facilities | 1212 (16.14%) | |
= 4 for mission or faith-based facilities | 660 (8.79%) | |
= 5 for others | 124 (1.66%) |
SD: standard deviation.
Source: Author's computation.
Indicator . | Definition . | Total . |
---|---|---|
Health outcome (mean±SD) | ||
Output | Total number of outpatient visits in the last full month | 7605±1552 |
Input variables (mean±SD) | ||
Density of health workers | Total number of health workers across health facilities | 7552±14 |
SRIs | Represents the percentage of list of various items that are consider essential for providing general health services, diseases specific health services in health facilities. The scores can be interpreted as lowest or highest, i.e. 0–100. | GSRI 54.96 (10.87) |
DSRI 35.86 (20.21) | ||
CDSRI 36.49 (25.23) | ||
RDSRI 25.23 (10.12) | ||
Covariates | ||
Factype | Type of health facility reported by the survey | |
= 1 for national/regional hospitals | 132 (1.76%) | |
= 2 for provincial hospital | 739 (9.84%) | |
= 3 for special hospital | 655 (8.73%) | |
= 4 for private hospital | 809 (10.78%) | |
= 5 for private clinic | 1549 (20.63%) | |
= 6 for health centres | 1072 (14.20%) | |
= 7 for dispensary | 646 (8.61%) | |
= 8 for primary health centres | 1440 (19.18%) | |
Facloc | Location of health facility reported by the survey | |
= 1 for urban area | 2236 (34.17%) | |
= 2 for rural area | 4308 (65.83%) | |
Facmagt | Management authority of the health facility | |
= 1 for public or government owned facilities | 4830 (64.34%) | |
= 2 for private-not-for profit facilities | 681 (9.07%) | |
= 3 for private-for-profit facilities | 1212 (16.14%) | |
= 4 for mission or faith-based facilities | 660 (8.79%) | |
= 5 for others | 124 (1.66%) |
Indicator . | Definition . | Total . |
---|---|---|
Health outcome (mean±SD) | ||
Output | Total number of outpatient visits in the last full month | 7605±1552 |
Input variables (mean±SD) | ||
Density of health workers | Total number of health workers across health facilities | 7552±14 |
SRIs | Represents the percentage of list of various items that are consider essential for providing general health services, diseases specific health services in health facilities. The scores can be interpreted as lowest or highest, i.e. 0–100. | GSRI 54.96 (10.87) |
DSRI 35.86 (20.21) | ||
CDSRI 36.49 (25.23) | ||
RDSRI 25.23 (10.12) | ||
Covariates | ||
Factype | Type of health facility reported by the survey | |
= 1 for national/regional hospitals | 132 (1.76%) | |
= 2 for provincial hospital | 739 (9.84%) | |
= 3 for special hospital | 655 (8.73%) | |
= 4 for private hospital | 809 (10.78%) | |
= 5 for private clinic | 1549 (20.63%) | |
= 6 for health centres | 1072 (14.20%) | |
= 7 for dispensary | 646 (8.61%) | |
= 8 for primary health centres | 1440 (19.18%) | |
Facloc | Location of health facility reported by the survey | |
= 1 for urban area | 2236 (34.17%) | |
= 2 for rural area | 4308 (65.83%) | |
Facmagt | Management authority of the health facility | |
= 1 for public or government owned facilities | 4830 (64.34%) | |
= 2 for private-not-for profit facilities | 681 (9.07%) | |
= 3 for private-for-profit facilities | 1212 (16.14%) | |
= 4 for mission or faith-based facilities | 660 (8.79%) | |
= 5 for others | 124 (1.66%) |
SD: standard deviation.
Source: Author's computation.
Health output
The health output variable used in this article is the total number of outpatients who visited health facilities (yi|${y}_i $|) in the last month. The survey reports data for the total number of patients who visited the facility not long ago.
Density of Health Workers
This variable enters the model as one of the health input indicators (xij).|$({x}_{ij}).$| It refers to the total number of health workers who belong to the generalist, specialists, clinicians, anaesthetists and nurse professionals serving in the facilities.
Services Readiness Index (SRI)
The General Services Readiness Index (GSRI), Diabetes Services Readiness Index (DSRI), Cardiovascular Disease Services Readiness Index (CDSRI) and Respiratory Disease Services Readiness Index (RDSRI) are used as supplementary input indicators in the model (xij). The GSRI is computed following the World Health Organization's Service Availability and Readiness Assessment (SARA) standard manual.23 The GSRI shows the overall strength of health facilities in providing general health services. Similarly, the SARA manual also provides guidelines for evaluating the capacity of health facilities in providing services for diabetes, cardiovascular and respiratory diseases.23 For each domain of the index, a mean score is computed based on the listed items per domain and eventually the mean values are generated as GSRI, DSRI, CDSRI and RDSRI, respectively.
Characteristics of health facilities
The type of health facility, its management type and its location are also included as covariates to control for the level of heterogeneity of health facilities across the countries.
Data and sample size
This article used the most recent round of Service Provision Assessment (SPA) survey data conducted from 2013 to 2019 in eight LMICs. The facility-level data includes the type of health facility, its management and its location, along with a wider range of health services that are offered in the facility. Moreover, it provides data on the number of outpatient visits during the successive period of the survey and the number of different health professionals that contribute to the efficient provision of health services. Further, the data report other essential indicators for computing SRIs. Importantly, the survey data were collected using stratified random sampling. The SPA data are freely accessible for researchers upon request from the Demographic and Health Surveys.24 Table A1 in the appendix presents the countries of this study and the details of the data.
In the eight countries of this study, the SPA data reported 6502 health facilities. This article included 128 national/regional hospitals, 744 provincial hospitals, 600 speciality hospitals, 618 private hospitals, 1294 private clinics, 982 health centres, 612 dispensaries and 1146 primary health centres that had no missing values and are common across these countries. Thus this reduced the sample size to 6124 health facilities considered as the focus of this analysis. However, the analysis examined the heterogeneity in the production function by adjusting for the facility-level differences. Thus this may help in understanding the differences in the mean score of the TE specific to national/regional facilities, provincial hospitals, private hospitals and other types of facilities included in the analysis.
Data analysis
Mainly descriptive statistics and SFA techniques are applied to the analysis of the data. Initially, as presented in Table 1, a descriptive statistic is used to summarize the variables included in the model. The same technique is applied to the estimates of SRIs and TE scores. Lastly, the TE scores of health facilities are predicted using the SFA. However, it is important to note that the density of health workers and the number of outpatient visits enter the model in their logarithmic form. Furthermore, the GSRI, along with the disease-specific services coverage index for providing both diagnosis and management of diabetes and cardiovascular and respiratory diseases is assessed using facility type as the unit of stratification. All data analysis is performed using Stata version 15.1 (StataCorp, College Station, TX, USA) and particularly its cross code for the analysis of stochastic frontier models using cross-sectional data.
Results
Table 2 presents the summary statistics of the total number of outpatient visits, the density of health workers and the GSRI, DSRI, CDSRI and RDSRI by accounting for the characteristics of health facilities in the countries of the study. Private hospitals and provincial hospitals have reported the lowest mean of outpatient visits and the density of health professionals is quite low for dispensaries and primary health centres. However, primary health centres had the highest mean of outpatient visits. As expected, national/regional and provincial hospitals have the highest mean density of professional health workers. Overall, primary healthcare has comparatively the lowest GSRI, DSRI and CDSRI. However, special hospitals have the lowest RDSRI. Furthermore, national/regional hospitals have demonstrated higher readiness for general and disease-specific health services while public health facilities have the lowest level of services readiness for general services and health services for chronic diseases. The health facilities driven by profit motives have the highest service readiness for providing care for chronic diseases and the mean number of outpatient visits. The same is true for health facilities located in urban areas. More visits were reported in urban health facilities, where health services are readily available.
Health facility indicator . | Outpatient visits . | Strength of health workers . | GSRI . | DSRI . | CDSRI . | RDSRI . | |||
---|---|---|---|---|---|---|---|---|---|
Type of health facility . | N . | Mean . | SD . | Mean . | SD . | Mean . | Mean . | Mean . | Mean . |
National/regional hospital | 128 | 13 435 | 49 047 | 31 | 73 | 76 | 55 | 52 | 41 |
Provincial hospital | 744 | 2062 | 3332 | 9 | 18 | 66 | 49 | 40 | 22 |
Specialty hospital | 600 | 3271 | 38 887 | 8 | 21 | 65 | 4 | 41 | 18 |
Private hospital | 618 | 2893 | 14 517 | 5 | 21 | 54 | 36 | 34 | 25 |
Private clinic | 1294 | 11 608 | 97 732 | 3 | 6 | 50 | 32 | 35 | 21 |
Health centres | 982 | 42 019 | 191 527 | 4 | 7 | 56 | 36 | 40 | 28 |
Dispensary | 612 | 59 180 | 229 771 | 1 | 1 | 49 | 28 | 32 | 20 |
Primary health centres | 1146 | 35 017 | 178 925 | 1 | 1 | 44 | 26 | 32 | 28 |
Total | 6124 | 169 485 | 803 738 | 62 | 148 | 55 | 36 | 36 | 25 |
Facility managing authority | |||||||||
Public or government | 3811 | 30 737 | 165 183 | 4 | 17 | 53 | 34 | 36 | 39 |
Private not-for-profit | 549 | 25 029 | 145 951 | 5 | 8 | 61 | 44 | 47 | 43 |
Private for-profit | 1123 | 33 220 | 167 752 | 6 | 11 | 61 | 47 | 47 | 43 |
Mission or faith-based | 641 | 1357 | 4842 | 4 | 6 | 62 | 47 | 41 | 39 |
Total | 6124 | 90 343 | 483 728 | 21 | 55 | 32 | 32 | 33 | |
Location of health facility | |||||||||
Urban | 2070 | 14 039 | 24 039 | 9 | 25 | 65 | 47 | 45 | 40 |
Rural | 4054 | 6180 | 10 233 | 2 | 4 | 51 | 32 | 34 | 34 |
Total | 6124 | 20 219 | 34 272 | 11 | 29 | 55 | 32 | 32 | 33 |
Health facility indicator . | Outpatient visits . | Strength of health workers . | GSRI . | DSRI . | CDSRI . | RDSRI . | |||
---|---|---|---|---|---|---|---|---|---|
Type of health facility . | N . | Mean . | SD . | Mean . | SD . | Mean . | Mean . | Mean . | Mean . |
National/regional hospital | 128 | 13 435 | 49 047 | 31 | 73 | 76 | 55 | 52 | 41 |
Provincial hospital | 744 | 2062 | 3332 | 9 | 18 | 66 | 49 | 40 | 22 |
Specialty hospital | 600 | 3271 | 38 887 | 8 | 21 | 65 | 4 | 41 | 18 |
Private hospital | 618 | 2893 | 14 517 | 5 | 21 | 54 | 36 | 34 | 25 |
Private clinic | 1294 | 11 608 | 97 732 | 3 | 6 | 50 | 32 | 35 | 21 |
Health centres | 982 | 42 019 | 191 527 | 4 | 7 | 56 | 36 | 40 | 28 |
Dispensary | 612 | 59 180 | 229 771 | 1 | 1 | 49 | 28 | 32 | 20 |
Primary health centres | 1146 | 35 017 | 178 925 | 1 | 1 | 44 | 26 | 32 | 28 |
Total | 6124 | 169 485 | 803 738 | 62 | 148 | 55 | 36 | 36 | 25 |
Facility managing authority | |||||||||
Public or government | 3811 | 30 737 | 165 183 | 4 | 17 | 53 | 34 | 36 | 39 |
Private not-for-profit | 549 | 25 029 | 145 951 | 5 | 8 | 61 | 44 | 47 | 43 |
Private for-profit | 1123 | 33 220 | 167 752 | 6 | 11 | 61 | 47 | 47 | 43 |
Mission or faith-based | 641 | 1357 | 4842 | 4 | 6 | 62 | 47 | 41 | 39 |
Total | 6124 | 90 343 | 483 728 | 21 | 55 | 32 | 32 | 33 | |
Location of health facility | |||||||||
Urban | 2070 | 14 039 | 24 039 | 9 | 25 | 65 | 47 | 45 | 40 |
Rural | 4054 | 6180 | 10 233 | 2 | 4 | 51 | 32 | 34 | 34 |
Total | 6124 | 20 219 | 34 272 | 11 | 29 | 55 | 32 | 32 | 33 |
SD: standard deviation.
Source: Author's computation.
Health facility indicator . | Outpatient visits . | Strength of health workers . | GSRI . | DSRI . | CDSRI . | RDSRI . | |||
---|---|---|---|---|---|---|---|---|---|
Type of health facility . | N . | Mean . | SD . | Mean . | SD . | Mean . | Mean . | Mean . | Mean . |
National/regional hospital | 128 | 13 435 | 49 047 | 31 | 73 | 76 | 55 | 52 | 41 |
Provincial hospital | 744 | 2062 | 3332 | 9 | 18 | 66 | 49 | 40 | 22 |
Specialty hospital | 600 | 3271 | 38 887 | 8 | 21 | 65 | 4 | 41 | 18 |
Private hospital | 618 | 2893 | 14 517 | 5 | 21 | 54 | 36 | 34 | 25 |
Private clinic | 1294 | 11 608 | 97 732 | 3 | 6 | 50 | 32 | 35 | 21 |
Health centres | 982 | 42 019 | 191 527 | 4 | 7 | 56 | 36 | 40 | 28 |
Dispensary | 612 | 59 180 | 229 771 | 1 | 1 | 49 | 28 | 32 | 20 |
Primary health centres | 1146 | 35 017 | 178 925 | 1 | 1 | 44 | 26 | 32 | 28 |
Total | 6124 | 169 485 | 803 738 | 62 | 148 | 55 | 36 | 36 | 25 |
Facility managing authority | |||||||||
Public or government | 3811 | 30 737 | 165 183 | 4 | 17 | 53 | 34 | 36 | 39 |
Private not-for-profit | 549 | 25 029 | 145 951 | 5 | 8 | 61 | 44 | 47 | 43 |
Private for-profit | 1123 | 33 220 | 167 752 | 6 | 11 | 61 | 47 | 47 | 43 |
Mission or faith-based | 641 | 1357 | 4842 | 4 | 6 | 62 | 47 | 41 | 39 |
Total | 6124 | 90 343 | 483 728 | 21 | 55 | 32 | 32 | 33 | |
Location of health facility | |||||||||
Urban | 2070 | 14 039 | 24 039 | 9 | 25 | 65 | 47 | 45 | 40 |
Rural | 4054 | 6180 | 10 233 | 2 | 4 | 51 | 32 | 34 | 34 |
Total | 6124 | 20 219 | 34 272 | 11 | 29 | 55 | 32 | 32 | 33 |
Health facility indicator . | Outpatient visits . | Strength of health workers . | GSRI . | DSRI . | CDSRI . | RDSRI . | |||
---|---|---|---|---|---|---|---|---|---|
Type of health facility . | N . | Mean . | SD . | Mean . | SD . | Mean . | Mean . | Mean . | Mean . |
National/regional hospital | 128 | 13 435 | 49 047 | 31 | 73 | 76 | 55 | 52 | 41 |
Provincial hospital | 744 | 2062 | 3332 | 9 | 18 | 66 | 49 | 40 | 22 |
Specialty hospital | 600 | 3271 | 38 887 | 8 | 21 | 65 | 4 | 41 | 18 |
Private hospital | 618 | 2893 | 14 517 | 5 | 21 | 54 | 36 | 34 | 25 |
Private clinic | 1294 | 11 608 | 97 732 | 3 | 6 | 50 | 32 | 35 | 21 |
Health centres | 982 | 42 019 | 191 527 | 4 | 7 | 56 | 36 | 40 | 28 |
Dispensary | 612 | 59 180 | 229 771 | 1 | 1 | 49 | 28 | 32 | 20 |
Primary health centres | 1146 | 35 017 | 178 925 | 1 | 1 | 44 | 26 | 32 | 28 |
Total | 6124 | 169 485 | 803 738 | 62 | 148 | 55 | 36 | 36 | 25 |
Facility managing authority | |||||||||
Public or government | 3811 | 30 737 | 165 183 | 4 | 17 | 53 | 34 | 36 | 39 |
Private not-for-profit | 549 | 25 029 | 145 951 | 5 | 8 | 61 | 44 | 47 | 43 |
Private for-profit | 1123 | 33 220 | 167 752 | 6 | 11 | 61 | 47 | 47 | 43 |
Mission or faith-based | 641 | 1357 | 4842 | 4 | 6 | 62 | 47 | 41 | 39 |
Total | 6124 | 90 343 | 483 728 | 21 | 55 | 32 | 32 | 33 | |
Location of health facility | |||||||||
Urban | 2070 | 14 039 | 24 039 | 9 | 25 | 65 | 47 | 45 | 40 |
Rural | 4054 | 6180 | 10 233 | 2 | 4 | 51 | 32 | 34 | 34 |
Total | 6124 | 20 219 | 34 272 | 11 | 29 | 55 | 32 | 32 | 33 |
SD: standard deviation.
Source: Author's computation.
Similarly, prior to conduct of the SFA, a preliminary test was performed to investigate the presence of technical inefficiency elements in the production function. It is important to conduct the relevant diagnostic test to validate if SFA is the right class of model to be applied to estimate the level of TE in the production function. Therefore, if the technical inefficiency component of the production function is not statistically different from zero, it means that the stochastic frontier model is reduced to a Cobb–Douglass model.20 This article follows Kumbhakar et al.19 and conducts the likelihood ratio test using estimates obtained from the restricted and unrestricted models. Thus the analysis rejects the null hypothesis, which asserts that the stochastic frontier model is not the preferred model for the analysis.
Finally, the analysis used information criteria to select the appropriate model among the three models for the four equations. Thus the estimates for the equation that included GSRI are (Akaike's Information Criteria [AIC] 14 972.08, 14 963.25 and 14 965.28; Bayesian Information Criteria [BIC] 15 104.35, 15 095.51 and 15 103.84) obtained from the half-normal, exponential and truncated distributions, respectively. These estimates were also obtained for the equation that included the DSRI, CSRI and RSRI. Therefore the results show that the exponential distribution has the lowest AIC and BIC values and thus is the preferred model for the analysis. It is important to highlight that the three-information criterion has little difference in their respective AIC and BIC values.
The parameter estimates of the equation that used GSRI for the three distributions are presented in Table 3. The GSRI and density of health workers have a positive and significant association with the number of outpatient visits. All else being constant, outpatient visits may increase by 14% per month with an increase in the density of health workers. Similarly, a unit increase in the GSRI per health facility may lead to an increase in outpatient visits of 0.3%. However, the estimates highlight that the level of technical inefficiency is lowest in private clinics. The three distributions resulted in almost the same estimates.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.023)*** | 0.14 (0.026)*** | 0.14 (0.026)*** | |
GSRI | 0.03 (0.004)*** | 0.03 (0.004)*** | 0.03(0.004)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)** | −1.22 (0.166)** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169) *** | −1.29 (0.168) *** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68(0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.187)*** | −1.90 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63(0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.070)*** | −0.69 (0.070)*** | |
Mission or faith-based | −1.03 (0.084)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.50 (0.060)*** | −0.50 (0.060)*** | −0.50 (0.060)*** | |
Constant | 6.55 (0.314)*** | 6.34 (0.291)*** | 6.34 (0.290)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.069)*** | 22.65 (36.81) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.50)*** | 0.42 (0.094)*** | 15.86 (36.81) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.71 | 830.67 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.023)*** | 0.14 (0.026)*** | 0.14 (0.026)*** | |
GSRI | 0.03 (0.004)*** | 0.03 (0.004)*** | 0.03(0.004)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)** | −1.22 (0.166)** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169) *** | −1.29 (0.168) *** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68(0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.187)*** | −1.90 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63(0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.070)*** | −0.69 (0.070)*** | |
Mission or faith-based | −1.03 (0.084)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.50 (0.060)*** | −0.50 (0.060)*** | −0.50 (0.060)*** | |
Constant | 6.55 (0.314)*** | 6.34 (0.291)*** | 6.34 (0.290)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.069)*** | 22.65 (36.81) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.50)*** | 0.42 (0.094)*** | 15.86 (36.81) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.71 | 830.67 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.023)*** | 0.14 (0.026)*** | 0.14 (0.026)*** | |
GSRI | 0.03 (0.004)*** | 0.03 (0.004)*** | 0.03(0.004)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)** | −1.22 (0.166)** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169) *** | −1.29 (0.168) *** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68(0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.187)*** | −1.90 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63(0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.070)*** | −0.69 (0.070)*** | |
Mission or faith-based | −1.03 (0.084)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.50 (0.060)*** | −0.50 (0.060)*** | −0.50 (0.060)*** | |
Constant | 6.55 (0.314)*** | 6.34 (0.291)*** | 6.34 (0.290)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.069)*** | 22.65 (36.81) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.50)*** | 0.42 (0.094)*** | 15.86 (36.81) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.71 | 830.67 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.023)*** | 0.14 (0.026)*** | 0.14 (0.026)*** | |
GSRI | 0.03 (0.004)*** | 0.03 (0.004)*** | 0.03(0.004)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)** | −1.22 (0.166)** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169) *** | −1.29 (0.168) *** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68(0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.187)*** | −1.90 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63(0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.070)*** | −0.69 (0.070)*** | |
Mission or faith-based | −1.03 (0.084)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.50 (0.060)*** | −0.50 (0.060)*** | −0.50 (0.060)*** | |
Constant | 6.55 (0.314)*** | 6.34 (0.291)*** | 6.34 (0.290)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.069)*** | 22.65 (36.81) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.50)*** | 0.42 (0.094)*** | 15.86 (36.81) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.71 | 830.67 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Table A2 in the appendix presents the estimates of TE scores across the three distributions. The mean TE scores indicate the existing operating capacity at which health facilities are providing healthcare with the given resource constraints. However, half-normal distribution has comparatively the lowest estimates. Disaggregated by health facility characteristics, the mean score of TE is 56% for national, provincial special, private hospitals, health centres and primary health centres. The same is true for health facilities under different management and location. Thus no significant variation is evident in the TE scores if the characteristics of health facilities are considered. Overall, the TE at which health facilities are operating lies within the range of 42–55%, regardless of the facility type, location or management. These estimates are the same as the estimates presented in Table 4, which are obtained from the equation that included the DSRI. Table A3 of the appendix presents the estimates of TE across the three distributions for the DSRI equation.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.03)*** | 0.14(0.02)*** | 0.14 (0.03)*** | |
DSRI | 0.03 (0.00)*** | 0.03 (0.00)*** | 0.03 (0.00)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.156)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.77 (0.158) *** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.65 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.160)*** | |
Dispensary | −1.87(0.188)*** | −1.90 (0.186)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.64 (0.163)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 3.41 (0.234)*** | 3.41 (0.234)*** | 3.04 (0.234)*** | |
Constant | 7.25 (0.258)*** | 6.34 (0.291)*** | 7.05 (0.224)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (25.10) |
|${\sigma }_\nu $| | 1.43 (0.053) *** | 1.43 (0.031) *** | 1.43 (0.032) *** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249) *** | 0.42 (0.094) *** | 15.86 (25.10) | |
Log likelihood | −7465.04 | −7460.62 | −7460.63 | |
Wald χ2 | 814.71 | 830.73 | 830.65 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.03)*** | 0.14(0.02)*** | 0.14 (0.03)*** | |
DSRI | 0.03 (0.00)*** | 0.03 (0.00)*** | 0.03 (0.00)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.156)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.77 (0.158) *** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.65 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.160)*** | |
Dispensary | −1.87(0.188)*** | −1.90 (0.186)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.64 (0.163)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 3.41 (0.234)*** | 3.41 (0.234)*** | 3.04 (0.234)*** | |
Constant | 7.25 (0.258)*** | 6.34 (0.291)*** | 7.05 (0.224)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (25.10) |
|${\sigma }_\nu $| | 1.43 (0.053) *** | 1.43 (0.031) *** | 1.43 (0.032) *** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249) *** | 0.42 (0.094) *** | 15.86 (25.10) | |
Log likelihood | −7465.04 | −7460.62 | −7460.63 | |
Wald χ2 | 814.71 | 830.73 | 830.65 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.03)*** | 0.14(0.02)*** | 0.14 (0.03)*** | |
DSRI | 0.03 (0.00)*** | 0.03 (0.00)*** | 0.03 (0.00)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.156)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.77 (0.158) *** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.65 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.160)*** | |
Dispensary | −1.87(0.188)*** | −1.90 (0.186)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.64 (0.163)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 3.41 (0.234)*** | 3.41 (0.234)*** | 3.04 (0.234)*** | |
Constant | 7.25 (0.258)*** | 6.34 (0.291)*** | 7.05 (0.224)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (25.10) |
|${\sigma }_\nu $| | 1.43 (0.053) *** | 1.43 (0.031) *** | 1.43 (0.032) *** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249) *** | 0.42 (0.094) *** | 15.86 (25.10) | |
Log likelihood | −7465.04 | −7460.62 | −7460.63 | |
Wald χ2 | 814.71 | 830.73 | 830.65 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.03)*** | 0.14(0.02)*** | 0.14 (0.03)*** | |
DSRI | 0.03 (0.00)*** | 0.03 (0.00)*** | 0.03 (0.00)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.156)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.77 (0.158) *** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.65 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.160)*** | |
Dispensary | −1.87(0.188)*** | −1.90 (0.186)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.64 (0.163)*** | |
Health facility management (public facilities are the reference group) | ||||
Private-not-for profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private-for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 3.41 (0.234)*** | 3.41 (0.234)*** | 3.04 (0.234)*** | |
Constant | 7.25 (0.258)*** | 6.34 (0.291)*** | 7.05 (0.224)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (25.10) |
|${\sigma }_\nu $| | 1.43 (0.053) *** | 1.43 (0.031) *** | 1.43 (0.032) *** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249) *** | 0.42 (0.094) *** | 15.86 (25.10) | |
Log likelihood | −7465.04 | −7460.62 | −7460.63 | |
Wald χ2 | 814.71 | 830.73 | 830.65 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Table 5 presents the result of the stochastic frontier model that included the CSRI. The estimates are similar to the estimates given in Table 1 across the three distributions. However, the coefficient of SRI is statistically significant and marginally higher in the model with the CSRI. This implied that a unit increase in the CSRI at a health facility may induce a 0.4% increase in the number of outpatient visits. Table A4 in the appendix shows the mean scores of TEs obtained from the model with the CSRI. The estimates are the same across distributions and after controlling for the characteristics of health facilities.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
CDSRI | 0.04 (0.005)*** | 0.04 (0.005)*** | 0.04 (0.005)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.156)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.167)*** | |
Private clinic | −0.78 (0.158)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.189)*** | −1.89 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.080)*** | −0.53 (0.081)*** | −0.54 (0.080)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 5.47 (0.281)*** | 5.47 (0.281)*** | 5.47 (0.281)*** | |
Constant | 6.81(0.292)*** | 6.56 (0.265)*** | 6.59 (0.265)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (2241) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.42 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249)*** | 0.42 (0.094)*** | 15.86 (22.41) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
CDSRI | 0.04 (0.005)*** | 0.04 (0.005)*** | 0.04 (0.005)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.156)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.167)*** | |
Private clinic | −0.78 (0.158)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.189)*** | −1.89 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.080)*** | −0.53 (0.081)*** | −0.54 (0.080)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 5.47 (0.281)*** | 5.47 (0.281)*** | 5.47 (0.281)*** | |
Constant | 6.81(0.292)*** | 6.56 (0.265)*** | 6.59 (0.265)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (2241) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.42 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249)*** | 0.42 (0.094)*** | 15.86 (22.41) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
CDSRI | 0.04 (0.005)*** | 0.04 (0.005)*** | 0.04 (0.005)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.156)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.167)*** | |
Private clinic | −0.78 (0.158)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.189)*** | −1.89 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.080)*** | −0.53 (0.081)*** | −0.54 (0.080)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 5.47 (0.281)*** | 5.47 (0.281)*** | 5.47 (0.281)*** | |
Constant | 6.81(0.292)*** | 6.56 (0.265)*** | 6.59 (0.265)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (2241) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.42 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249)*** | 0.42 (0.094)*** | 15.86 (22.41) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
CDSRI | 0.04 (0.005)*** | 0.04 (0.005)*** | 0.04 (0.005)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.156)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.28 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.167)*** | |
Private clinic | −0.78 (0.158)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.189)*** | −1.89 (0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.080)*** | −0.53 (0.081)*** | −0.54 (0.080)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | 5.47 (0.281)*** | 5.47 (0.281)*** | 5.47 (0.281)*** | |
Constant | 6.81(0.292)*** | 6.56 (0.265)*** | 6.59 (0.265)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (2241) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.42 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.249)*** | 0.42 (0.094)*** | 15.86 (22.41) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Tables A4 and A5 in the appendix present the results of the stochastic frontier model and the mean scores of TEs obtained from the model that used the RDSRI across the three distributions. Clearly they indicate that a unit increase in the RDSRI at the health facility level may bring about an increase in outpatient visits of 0.8%, all things being equal.
Discussion
This article investigates the association of health worker density and SRIs with outpatient visits using the stochastic frontier model. The production function used health worker density and the GSRI, DSRI, CDSRI and RDSRI as health inputs. The characteristics of health facilities are also included as an input in the production function to control for the differences in the type of health facilities, location and management. The production function is specified in the Cobb–Douglass and translog type of production function. The mean scores of TEs are estimated using three different distributions: half-normal, exponential and truncated. The model used the total number of outpatient visits per month as the health output in the analysis. The estimates for the service readiness for chronic diseases are quite low. This reveals that health facilities in the countries of this study are not adequately prepared to provide services for diabetes and cardiovascular and respiratory diseases.
To the best of the authors’ knowledge, no previous studies have investigated the association between health worker density and disease-specific SRIs with outpatient visits using the stochastic frontier model. However, a previous study of service readiness for NCDs in five LMICs supports the findings of the current study.25 Data from the recent waves of the facility-level survey for Bangladesh show that 58% and 24.1% of the health facilities had the capacity for the diagnosis and treatment of diabetes and cardiovascular diseases, respectively.26 Moreover, in Haiti, recent evidence highlights that the strength of health workers and the level of the general SRI are positively associated with outpatient visits.27
Apparently, across the four different equations—GSRI, DSRI, CDSRI and RDSRI—the stochastic frontier model estimates yield almost the same results regarding the positive and significant association between health worker density and SRIs. However, all else being constant, an increase in health worker density may induce a 14% increase in the utilization of health services by outpatient visitors. Moreover, the GSRI and DSRI have the same associational effects with the utilization of health services by outpatient visitors. That is, a unit increase in the GSRI and DSRI may lead to an increase in outpatient visits by 0.3%. The estimates of the model with the CDSRI and RDSRI are comparatively higher. A unit increase in the CDSRI at the health facility level may lead to an increase in outpatient visits of 0.4%. Importantly, a unit increase in the RDSRI at the facility level may induce greater utilization of health services of 0.8%. Overall, these results indicate that a unit increase in the RDSRI may lead to the greatest increase in outpatient visits, all else held constant.
Furthermore, these results have some interesting policy implications. The positive and significant association between health worker density and the utilization of health services by outpatients underscores the potential gains in health outcomes that may result as the supply of health professionals is augmented at the facility level. For instance, since the strength of health workers is a key factor to be considered for the treatment of diabetic patients, health facilities with lower levels of health professionals may not be efficient in providing care for chronic diseases. However, ensuring proper health worker staffing alone may not guarantee a higher level of TE for health facilities. The employers of health professionals should provide reasonable incentives to health workers to boost their production efficiency.
In particular, the SRI is lowest for respiratory diseases with special reference to speciality hospitals. This stressed the urgent need for investment in a high-quality health system to tackle the menace of chronic NCDs in the countries of this study and other LMICs. Although the mean level of diagnostic capacity of health facilities is above average (59%, 73% and 73% for diabetes, cardiovascular diseases and respiratory diseases), the availability of essential medicines for NCDs is quite low. Essential medicines have mean domain scores of 42%, 36% and 23% for diabetes, cardiovascular diseases and respiratory diseases, respectively. Further details are given in the supplementary materials.
Central to the analysis of these results are the estimates of the mean values of TEs across the three distributions and by controlling for the characteristics of health facilities. Overall, health facilities have a mean TE score of 56%. This suggests that health facilities are under-providing satisfactory health services to outpatient visitors. Therefore, outpatient visits would increase by 44% of the current estimates per month if best practices are fully implemented. Thus, compared with these findings, lower levels of TE were documented by the Novignon and Nonvignon study.14
Nevertheless, this article has some limitations. First, only the major types of health facilities that are common across the countries of the study are included. Therefore health facilities that do not share common characteristics either by type, location or management were not included as part of the population. Second, in Afghanistan, the SPA data were collected from only one region of the country and thus do not cover the entire country. Third, data on outpatient visits to health facilities are not disaggregated by the types of health services utilized. Specifically, the survey does not report data on outpatient visits for diabetes, cardiovascular diseases and chronic respiratory diseases. Future studies could investigate the potential determinants of general and disease-specific service readiness and how they affect health outcomes. Moreover, the study was conducted by using data from eight countries, and they have differences in many settings that have not been fully accounted for in this study.
Conclusions
This article estimates the level of TEs of health facilities in providing healthcare in eight LMICs using the stochastic frontier model. The production function used the general and chronic disease-specific SRIs and examined their association with facility-level utilization of health services by outpatients. The present article found that the general and chronic disease SRIs are associated with a significant increase in outpatient visits. Moreover, the overall mean value of TE of health production is computed at 56%, suggesting that if health facilities could ameliorate the existing levels of TEs by ensuring best practices, facility level utilization of health services by outpatients may increase by 44%, all else being constant. Therefore, there are huge potentials for improvement in health outcomes, particularly access to care for NCDs, if investment into a high-quality health system is accompanied by the implementation of best practices by the providers.
Authors’ contributions
SS and MMB conceptualized and designed the study, defined the methodology and analysed and interpreted the results. MMB and DKG designed the study implementation and collected the data. MMB drafted the manuscript. SS and DKG critically revised the manuscript. All authors read and approved the final manuscript.
Acknowledgements
We would like to acknowledge the SRM University-AP for providing the database access and research software required for completion of this study. The authors are also thankful to the referees and the editorial team of the journal for their useful suggestions to improve the quality of the article.
Funding
None.
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical approval
Not required.
Data availability
The data underlying this article will be shared on reasonable request to the corresponding author.
References
Appendix
Countries . | Year of SPA . | Survey coverage . | Facilities surveyed, n . |
---|---|---|---|
Afghanistan | 2018–2019 | Regional | 160 |
Bangladesh | 2017 | National | 1600 |
Congo Democratic Republic | 2017–18 | National | 1414 |
Haiti | 2017–18 | National | 1033 |
Malawi | 2013–14 | National | 1060 |
Nepal | 2015 | National | 992 |
Senegal | 2019 | National | 454 |
Tanzania | 2014–15 | National | 1200 |
Countries . | Year of SPA . | Survey coverage . | Facilities surveyed, n . |
---|---|---|---|
Afghanistan | 2018–2019 | Regional | 160 |
Bangladesh | 2017 | National | 1600 |
Congo Democratic Republic | 2017–18 | National | 1414 |
Haiti | 2017–18 | National | 1033 |
Malawi | 2013–14 | National | 1060 |
Nepal | 2015 | National | 992 |
Senegal | 2019 | National | 454 |
Tanzania | 2014–15 | National | 1200 |
Source: Demographic and Health Surveys.
Countries . | Year of SPA . | Survey coverage . | Facilities surveyed, n . |
---|---|---|---|
Afghanistan | 2018–2019 | Regional | 160 |
Bangladesh | 2017 | National | 1600 |
Congo Democratic Republic | 2017–18 | National | 1414 |
Haiti | 2017–18 | National | 1033 |
Malawi | 2013–14 | National | 1060 |
Nepal | 2015 | National | 992 |
Senegal | 2019 | National | 454 |
Tanzania | 2014–15 | National | 1200 |
Countries . | Year of SPA . | Survey coverage . | Facilities surveyed, n . |
---|---|---|---|
Afghanistan | 2018–2019 | Regional | 160 |
Bangladesh | 2017 | National | 1600 |
Congo Democratic Republic | 2017–18 | National | 1414 |
Haiti | 2017–18 | National | 1033 |
Malawi | 2013–14 | National | 1060 |
Nepal | 2015 | National | 992 |
Senegal | 2019 | National | 454 |
Tanzania | 2014–15 | National | 1200 |
Source: Demographic and Health Surveys.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.11 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.69 | ||
Truncated | 128 | 0.56 | 0.11 | 0.00 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.13 | 0.11 | 0.75 | ||
Truncated | 744 | 0.56 | 0.12 | 0.11 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.10 | 0.73 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.56 | 0.14 | 0.02 | 0.79 | ||
Truncated | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.55 | 0.13 | 0.04 | 0.04 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 982 | 0.56 | 0.11 | 0.07 | 0.79 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.11 | 0.16 | 0.74 | ||
Truncated | 612 | 0.55 | 0.11 | 0.16 | 0.74 | ||
Primary health centres | Half-normal | 1146 | 0.56 | 0.10 | 0.19 | 0.75 | |
Exponential | 1146 | 0.56 | 0.09 | 0.07 | 0.75 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.12 | 0.01 | 0.74 | ||
Private not-for-profit | Half-normal | 549 | 0.47 | 0.11 | 0.09 | 0.72 | |
Exponential | 549 | 0.56 | 0.12 | 0.07 | 0.78 | ||
Truncated | 549 | 0.56 | 0.12 | 0.09 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.12 | 0.06 | 0.72 | |
Exponential | 1123 | 0.55 | 0.13 | 0.02 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.11 | 0.07 | 0.68 | |
Exponential | 641 | 0.56 | 0.11 | 0.04 | 0.76 | ||
Truncated | 641 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.12 | 0.03 | 0.72 |
Exponential | 2070 | 0.56 | 0.13 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.11 | 0.09 | 0.68 | |
Exponential | 4054 | 0.56 | 0.11 | 0.06 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.11 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.11 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.69 | ||
Truncated | 128 | 0.56 | 0.11 | 0.00 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.13 | 0.11 | 0.75 | ||
Truncated | 744 | 0.56 | 0.12 | 0.11 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.10 | 0.73 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.56 | 0.14 | 0.02 | 0.79 | ||
Truncated | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.55 | 0.13 | 0.04 | 0.04 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 982 | 0.56 | 0.11 | 0.07 | 0.79 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.11 | 0.16 | 0.74 | ||
Truncated | 612 | 0.55 | 0.11 | 0.16 | 0.74 | ||
Primary health centres | Half-normal | 1146 | 0.56 | 0.10 | 0.19 | 0.75 | |
Exponential | 1146 | 0.56 | 0.09 | 0.07 | 0.75 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.12 | 0.01 | 0.74 | ||
Private not-for-profit | Half-normal | 549 | 0.47 | 0.11 | 0.09 | 0.72 | |
Exponential | 549 | 0.56 | 0.12 | 0.07 | 0.78 | ||
Truncated | 549 | 0.56 | 0.12 | 0.09 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.12 | 0.06 | 0.72 | |
Exponential | 1123 | 0.55 | 0.13 | 0.02 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.11 | 0.07 | 0.68 | |
Exponential | 641 | 0.56 | 0.11 | 0.04 | 0.76 | ||
Truncated | 641 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.12 | 0.03 | 0.72 |
Exponential | 2070 | 0.56 | 0.13 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.11 | 0.09 | 0.68 | |
Exponential | 4054 | 0.56 | 0.11 | 0.06 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.11 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.11 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.69 | ||
Truncated | 128 | 0.56 | 0.11 | 0.00 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.13 | 0.11 | 0.75 | ||
Truncated | 744 | 0.56 | 0.12 | 0.11 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.10 | 0.73 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.56 | 0.14 | 0.02 | 0.79 | ||
Truncated | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.55 | 0.13 | 0.04 | 0.04 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 982 | 0.56 | 0.11 | 0.07 | 0.79 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.11 | 0.16 | 0.74 | ||
Truncated | 612 | 0.55 | 0.11 | 0.16 | 0.74 | ||
Primary health centres | Half-normal | 1146 | 0.56 | 0.10 | 0.19 | 0.75 | |
Exponential | 1146 | 0.56 | 0.09 | 0.07 | 0.75 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.12 | 0.01 | 0.74 | ||
Private not-for-profit | Half-normal | 549 | 0.47 | 0.11 | 0.09 | 0.72 | |
Exponential | 549 | 0.56 | 0.12 | 0.07 | 0.78 | ||
Truncated | 549 | 0.56 | 0.12 | 0.09 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.12 | 0.06 | 0.72 | |
Exponential | 1123 | 0.55 | 0.13 | 0.02 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.11 | 0.07 | 0.68 | |
Exponential | 641 | 0.56 | 0.11 | 0.04 | 0.76 | ||
Truncated | 641 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.12 | 0.03 | 0.72 |
Exponential | 2070 | 0.56 | 0.13 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.11 | 0.09 | 0.68 | |
Exponential | 4054 | 0.56 | 0.11 | 0.06 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.11 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.11 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.69 | ||
Truncated | 128 | 0.56 | 0.11 | 0.00 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.13 | 0.11 | 0.75 | ||
Truncated | 744 | 0.56 | 0.12 | 0.11 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.10 | 0.73 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.56 | 0.14 | 0.02 | 0.79 | ||
Truncated | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.55 | 0.13 | 0.04 | 0.04 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 982 | 0.56 | 0.11 | 0.07 | 0.79 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.11 | 0.16 | 0.74 | ||
Truncated | 612 | 0.55 | 0.11 | 0.16 | 0.74 | ||
Primary health centres | Half-normal | 1146 | 0.56 | 0.10 | 0.19 | 0.75 | |
Exponential | 1146 | 0.56 | 0.09 | 0.07 | 0.75 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.12 | 0.01 | 0.74 | ||
Private not-for-profit | Half-normal | 549 | 0.47 | 0.11 | 0.09 | 0.72 | |
Exponential | 549 | 0.56 | 0.12 | 0.07 | 0.78 | ||
Truncated | 549 | 0.56 | 0.12 | 0.09 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.12 | 0.06 | 0.72 | |
Exponential | 1123 | 0.55 | 0.13 | 0.02 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.11 | 0.07 | 0.68 | |
Exponential | 641 | 0.56 | 0.11 | 0.04 | 0.76 | ||
Truncated | 641 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.12 | 0.03 | 0.72 |
Exponential | 2070 | 0.56 | 0.13 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.11 | 0.09 | 0.68 | |
Exponential | 4054 | 0.56 | 0.11 | 0.06 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.11 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.00 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.12 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.55 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 612 | 0.57 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for- profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 2068 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.00 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.12 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.55 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 612 | 0.57 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for- profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 2068 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.00 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.12 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.55 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 612 | 0.57 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for- profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 2068 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.61 |
Exponential | 128 | 0.56 | 0.12 | 0.00 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.12 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.55 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.04 | 0.78 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.57 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 612 | 0.57 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for- profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 2068 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.02 | 0.74 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.12 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 600 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.72 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.10 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.66 | |
Exponential | 982 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.76 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.05 | 0.09 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0 .11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.10 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.02 | 0.74 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.12 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 600 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.72 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.10 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.66 | |
Exponential | 982 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.76 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.05 | 0.09 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0 .11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.10 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.02 | 0.74 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.12 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 600 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.72 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.10 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.66 | |
Exponential | 982 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.76 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.05 | 0.09 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0 .11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.10 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-normal | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.02 | 0.74 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.12 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 600 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.72 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.10 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.56 | 0.12 | 0.05 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.66 | |
Exponential | 982 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.76 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.05 | 0.09 | 0.76 | ||
Truncated | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0 .11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.10 | 0.11 | 0.66 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
RDSRI | 0.08 (0.009)*** | 0.08 (0.009)*** | 0.08 (0.009)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.29 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.188)*** | −1.89(0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.49 (0.059)*** | −0.4965 (0.0590)*** | −0.49650 (0.0590) | |
Constant | 5.62 (0.406)*** | 5.39 (0.391)*** | 5.39 (0.391)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (21.74) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.250)*** | 0.42 (0.094)*** | 15.86 (21.75) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
RDSRI | 0.08 (0.009)*** | 0.08 (0.009)*** | 0.08 (0.009)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.29 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.188)*** | −1.89(0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.49 (0.059)*** | −0.4965 (0.0590)*** | −0.49650 (0.0590) | |
Constant | 5.62 (0.406)*** | 5.39 (0.391)*** | 5.39 (0.391)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (21.74) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.250)*** | 0.42 (0.094)*** | 15.86 (21.75) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
RDSRI | 0.08 (0.009)*** | 0.08 (0.009)*** | 0.08 (0.009)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.29 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.188)*** | −1.89(0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.49 (0.059)*** | −0.4965 (0.0590)*** | −0.49650 (0.0590) | |
Constant | 5.62 (0.406)*** | 5.39 (0.391)*** | 5.39 (0.391)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (21.74) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.250)*** | 0.42 (0.094)*** | 15.86 (21.75) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
Stochastic production function . | Variable . | Half-normal distribution, coefficient (SE) . | Exponential distribution, coefficient (SE) . | Truncated distribution, coefficient (SE) . |
---|---|---|---|---|
loghwd | 0.14 (0.026)*** | 0.14(0.026)*** | 0.14 (0.026)*** | |
RDSRI | 0.08 (0.009)*** | 0.08 (0.009)*** | 0.08 (0.009)*** | |
Type of health facility (national/regional facility is the reference group) | ||||
Provincial hospital | −1.33 (0.157)*** | −1.35 (0.157)*** | −1.35 (0.157)*** | |
Special hospital | −1.19 (0.167)*** | −1.22 (0.166)*** | −1.22 (0.166)*** | |
Private hospital | −1.29 (0.169)*** | −1.29 (0.169)*** | −1.29 (0.169)*** | |
Private clinic | −0.78 (0.159)*** | −0.79 (0.158)*** | −0.79 (0.158)*** | |
Health centres | −1.66 (0.159)*** | −1.68 (0.159)*** | −1.68 (0.159)*** | |
Dispensary | −1.87 (0.188)*** | −1.89(0.187)*** | −1.89 (0.187)*** | |
Primary health centres | −1.60 (0.166)*** | −1.63(0.165)*** | −1.63 (0.165)*** | |
Health facility management (public facilities are the reference group) | ||||
Private not-for-profit | −0.54 (0.081)*** | −0.54 (0.081)*** | −0.54 (0.081)*** | |
Private for-profit | −0.70 (0.070)*** | −0.69 (0.069)*** | −0.69 (0.069)*** | |
Mission or faith-based | −1.03 (0.083)*** | −1.03 (0.083)*** | −1.03 (0.083)*** | |
Location of health facility (urban is the reference group) | ||||
Rural | −0.49 (0.059)*** | −0.4965 (0.0590)*** | −0.49650 (0.0590) | |
Constant | 5.62 (0.406)*** | 5.39 (0.391)*** | 5.39 (0.391)*** | |
Distribution u and v σ | |${\sigma }_\mu $| | 1.02 (0.199)*** | 0.60 (0.068)*** | 22.66 (21.74) |
|${\sigma }_\nu $| | 1.43 (0.053)*** | 1.43 (0.031)*** | 1.43 (0.031)*** | |
|$\lambda = \frac{{{\sigma }_\mu }}{{{\sigma }_\nu }}$| | 0.72 (0.250)*** | 0.42 (0.094)*** | 15.86 (21.75) | |
Log likelihood | −7465.04 | −7460.62 | −7460.64 | |
Wald χ2 | 814.71 | 830.73 | 830.64 | |
Prob > χ2 | 0.0000 | 0.0000 | 0.0000 |
SE: standard error.
Source: Author's computation.
***Estimates are significant at 1% level.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-n | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.55 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.69 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-n | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.55 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.69 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-n | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.55 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.69 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
Facility variable . | Identifier . | Distribution . | N . | Mean . | SD . | Min . | Max . |
---|---|---|---|---|---|---|---|
Type of health facility | National/regional | Half-n | 128 | 0.46 | 0.10 | 0.05 | 0.60 |
Exponential | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Truncated | 128 | 0.56 | 0.12 | 0.01 | 0.70 | ||
Provincial hospital | Half-normal | 744 | 0.45 | 0.11 | 0.16 | 0.68 | |
Exponential | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Truncated | 744 | 0.56 | 0.12 | 0.13 | 0.76 | ||
Special hospital | Half-normal | 600 | 0.46 | 0.10 | 0.15 | 0.65 | |
Exponential | 600 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Truncated | 600 | 0.56 | 0.11 | 0.12 | 0.74 | ||
Private hospital | Half-normal | 618 | 0.45 | 0.12 | 0.09 | 0.73 | |
Exponential | 618 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Truncated | 618 | 0.56 | 0.12 | 0.12 | 0.74 | ||
Private clinic | Half-normal | 1292 | 0.46 | 0.10 | 0.11 | 0.71 | |
Exponential | 1292 | 0.56 | 0.12 | 0.05 | 0.78 | ||
Truncated | 1292 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Health centres | Half-normal | 982 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 982 | 0.56 | 0.10 | 0.08 | 0.76 | ||
Truncated | 982 | 0.55 | 0.10 | 0.08 | 0.76 | ||
Dispensary | Half-normal | 612 | 0.46 | 0.09 | 0.19 | 0.66 | |
Exponential | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Truncated | 612 | 0.56 | 0.10 | 0.19 | 0.75 | ||
Primary health centres | Half-normal | 1146 | 0.46 | 0.09 | 0.13 | 0.68 | |
Exponential | 1146 | 0.57 | 0.09 | 0.08 | 0.76 | ||
Truncated | 1146 | 0.56 | 0.09 | 0.08 | 0.76 | ||
Facility management | Public/government | Half-normal | 3811 | 0.46 | 0.09 | 0.05 | 0.66 |
Exponential | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Truncated | 3811 | 0.56 | 0.11 | 0.01 | 0.75 | ||
Private not-for-profit | Half-normal | 549 | 0.46 | 0.10 | 0.13 | 0.73 | |
Exponential | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Truncated | 549 | 0.56 | 0.12 | 0.08 | 0.79 | ||
Private for-profit | Half-normal | 1123 | 0.45 | 0.11 | 0.09 | 0.73 | |
Exponential | 1123 | 0.56 | 0.13 | 0.03 | 0.79 | ||
Truncated | 1123 | 0.55 | 0.13 | 0.03 | 0.79 | ||
Mission or faith-based | Half-normal | 641 | 0.46 | 0.09 | 0.11 | 0.69 | |
Exponential | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Truncated | 641 | 0.56 | 0.11 | 0.05 | 0.76 | ||
Facility location | Rural | Half-normal | 2070 | 0.45 | 0.11 | 0.05 | 0.73 |
Exponential | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Truncated | 2070 | 0.56 | 0.12 | 0.01 | 0.79 | ||
Urban | Half-normal | 4054 | 0.46 | 0.09 | 0.13 | 0.69 | |
Exponential | 4054 | 0.56 | 0.11 | 0.08 | 0.76 | ||
Truncated | 4054 | 0.56 | 0.10 | 0.08 | 0.76 |
SD: standard deviation; min: minimum; max: maximum.
Author notes
The authors wish it to be known that, in their opinion, the first two authors should be regarded as joint first authors.
- cardiovascular diseases
- diabetes mellitus
- exposure
- cardiovascular system
- chronic disease
- developing countries
- hospitals, private
- investments
- outpatients
- respiration disorders
- serotonin uptake inhibitors
- public health medicine
- health outcomes
- health care systems
- transanal endoscopic surgery
- noncommunicable diseases
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