Generalized linear model with Bayes estimator: modeling the number of children in married couples

Abstract

The number of children in a married couple is related to the welfare and resilience of the family. Modeling the number of children involves a binary response variable. This research aims to compare GLM modeling with Bayes estimators for response variables that follow the Poisson and Binomial distributions. The research results show that the Bayes parameter estimator in the GLM model with binary response variables in the case of the number of children in Depok City in 2020 is greatly influenced by the prior distribution used. The best model in this case is GLM of binary response variables with a prior distribution following the Cauchy distribution with a scale parameter of 10, compared to other models because it has the smallest AIC value, 273.1. Meanwhile, the Bayes estimator in the GLM model with count data variables (assumed to follow the Poisson distribution), namely the number of children, both with prior distributions following the Normal Distribution and Cauchy Distribution, have almost the same estimator values and nearly the same AIC model values. This research theoretically contributes to the Bayes estimation method, with the result that for binary response variables, the Cauchy prior distribution is more appropriate to use than using the Normal Distribution as a prior distribution in the case of a number of children. Apart from that, in real terms, this research helps know the factors that influence the number of children.