A bivariate Bernoulli model for analyzing malnutrition data

Multivariate binary responses from the same subject are usually correlated. For example, malnutrition of children are usually measured using ‘stunting’ (low height-for-age) and ‘wasting’ (low weight-for-age) calculated from their height, weight and age, and hence the status of being stunted may depend on the status of being wasted and vice-versa. For analyzing such malnutrition data, one needs special statistical models allowing for dependence between the responses to avoid misleading inference. The problem of dependence in multivariate binary responses is generally addressed by using marginal models with generalized estimating equation. However, using the marginal models alone, it is difficult to specify the measures of dependence between the responses precisely. Islam et al. (J Appl Stat 40(5):1064–1075, 2013) proposed a joint modeling approach for bivariate binary responses using both the conditional and marginal models where the dependence between the responses can be measured and tested using a link function of the models. However, the author didn’t examine the properties of the regression coefficient except for the dependence parameter. This paper has given further insight into the joint model and investigated the properties of regression coefficients using an extensive simulation study. The simulation results showed that the maximum likelihood estimators (MLEs) of the regression coefficients of the joint model showed well performance in terms of bias, mean squared error and coverage probability particularly when sample size large. Generally speaking, the MLEs of the parameters associated with joint models possessed the same asymptotic properties as the MLEs of those associated with standard generalized linear models, except for the interpretations. Further the paper provided an application of joint model for analyzing malnutrition data from Bangladesh demographic and health survey 2011. The results revealed that the estimates of the both marginal and condition regression coefficients of the joint model have meaningful interpretation and explanation, which will in turn help the policy makers for designing appropriate policies for improving nutrition status.