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Analysis of Overdispersed Count Data: a Multilevel Modeling Approach

Fazle Elahi
Department of Agricultural and Applied Statistics, Bangladesh Agricultural University, Mymensingh 2202, Bangladesh

Soma Chowdury Biswas
Department of Statistics, University of Chittagong, Chittagong 4331, Bangladesh

Abstract/ Executive Summary:

In this study, it is aimed to apply multilevel model with two levels in Poisson and Negative binomial regression models and to make comparison between these models to select a model which fits well the over-dispersed count data and finally, to identify the significant factors which influence the number of antenatal care visits of women during their pregnancy period. In this study, two mixed effect models (Poisson regression model with random effect and negative binomial regression model with random effect) are applied to a real data set to obtain the potential determinants of number of antenatal care (ANC) visits of women during pregnancy in Bangladesh, where data are extracted from Bangladesh Demographic and Health Survey (BDHS), 2014. The individual or within variation in each division is lower level (level-1) and between variation among the division is higher level (level-2). It is observed that between two mixed effect models-Negative Binomial regression model with random effect is selected as better model based on AIC, BIC and dispersion parameter for modeling the number of antenatal care visits of women in Bangladesh which is over-dispersed count data. Among the significant covariates, the place of residence, respondent’s education, wealth index, respondent’s husband’s education, decision maker on respondent’s health care and access to mass media are notable factors that are found highly associated with the number of antenatal care visits of women during their pregnancy period. Although both individual- and division-level characteristics have an influence on the inadequate and non-use of ANC, division-level factors have a stronger influence in the rural areas. The results suggest that for over dispersed count data, the negative binomial regression model with random effect is more suitable than Poisson. The results also suggest that much sensitization has to be done specifically in these rural areas to empower pregnant women and their husbands as to improve ANC attendance and utilization. Furthermore, health promotion programs need to increase consciousness about the importance of ANC visits during pregnancy in rural area to ensure the ANC visits among the rural women.

Keywords: Over-dispersed count data, Multilevel model, Antenatal care, Maternal health services, Bangladesh

Location: All over Bangladesh

Start Date: 00-00-2014

End Date: 00-00-2014

Program Area: Socio-economic and Policy

Non-commodity: Data collection and collation

Objectives:

To determine and analysis of over dispersed count data: A multilevel modeling approach

Methodology:

Data and variable: We used secondary data obtained from BDHS-2014. In this study, the dependent variable is “Number of Antenatal Care Visits of Women in Bangladesh” which ranges 0 to 10 times of visits. On the other hand, in this study nine predictor variables are respondent’s age, place of residence, division, source of drinking water, respondent’s education, wealth index, respondents’ husband’s education, decision maker on respondent’s health care and access to mass media. From these independent variables, we consider ‘Division’ as the level-2 variation or the random effect and the rest are fixed effect. To analyze the data we used two-level and multilevel regression models. Several types of tests, viz. goodness of fit, description of AIC (Makalic, D.F. November 22, 2008. Model selection Tutorial#1: Akaike’s Information Criterion), BIC etc. are used to find the best model used in the study. In this study, R statistical software version R i386 3.3.2 (package lme4) are used. The model and estimation procedures Multilevel analysis is a suitable approach to take into account the social contexts as well as the individual respondents or subjects (Snijders, 2011). Normally these situations can be seen in the data collected by multi-stage stratified clustered sampling. The simplest and the most common multilevel model consider only two-level of analysis and this study deals only with this. A multilevel model or a mixed model can be represented as, Y_i =x_i ß + Z_i + ?. Where, Y is known vector of observations, with mean E (Y_i) = θ_{i =}= log μ_i = x_i' ß; x_i is the fixed effect vector of covariates; β is an unknown vector of regression coefficients of fixed effects; Z_i(i=1, 2,…,7) is the unknown random effects; ? is an unknown random errors, with mean E(?) = 0 and variance, Var (?) = R, Let, θ_i= x_i' β = β₀ + β₁x₁+β₂x₂ +……….+ β_kx_k. In this process, we consider a generalized linear model with link log, i.e. we get, θ_i= x_i' ß; Poisson regression model with random effect Poisson model with random effect is, Y_i/θ_i ? Poisson (e ^θi*); where θ_i^* = log µ_{i =}x_i^' β + Z_i; log µ_{i =}β₀ + β₁x_1J + β₂x_2J + ..........................β_px_pJ +Z_i; µ_{i =}e^{θi* =}exp(x_i' β+ z_i); Here, θ_i^* = x_i' β+ z_i; where z_i(i=1, 2, ......7) is random effects and Zi ? N(0,Ψ). Negative binomial regression model with random effect In negative binomial regression with random effects the parameter µ_i is modeled.

Source of Information: J Bangladesh Agril Univ 18(2): 502–508, 2020

Article Link (Online Journal): https://doi.org/10.5455/JBAU.82599

Funding Source:

Budget:

Total Budget (Tk.) :

Achievement/Findings:

In this study it is found that the multilevel effects (division level) are significant and have to take into consideration in mixed effect model which leads multilevel analysis. The study provides evidence that, while both individual and division-level factors are instrumental in determining the attendance and utilization of ANC. The results suggest that for over dispersed count data, the negative binomial regression model with random effect is more suitable than Poisson. Based on findings of this study, we can say that the women who have secondary educational qualification, come from rich family, live in urban area of Bangladesh, whose husband’s educational qualification is above secondary, take the decision on their health care alone and have access to mass media (Radio, Television and Newspaper) visit more times for antenatal care among the women who visit for antenatal care, whereas in the class of women who have no educational qualification, come from poor family, live in rural area of Bangladesh whose husbands are illiterate and have no access to mass media. So we may conclude that this study can help policymakers and program managers have to track the progress of mothers’ health and refocus efforts to meet the goal of reducing maternal and child mortality and morbidity to a great extent.

Knowledge Management: Journal