Data exploratory
Table 3 depicted the prevalence of under-nutrition of sampled children using each of the anthropometric measures separately and a single composite measure respectively. For instance, about 38.3% of sampled children were stunted (21.0% moderately and 17.3% severely). According to composite index of Failure, out of sampled children in Ethiopia about 46.6% of children were undernourished. The single composite index of anthropometric indicators showed that 49.0% of sample children were undernourished (19.8% moderately and 29.2% severely).
Ordinal logistic regression models
Test of parallel regression assumption
All the significant explanatory variables from uni-variable generalized ordered logistic regression models were included and their significance was assessed (at 5% significance level) in the proposed ordinal logistic regression models. The Brant test of parallel regression assumption from POM yielded a Chi-Square value of 90.27 with p-value=0.000, indicating that the proportional odds assumptions for the full-model was not upheld. This suggested that the effect of one or more of the explanatory variables was likely to differ across separate binary models fit to the cumulative cut points. This indicates that the null hypothesis i.e., the model parameters are equal across categories (i.e. parallel regression assumption) is rejected. When the parallel regression assumptions are violated, models based on the parallel assumption for all the independent variables cannot be accurately applied to the whole population: theyare biased. Consequently, proportional odds were excluded from further analysis. Generalized ordered logit model and partial proportional odds models were fitted to the data and a comparison of the models made.
Goodness of fit and model selection
From Table 4, it can be concluded that both of the full models improve significantly over their null model (model only with intercept term) as there are evidences against the null hypothesis that all the coefficients of the predictors are zero (Prob>chi-square =0.000).
The model which represents the best fit according to AIC and BIC is PPOM as it has the smallest AIC and BIC (Table 4) and it is also more parsimonious. Thus, PPOM was used to identify significant determinants of under-nutrition and parameter estimates of the PPOM are presented and interpreted for the significant predictors.
Results of Partial Proportional Odds Model
Table 4 and 5 show two result panels. . The first (Table 5) contrasts the moderately and severely undernourished. In contrast to the remaining two categories of under-nutrition, signs of the coefficients in the first panel imply how likely nourishment of the child is. . Similarly, the second panel (Table 6) contrasts the severely undernourished category with nourished and moderately undernourished. Hence, positive coefficients indicate that higher category values on the explanatory variable make it more likely that the respondent will be in a higher category of Y than the current one, whereas negative coefficients indicate that higher category values on the explanatory variable increase the likelihood of being in the current or a lower category.
From the partial proportional odds model the categories Afar, Oromia, Somali, SNNPR, Gambela, Harari, Dire Dawa,; as well as richest’s wealth index; husband’s education, birth order and sex violated the parallel lines assumption. The model therefore allows the coefficients of these variables to vary across the two equations. From PPOM results, region, mother’s education and source of drinking water, number of under five children, wealth, anemia, multiple birth,, age and sex of the child, fever, , mother’s age at birth and body-mass index, and husband’s educational level significantly related with under-nutrition.
Predictors that do not violate the parallel line assumption
The results of PPOM revealed that holding all variables constant, as compared to a child in Tigray, a child in Amhara was 1.4 (OR=1.4; CI: 1.14 - 1.69) times more likely to be in moderate or severe under-nutrition status. . Similarly, compared to a child in Tigray, a child in Amhara was 1.4 (p-value =0.0001) times more likely to be in severe rather than in the moderate or nourished undernutrition statuses . Holding other variables constant, the odds of being undernourished was worse, 2.3(OR=0.44; CI: 0.32-0.62) times in children of Tigray’s as compared to children of Addis Ababa. .
The fitted model showed that compared with children whose mother had secondary or higher education, children from uneducated mother have risk of an even worse under-nutrition status 1.7= (0.58)-1 (OR=0.58; CI: 0.46 - 0.73) Compared with the children with illiterate fathers, children with secondary or higher educated fathers were around 8% (OR=0.92; p-value =0.045) and less likely to be in the worst nutrition status,. The risk of being in an even worse under-nutrition status decreased by 11% (OR=0.89; p-value =0.025) in a child born from a mother aged 20-34 years as compared to a child born from a mother aged <20 years. Keeping all other variables constant, as opposed to a child who had normal and obese mother, a child with mother of BMI<18.5 was 1.4 (OR=0.71; CI: 0.63 - 0 .79) and 2.6 (OR=0.39; CI: 0.31 - 0.65) times more likely to be in worse under-nutrition status respectively,
The results of this study revealed that as compared to children from families having a single child aged under five years, the odds of being in a worse under-nutrition status were 1.2 (OR=1.2; p-value =0.007) times higher for children from families having 3 or more under-five children. Contrary to children from households with poorest wealth index, the risk of undernourishment decreased by 18% (OR=0.82; p-value =0.008) and by 36% (OR=0.64; p-value=0.000) in children from families with middle wealth and richer wealth index respectively. The first and second born of the multiple children were 2.1 (OR=2.1; p-value =0.001) and 2.2 (OR=2.2; CI: 1.43-3.43) times more likely to have a respectively worse under-nutrition status as compared to children from a family of single birth. Holding all other variables constant,
children aged 6-11, 12-23, 24-35, 36-47 and 48-59 months were respectively 1.8 (OR=1.8; CI: 1.4-2.3), 5.2 (CI: 4.2-6.4), 7.8 (CI: 6.3-9.6), 7.2 (CI: 5.9-8.9) and 6.4 (CI: 5.2-7.9) times more likely to be in a worse under-nutrition status as opposed to children aged 0-6 months,
Holding all variables constant, the fitted model indicated that the risk of having worse under-nutrition status was 1.2 (OR=1.2; CI: 1.1-1.3) times higher among anemic children when compared to the non-anemic children. Compared to children who had no fever, the risk of being in a worse under-nutrition status was 1.3 (OR=1.3; p-value=0.002) times higher among children who had fever in the last two weeks before the survey . Compared to children from household who have consumed water from improved source,the odds of being undernourished increased by 10% (OR=1.1; p-value=0.045) among children from households who have not consumed water from improved source
Predictors that violate the parallel regression assumption
The results of PPOM showed that compared to a child from Oromia, Somali, SNNP and Gambella, a child from Tigray region was 1.4 (OR=0.69; CI: 0.58-0.83), 2 (OR=0.50; CI: 0.41-0.63), 1.4 (OR=0.70; CI: 0.58-0.85) and 2 (OR=0.49; CI: 0.38-0.63) times more likely to be in a moderate or severe under-nutrition .Compared to a child in Somali and Gambella, a child from Tigray region was 1.4 (p-value =0.006) and 1.5 (p-value =0.002) times more likely to be in a severe rather than in a nourished or moderate under-nutrition status. In Contrast to a child fromTigray region, a child from Benshangul region was 1.34 (p-value =0.01) times more likely to be in a severe under-nutrition status rather than in a nourished or moderate under-nutrition status. The children from families with poorest wealth index were found 1.5 (OR=0.64; CI: 0.51-0.80) times more likely to be in moderate or severe under-nutrition rather than in a nourished status when compared to children with richest wealth index households. Keeping all other variables constant, in contrast to children from families with richest wealth index, the children with families of poorest wealth index were 1.8 (OR=0.54; CI: 0.43-0.69) times more likely to be in a severe rather than nourished or moderate under-nutrition status. In comparison to females, the fitted model had showed that male children were 1.1 (p-value =0.024) times more likely to be in moderate or severe under-nutrition rather than in a nourished status. In contrast to female children, the risk of male children to be in a severe under-nutrition status was 1.2 (OR=0.81; CI: 0.73-0.89) times higher than those children in a nourished or moderate status as compared to children born to husband with secondary or higher education. Holding all other variables constant, the risk of children born from a husband without education to be in severe under-nutrition status was1.2 (p-value =0.003) times higher than those in a nourished or moderate status