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, respondentís education, wealth index, respondentís husbandís education, decision maker on respondentís 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.
over-dispersed count data, multilevel model, antenatal care, maternal health services, Bangladesh.