A comparison of Logit and Probit models using Monte Carlo simulation

The Logit model and the Probit model are statistical models of Logistic regression and probability-based pattern recognition algorithms. The cases in which the Logit model and the Probit model fit better, respectively, are assessed to provide selection suggestions. Criteria, such as the AIC, Deviance, and Pseudo R-square, are selected to assess the goodness-of-fit of the two models. Using Monte Carlo simulation in different data scenarios found that some criteria have limited applicability in assessing the goodness of fit and two models are not sensitive to whether or not the independent variables are independent of each other. The difference between the two models is mainly in the sample size and the kurtosis of the data. The Probit model fits well to the smaller data set generated for all kurtosis cases, while the Logit model fits better when the sample size from the Leptokurtic distribution is larger.