Applying non-informative G-prior for logistic regression models with different patterns of data points

In logistic regression models, different patterns of data points in observed data can cause large bias in parameter estimates, especially when separation is present in the observed data. In the frequentist approach, maximum likelihood estimates fail to exist when separation occurs in the observed data. In the Bayesian approach, the existence of posterior means is also affected by the presence of separation depending on the form of prior distributions. In this paper, a non-informative G-prior for Bayesian method is proposed to reduce the bias of the parameter estimation when prior distributions of parameters do not have information and separation is present in the data. In this proposed method, the information from observed data and ideas of a normal regression model are implemented to form the mean and standard deviation of the normal prior distributions. The Markov chain Monte Carlo algorithm is then employed by using Metropolis Hasting algorithm to sample for the target posterior distribution. Results show that estimates from the proposed Bayesian method are more accurate and reliable than from the classical approach when separation is present or is not present in the observed data. Moreover, the proposed Bayesian method can provide better estimated results compared to the default Cauchy prior Bayesian approach when the prior distribution does not have information. The proposed method is also validated by applying it to a case study of MROZ data.

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