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Monte Carlo Evaluation of Consistency and Normality of Dichotomous Logistic and Multinomial Logistic Regression Models

Naima Shifa & Mamunur Rashid


The dichotomous logistic regression model is one of the popular mathematical models for the analysis of binary data with applications in physical, biomedical, and behavioral sciences, among others. The feature of this model is to quantify the effects of several explanatory variables on one dichotomous outcome variable. Multinomial logistic regression model, on the other hand, handles the categorical dependent outcome variable with more than two levels. Normally, the asymptotic properties of the maximum likelihood estimates for the model parameters are used for statistical inference, for example, normality allows one to compute the confidence interval and perform statistical tests in a manner analogous to the analysis of linear multiple regression models, provided the sample size is large. However, asymptotic properties of the maximum likelihood (ML) estimator in logistic models had been studied earlier, see, for example, Gourieroux and Monfort (1981) and Amemiya (1985), and different results have been established. As none of the authors verified their work via the Monte Carlo simulation study,
this research article performs an extensive Monte Carlo simulation study to examine consistency and normality of the maximum likelihood estimators for parameters of both the dichotomous logistic and multinomial logistic regression models.

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