Beta-Geometric Regression for Modeling Count Data on First Antenatal Care Visit (ANC) with Application

Introduction: Little attention has been paid to modeling count data with the geometric distribution. There are many real-life phenomena with a constant probability of first success. However, in practice, the probability of the first success may vary, making simple geometric models unsuitable for modeling such data. One can assume one of many continuous distributions for modeling the probability of first success with the parameter space [0, 1]. In this respect Beta distribution defined on the standard unit interval [0,1] is the most useful distribution due to its ability to accommodate a wide range of shapes. Thus, in this paper, by mixing Beta and geometric distribution, we developed a Beta-geometric distribution for modeling the count data through application to real-life count data on time to the first antenatal care (ANC) visit. Methods: The estimation of the distribution parameters using the method of moments, maximum likelihood estimation (MLE) method, and Bayesian estimation approach are provided. Based on the Beta-geometric distribution, we developed a new Beta-geometric regression model for analyzing count data that follow the geometric distribution. The goodness of fit of the derived model has been tested using real data on time to the first ANC visit. Results: Beta-geometric distribution has a simple form for its probability mass function (pmf), and is flexible in capturing both underdispersion and overdispersion that may present in count data. It was found that the proposed Beta-geometric regression model fit the count data on the first ANC visit better than simple geometric distribution or Negative Binomial distribution. Conclusion: Unlike the Poisson or Negative Binomial distribution, Beta-geometric distribution does not need an additional parameter to accommodate underdispersion or overdispersion and thus could be a flexible choice for analyzing any count data. The goodness of fit test of the Beta-geometric model provides better fitting of the model to real data on time to first ANC visit than geometric or Negative binomial models.