Data Analysis Comparison Logit and Probit Regression Using Gibbs-Sampler

Abstract

Binary regression using probit and logit regression is widely used in applied statistics. In the classical approach, the parameters of the models to be viewed as unknown constants and the maximum likelihood is the most popular inference method. If we know the prior distribution of the parameters then the Bayesian approach will be the suitable methods for data analysis as its ability to incorporate prior information which can increase the precision of parameter estimates. If certain prior distributions are particularly convenient for samples from certain other distributions then the explicit posterior distributions are easily been derived. For example, a random sample is taken from Poisson distribution and the prior distribution of θ is a Gamma distribution, then the posterior distribution of θ will be a Gamma distribution. The straight forward calculation of the posterior distribution is generally impossible if the parameter space is high dimensional form or have no explicit functional form. In that case, the role of computer intensive method in summarizing posterior distribution is conducted through Markov Chain Monte Carlo. In general, the Gibbs sampler is a technique to develop Markov Chain such that it can generate sample from the posterior distribution without calculating the density instead of simulating individual parameters from a set of p conditional distribution. In this paper, we study the Gibbs sampling applied to low birth weight study related to issues of implementation of the Millenium Development goal in special region of Yogyakarta. In addition, we shows the comparison between logit and probit estimates.