A bivariate Bernoulli model for analyzing malnutrition data

  • Mohammad Junayed Bhuyan
  • M. Ataharul Islam
  • M. Shafiqur RahmanEmail author


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.


Correlated responses Marginal model Conditional model Bernoulli model Link function Nutritional data 



The authors acknowledge the National Institute of Population Research and Training (NIPORT), ICF International (USA), and Mitra and Associates who work for this survey under the world-wide Demographic and Health Survey (DHS) program for providing data.


This study received no specific funding. However, the author M. Ataharul Islam has received research grant (CP 3293) from the Higher Education Quality Enhancement Project (HEQEP) funder by the World Bank.

Compliance with Ethical Standards

Author’s contribution

MJB analyzed the data. MSR and MJB drafted the paper. MAI provided constructive comments to improve the paper. All authors approved the final version of the paper.

Availability of data

The dataset used in this research are from a secondary source at Demographic and Health Survey (DHS) program and can be downloaded upon request from

Conflict of interest

The author Mohammad Junayed Bhuyan has received travel grant from International Statistical Institute (ISI) for presenting this work at the Public Health Workshop organized by ISI and University of Kolkata. The author M. Ataharul Islam has received research grant from HEQEP and M. Shafiqur Rahman has declared no conflicts of interest.

Ethical approval

The data used in this research are from secondary source and the respective authority (NIPORT, ICF International, and Mitra and Associates) who collected data from individual has ethical approval from the national ethical review committee.

Informed consent

Informed consent was obtained by the respective authority who collected data from all individual participants included in the study.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Mohammad Junayed Bhuyan
    • 1
  • M. Ataharul Islam
    • 1
  • M. Shafiqur Rahman
    • 1
    Email author
  1. 1.Institute of Statistical Research and TrainingUniversity of DhakaDhakaBangladesh

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