3.1 Descriptive Statistics
This research utilized the national wide Ethiopia Demographic and Health Survey (EDHS) 2016 collected data on the stunting of children. The analysis presented in the study is based on 11654 under-five children with complete weight-for-age anthropometric index as indicator of a children’s stunting and health status among other indices, since it is an excellent overall indicator of a population’s stunting and health status. Table 2: below, shows that the percentage of the severity status of child’s stunting
As presented in Table 2, the prevalence of stunting found was at 48.74% were female, where males were 49.62%. It shows that 49.82% of urban children were stunted, 48.54% rural of children were stunted and 46.89% of children were stunted their family no education.51.67% of children were stunted their family were primary education, 65.28% of children were stunted their family education were secondary and 75.51% of children were stunted where their family were higher education.
As presented in Table 2, the prevalence of stunting found was 48.85% of children were stunted where their toilet was unsafe and 54.68% of children were stunted where their toilet was safe.40.17% of children were stunted where poorest and 69.90% of children were stunted where richest.
Table 2 shows 46.78% of children were stunted whether currently pregnant or not 68.30% of children were stunted where they were currently pregnant. And 52% of children were stunted where they were not used a soup. 47.26% of children were stunted that they used a soup and 49.28% of children were stunted that they were not found nutrients and 46.05% of children were stunted that they were found nutrients.
Figure1: shows that the Predicted Probability of under five children stunting by predictors vs Region. The Maximum predicted log-odds range is considered as regionally varied variables thus variable duration of breast feeding is regionally varied variables and have high random effects on under-five children stunting compare to the other variables. This variable is used in the random slope model.
3.2 Results of Multilevel Logistic Regression Analysis
In the multilevel analysis, a two-level structure is used with regions as the second-level units and under five children as the first level units. This is basically the analysis of region wise variation of stunting among under-five children. Children were nested in regions with a total of 5732 children included in this study.
3.2.1 Multilevel Logistic Regression Model Comparison
The Maximum predicted log-odds range is considered as regionally varied variables thus variable age and stunting are regionally varied variables and have high random effects on under-five children stunting morbidity compare to the other variables. These variables are used in the random slope model.
The deviance-based chi-square value for the empty model shown in the above Table 3: is the difference in log likelihoods between an empty model of single level logistic regression and empty model of multilevel logistic regression, which is to be compared with the critical value from the chi-squared distribution with 1 degree of freedom. The significance of this test implies that an empty model with random intercept is better than an empty model without random intercept. The significant deviance-based chi-square value and smallest AIC for random intercept model indicates that the random intercept and fixed slope model is a better fit as compared to the empty model. The deviance-based chi-square test of random effects for random coefficient model is not statistically significant and has larger AIC. This implies that as compared to the model with random intercept and fixed slope model, the random coefficients model is not a better fit. Thus, in the above Table 3: shows that among multilevel logistic regression models, the random intercept and fixed slope model fits significantly better than the other multilevel logistic regression models.
3.2.2 Results of Empty Multilevel Logistic Regression Model
The variance of the random factor is significant which indicates that there is regional variation in experiencing stunting among under-five children (Table 4).The intercept βO = -1.18546 is interpreted as the odds of stunting in an average region. That is the intercept informs us that the average probability of incidence of stunting everywhere in Ethiopia is exp (-1.18546) / [1+exp (-1.18546)] = 0.234. The intra-region correlation in intercept only model is 0.049 which is significant at 5% level of significance. This result implied that 4.9% of the variation in the incidence of stunting can be explained by grouping the under-five children in regions (higher level units). The remaining (100-4.9%=95.1% of the variation of incidence of stunting is explained within region-lower level units.
The variance of the regional level residuals errors, symbolized by is estimated to be 0. 140688. This parameter estimate is larger than the corresponding standard errors and calculation of the Z-test shows that it is significant at p<0. 025. The significance of this residual term indicates that there are regional differences in the women unemployment status in Ethiopia.
The deviance-based Chi-square (deviance = 521.19) indicated in table below is the difference in deviance between an empty model without random effect (deviance = 15,764.71) and an empty model with random effect (deviance =15,243.52). This value is compared to chi-square distribution with 1 degree of freedom. The significant of it (X2 = 521.19, P-value < 0.0001) implies that an empty model with random intercept is better than an empty model without random intercept. The deviance reported in the above Table is a measure of model misfit; when we add explanatory variables to the model, the deviance is expected to go down.
3.2.3 Results of Random Intercept and Fixed Slope Logistic Regression Model
The random intercept and fixed slope logistic regression model is a multilevel model which has random intercept and fixed coefficient of predictors. As can be seen from Table 5: the analysis of multilevel logistic regression revealed that incidence of stunting in under-five children varied among regions. The value of is the estimated variance of the intercept in random intercept and fixed coefficients model. The result displayed that the region-wise difference in the incidence of childhood stunting was statistically significant. In addition, age of child, maternal working status, duration of breastfeeding, stunting, wasting, and underweight were also found to be significant determinants of incidence of stunting among the regions.
The deviance-based Chi-square (deviance = 928.61) taken from single logistic regression analysis is the difference in deviance between the empty model with random intercept (deviance = 15,243.52) and fixed slope model with random intercept (deviance = 14,314.91). The significant of it (X2 =928.61, DF = 15, P-value < 0.0001) implies that fixed slope model with random intercept model is better than empty model with random intercept. Therefore, this model is a better fit as compared to the empty model with random intercept.
Moreover, the AIC and BIC value for fixed slope model with random intercept (AIC=14,751.85, and BIC=14,762.01) are less than those for the empty model with random intercept (AIC = 15,247.52 and BIC = 15,248.31). This indicates that fixed slope model with random intercept is a better fit as compared to the empty model with random intercept model.
3.2.4 Results of Random Coefficient Multilevel Logistic Regression Model
Table 6: reveals the effect of the intercept on region j is estimated to be -1.4765 (0.3124) + U0j and their variance 0.024 (Standard error 0.070). The intercept variance of 0.024 (Standard error 0.070) is interpreted as the between-region variance when all other variables are held constant (i.e. equal to zero). Their mean is -1.4765 (standard error 0. 3124) and their variance is 0.024 (standard error 0.070). The between-region variance of slope of Breast feeding status is estimated to be 0.004 (standard error 0.002). Likewise individual region slopes of Breast feeding status vary about with a variance 0.004 (standard error 0.002). The negative covariance estimate of -0.001 (standard error 0.004) between intercept and slopes of Breast feeding status, suggest that regions with a high intercept (above-average) tends to have a flatter-than-average slope.
The quantities AIC and BIC can be used to make an overall comparison of this more complicated model with the random intercept model with fixed slope model. We see that from Table 6: the value of fit statistics for random coefficient model (AIC = 14720.79 and BIC = 14731.35) is less than random intercept model (AIC=14,751.85 and BIC=14,762.01. This indicates that the random coefficient model is a better fit as compared to the random intercept and fixed effect model.
The odds of stunting of child’s from mothers who have still breast feeding were 0.601 (OR=0.601) times higher than the odds of stunting of child’s from mothers who never breasted controlling other variables in the model and random effects at level two. Women who live in rural households are 0.647 more likely to be stunted (OR=0.647) than women who reside in urban households controlling for other variables in the model and random effects at level two. The odds of stunting status of child from women who are pregnant is more likely to be stunted 4.157 compared to non-pregnant women controlling for other variables in the model and random effects at level two. Women who feed nutrient food to their child are 1.239 more likely to be stunted (OR=1.239) than women who didn’t feed nutrient food controlling for other variables in the model and random effects at level two.