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Bias reduction in the logistic model parameters with the LogF(1,1) penalty under MAR assumption

In this paper, we present a novel validated penalization method for bias reduction to estimate parameters for the logistic model when data are missing at random (MAR). Specific focus was given to address the data missingness problem among categorical model covariates. We penalize a logit log-likelihood with a novel prior distribution based on the family of the LogF(m,m) generalized distribution. The principle of expectation-maximization with weights was employed with the Louis' method to derive an information matrix, while a closed form for the exact bias was derived following the Cox and Snell's equation. A combination of simulation studies and real life data were used to validate the proposed method. Findings from the validation studies show that our model's standard errors are consistently lower than those derived from other bias reduction methods for the missing at random data mechanism. Consequently, we conclude that in most cases, our method's performance in parameter estimation is superior to the other classical methods for bias reduction when data are MAR.