Correlates of Undeer Five Mortality in SNNPR Regional State, Spatial Data Analysis

The main aim of this study was to identify determinants of under-five child mortality, to describe spatial dependence of child mortality and develop models specifying risk factors used to diagnosis of child mortality among districts in SNNPR State of Ethiopia by using 2016 EDHS collected for 75 weredas/districts by employing spatial models. Spatial lag and spatial error model were fitted to the data, though spatial lag model specification was taken as the best fit for child mortality rate. Accordingly, from global and local spatial analysis it was found that children mortality rate in one district was directly affected by that of its neighbors. The results revealed that water closet, proportion of children under five, toilet availability, and mothers basic education attainment, vaccination coverage, size at birth, mother current working status, ORS information, altitude, stunting score and wasting score of children were significant determinants of children mortality rate. Thus, it is suggested that the geographically targeted preparation on accumulation of treatment that can be useful to control and stabilize spillover (nearest area spread) of disease such as diarrhea, malaria, and fever over space is recommended. It can be suggested for this states’ that the government needs to make intervention to mitigate the spatial variation of the prevalence across regions.

such as malaria, pneumonia and diarrhea.

Statements of the Problem
The study of under-five mortality becomes one of the most important researches in developing countries because there is high level of children mortality. There is much research on the patterns of determinants of under-five mortality, by analyzing how less than under-five mortality is differently affected by demographic, socioeconomic and environmental variables. This paper presents an analysis of the impact of demographic, socioeconomic and environmental variables on under-five mortality. The overall purpose of the paper is to determine the relative importance of various demographic, socioeconomic and environmental variables on under-five mortality in SNNPR. In this regard, the research questions of the interest were: 1. Does child mortality rate have spatial correlation? 2. Are socio-economic, demographic, environmental, and health related factors proximate characteristics related to experiencing of morbidity among children in the regions? 3. Do the effects of factors on mortality rate among children differ among districts?

Objectives of the Study
The main objective of this study is to identify determinants of child mortality, to describe spatial dependence of morality rate and develop spatial models specifying risk factors used to diagnosis of morbidity in SNNP Regional State. Specific objectives are:- To determine important socio-economic and bio-demographic and environmental factors that contributes to morbidity including geographical effects as a surrogate for unobserved covariates with spatial information.  To assess whether spatial association of mortality rate and its determinants exist in districts and also to identify territories of high risk.  To provide scientific information to decision/policy based on empirical results

Methodology 2.1. Study Area and population
The Southern Nations, Nationalities and People's Region (SNNPR) is located in the Southern and south-western part of Ethiopia. It is bordered with Kenya in south, the Sudan in southwest, Gambella region in northwest and surrounded by Oromia region in northwest, north and east directions. The total area of the region estimated to be 110,931.9 Square Km which is 10% of the country. Since 2007 the region total population is about 15,042,531 accounting nearly 20% of the total population of the country; of population 49.7 % are male and 50.3% are females (CSA, 2008). The population density of the region became 142 persons per sq.k.m, which makes the region one of the most densely populated parts of the country. The region is a multination, which consists of about 56 ethnic groups with their own distinct geographical location, language, cultures, and social identities living together. Among which Omotic and Cushetic are the most populous and diversified ones with the largest area coverage in region respectively. Based on ethnic and linguistic identities the region was divided into 16 zones sub-divided in to 126 weredas (districts), 22 administration town, and 8 special weredas with 3678 rural kebeles and 238 urban kebeles.

Target Population
The populations studied in this research were under-five children in SNNPR. A sample of 1277 children with their mother were used in 2016 Ethiopia demographic and health survey (EDHS, 2016).

Variables Included in the Study
In this study we employed two types of variables, these are dependent (response variable) and independent (Explanatory variables) variables.

Dependent variable
The dependent variable of child mortality (under-five mortality rate) is relative risk of dying in a specific age of below five years range of childhood) Independent variables Researcher used lot independent variables in study which was expected to cause child mortality in study area.

Spatial Data Analysis
In classical linear regression model Y=Xβ+ , the response variable Y is assumed to be independent normal or Gaussian distributed and covariates, X 1 …X P act linear on the response. By assumption the conditional expectation of Y is Where Y is vector of dependent variable, X is designed matrix of predicators, β is vector of parameters (coefficient)and ε is vector of independently and identically distributed error terms.
Andthe regression coefficient β 1 … β P determines the strength of influence of the covariate, and the linear predictor is the sum of the covariate effect. Here each observation has an underlining mean of i ij x   and normally distributed random error term . Generally, the random error term ε 1 ε 2… ε p has zero mean and uncorrelated variance covariance matrixε~N(0,δ 2 I)where 2  I=Var(y) and an I is pxp identity matrix the assumption of independent observation also implies that

2.4.1Quantification of Locations/Positions
Contiguity information is quantified as contiguity (spatial neighbors) matrix that contains the elements 1and 0. where: n is number of districts /locations under study c ij is element of C represents quantity local position of i th and j th districts for i, j =1, 2…n.Contiguity matrix C is constructed based on linear contiguity: define asc ij =1 for entities that share common edge to the immediate right or left of region of interest otherwise 0.

Spatial Regression Model
In the spatial linear regression model, spatial dependence can be incorporated in two distinct ways: as an additional regresor in the form of a spatially lagged dependent variable (C*Y) provide spatial lag model, or in the error structure (Cε) provides spatial error model. To test for spatial effects in models, spatial weights matrices are constructed and then included in a specified regression model. Thus, inference on the parameters allows one to explain the pattern for all locations as a function of exogenous variables (Cressie, 1993).

Spatial Lag Model
This is type of spatial regression which appropriate when the focus of interest is the assessment of the existence and strength of spatial interaction; suitable to filter out spatial dependence that comes from spatial spillovers. The matrix notation of the model is where ρ is a spatial autoregressive coefficient of the lag variable CY called spatial lag operator and given as . A random vector of error terms; ε is independent and identically normally distributed with mean zero and constant variance δ 2 I n , for all I, Yis vector of dependent variables, X is a designed matrix of explanatory variables and β is vector of coefficients of regression model. The single notation of the model is Y i = ρc i Y + x i β + ε i , where c i is the i th row of C. Parameters (β, δ 2 ) are estimated using maximum likelihood method of log likelihood function of transformed model and regressions was carried out along with a univariate parameter optimization of the concentrated likelihood function over values of the autoregressive parameter ρ. Given the above model as Y = ρC*Y + Xβ + ε, then the transformed model:A*Y = Xβ + u implies Y= A -1 Xβ + A -1 u With ε ~ N (0, δ 2 I), A=(I-ρC) and C is row standardized spatial weights matrix. The log likelihood functions of transformed equation.
Where, A is determinant of matrix A, and n is number of district under study.
Maximizing the likelihood with respect to β, δ, and ρ gives the values of parameters that provide the highest likelihood of the joint occurrence of the sample dependent variable. Anselin (1988) suggest a way to maximize the log likelihood and get estimator for β: We can now use all these to write down a version of the log-likelihood function in terms of ρ only, the result is the Concentrated log-likelihood (lnL*) CO doesn't involve unknown parameters and estimate of ρ is obtained by maximizing lnL* with respect to ρ. And also covariance-variance matrix of estimated parameters is estimated by maximum likelihood for large sample that attains Cramer's Rao lower bound. Moreover, clearly, we should be hesitant to make inferences about the effects of a covariate x i in a spatially lagged Y model without considering the spatial multiplier and the variation that will exist across spatial units (Ertur et al., 2007).

Descriptive Results of Determinants
Table1 below displays descriptive statistics for variables considered under study. The child mortality rate ranges from 0.00% (no mortality within 15 in that woreda) to 14.55 %( highly rate of mortality woreda/district) with mean 4.2 children died out of 100 live children and standard deviation of 5.59% in the Regional State. The drinking water closet in district varies from 2 minute to 996 minute with mean 123.81 minutes and standard deviation of 186.71 minutes. Percentage of mother who attended basic education ranges from 1% to 98% with mean 38.77% and standard deviation 26.63%. Proportion of children ever vaccinated among district varies from 2.63% to 84.21% with mean 34.38% and standard deviation16.36%. Birth interval time from preceding and succeeding children ranges from 41.50 month to 88.00 month with mean birth interval 62.16 month and standard deviation 9.68 month. Table 1 also provided maximum, minimum, mean and standard deviation in percentage for factors: Proportion of household having protected toilet, Proportion of households disposing younger children stools when not using toilet, Proportion of children whose size at birth is below average, Proportion of children under five, Proportion of respondents heard about ORS, Percentage mother employed, Percentage mother currently working among districts. 78 From nutritional factor point of view stunting score and wasting score shows that stunting score ranges from -2.28 (severely stunted area) to 3.70 (normal) with overall mean -1.124 and variance 0.57, and wasting score ranges from -1.99(severely wasted area) to 3.5416(normal) with mean -1.11 and standard deviation 0.77. Woreda's altitude also varies from 979 meter (low altitude) to 3012 meter (high altitude). And Mean wealth index factor score ranges from -78404.00 to 255217 with mean -32043.64 and standard deviation 58895.95.

Exploratory Spatial Data Analysis (ESDA) Results
As presented in Table 2 the Moran's I scatter statistic for mortality shows those districts with above average mortality rates shares boundaries with neighboring districts that also have above average infection rates (High-High). It also shows those districts with below average mortality rates shares boundaries with neighboring districts that also have below average infection rates (Low-Low. And therefore, it leads us to observe that there is spatial autocorrelation in diarrheal rates in the regions.

Spatial Regression Analysis Results
In this section we described a statistical model that incorporates spatial dependence raised from spatial lag explicitly by adding a spatially lagged dependent variable Y ' =CY on the right hand side of the OLS regression equation Y=Xβ+ε where C is spatial weight matrix. As a consequence, findings of this section allow us to understand which variable among the independent variables are related to the variation in mortality rates, and to explore the forms of these relationships. Table 3 reported maximum likelihood estimate for determinants of diarrhea prevalence rate in spatial lag model, test statistic with corresponding p-value, and their standard errors that come from the heteroskedasticity consistent estimator of the covariance matrix of the maximum likelihood parameters. The significance of the coefficient of the spatially lagged dependent variable (ρ) suggests that neighboring districts mortality rates are important determinants of a given district's mortality rate. This result is consistent with the findings of Frank (2006). More specifically, geographic spillover effects are important in our model of diarrhea morbidity rate variation.
Variables with positive and statistically significant effect on mortality rate are water closet (WC) ,proportion of children under five(PCU5),proportion children born below average size (PCBAV SIZE),where as variables with negative effect and statistically significant coefficients at 5% level of significance are proportion of children ever vaccinated(VACOV_100),proportion of household having controlled toilet(TOILET_100),proportion of households disposing younger disposal when not using toilet(DISPOSAL YOUNG_100), proportion of respondent heard about ORS(HEARD ORS),stunting score ,wasting score and altitude.
Positive effect means that for a unit change in explanatory variable increase mortality rate in certain district by magnitude of estimate of parameter for that explanatory variable controlling for the effect of neighbor districts and other variable, whereas negative effect mean that for unit change in explanatory variable decrease mortality rate in district by magnitude of estimate of parameter for explanatory variable conditioning the neighbor districts mortality rate effect and other variable constant. For example for one minute increase in time to get drinking water (WC) in certain district increase mortality rate in that district by 0.00417% keeping other variable fixed. In another word, as the a distance to drinking water in a particular district increases by one minute, the possibility of mortality in that district increased by 0.00417% .This result is similar with study conducted in Nekemte town, western Ethiopia, by Girma et al. (2008) and Chabala and Mamo(2001) that showed risk factors including distance of drinking water source (time taken to-and-from the source) appeared to be significantly associated with under-five childhood diarrheal morbidity.
The change in proportion of house hold having protected toilet and disposing young children stools were found to be negative and significant (at 5% level). This result is similar with findings of Girma et al. (2008) and study done in SSA countries which showed that children in SSA living in households with some kind of toilet facility are less likely to experience diarrhea morbidity than children in households that do not have toilet facilities.
The parameter estimate 0.0542 for proportion of children under five(PCU5) indicates that a unit increase in proportion of children under five in district increase mortality in that district by 0.0542% keeping the effect of other independent variable constant. The sign tells that high proportion of children (below 5) in one district may aggravate population in the same area to participate in productivity discharge their responsibility to care them. These results share idea of (Berisha, 2011; Fahrrmeir and Khatab, 2007).
The coefficient estimate -0.0121 indicates that 1% increase proportion of household having protected toilet (TOILET_100) decreases mortality in distinct by 0.0121% remaining other variable influence constant.
The parameter estimate -0.005 for proportion of children ever vaccinated indicates that for 1% increase in proportion of children ever vaccinated in certain district decrease mortality rate in that particular district by 0.005% keeping others variables fixed. And Proportion of children born below average size (PCBAV SIZE) is significant and has positive effect on mortality rate of districts. This is due the fact that the greater the proportion of the children born below average size in district, higher the probability morbidity and mortality finally. Children who had low birth weight were more likely to be sick longer than infants who had appropriate birth weight or children born below average size can't defend childhood disease such as diarrhea, fever and malaria. This result is consistent with study done Teshager (2011) using 2005 EDHS and similar with the study done in Northeast Brazil by Lira et al. (1996) who showed that children with low birth size experienced 33% more days with diarrhea and 32% more days with vomiting.
In basic knowledge point of view proportion of mothers who attained basic education (EDAT_100), proportion of respondents who heard about ORS (HEARD_ ORS) both have negative and significant effect among district. Nevertheless percentage mother educated primary and above determine mortality rate in certain district, some mothers have no basic education skills which of course necessarily need education for mother. The same interpretation was given for ORS information.
The negative coefficient and significant value for stunting score and wasting score indicates that the less stunt score or waste score the higher mortality rate. Most literature shows that stunting and wasting are problem that highly correlated with childhood morbidity. A vicious cycle between mortality and stunting means that children with stunted were more likely to attacked by diarrhea .The results may be due to shortage of nutrition leads to non health (more vulnerable to diarrhea).
For altitude interpretation is slightly different because it is fixed for certain district and is fixed effect to diarrhea prevalence in certain district; therefore coefficient can be interpreted as districts with high altitude are less likely to be infected by diarrhea. This is may be due to polluted water flow from high to low (see discussion part for more details). Table 3 also present measures of fit for models in discussion part. R-square = 0.5682 which tells us that 56.82% of variation in diarrhea prevalence rate was explained due to variation in the explanatory variable in the model and spatial lag dependent variable.
Finally Table 3 contains Diagnostics Tests Spatial lag Model of Mortality Rate. Three measures that are included to maintain comparability with the fit of spatial lag models that are the log likelihood (-60.83), the Akaike information criteria(147.653) and Schwarz criteria(186.261). These three measures are based on assumption of multivariate normality and corresponding likelihood function for standard regression model. The higher log likelihood, the better the fit (less negative). For the AIC and SC information criteria the direction is opposite, the smaller the measure, the better the fit.

CONCLUSIONS AND RECOMMENDATIONS 4.1 Conclusions
Geographically close districts with similar socio-economic and demographic characteristics and vulnerability dimensions are more conducive to grouping forces, such as using of unprotected drink water. The clustering of underlying disease dimensions might be due to a number of reasons including sanitation that has been applied to groups of areas or socio-economic issues that lead to spatial clustering of mortality rate. Our estimation results of spatial lag model for mortality rate indicate that water closet, proportion of children under five, protected toilet availability, mothers basic education attainment, vaccination coverage, size at birth, mother current working, ORS information, altitude from sea level, stunting score and wasting score of children have significant influence in explanation of mortality rate differentials across districts in the regions.

Recommendations
Based on findings and other related literatures study we forward the following recommendations to mitigate regional mortality.  The expanded program on immunization should be spread out to reduce child mortality in study area.  The study suggests that efforts should be made to build public and private toilet facilities.  Improvements in access to clean water and adequate sanitation, along with the promotion of good hygiene practices (particularly hand washing with soap) can help to prevent childhood diarrhea morbidity and mortality in turn.  The study also suggest that basic education to mother, improve the nutritional status of children, community participation on hygiene and sanitation will be important measure in geographically targeted preparation to reduce possibilities of occurrence morbidity.  Further study will recommend to be conducted by incorporating time or employing other forms of spatial models and including other excluded districts. Thus, we suggest that the most effective policy mix for alleviating differences amongst the regions districts mortality rate, balancing hospital composition and providing sanitation, and encouraging community to participate in sanitation and environment protection. Furthermore reducing average family, encouraging mother to take basic education in regions may reduce morbidity of child and mortality in turn.