The Behaviour of the Dispersion Matrix of the Information Matrix Test under the Wrong Logistic Regression Model

The Information Matrix Tests (IMT) considers as one of the important global goodness of fit test. The IMT provides a unified framework for specification goodness of fit tests for a wide variety of distribution, multivariate or univariate, discrete or continuous. Many researchers discussed the IMT in cases of the outcome covariate is a continuous variable which reported it has reasonable behaviour. This article considers using IMT as a goodness of fit test for the logistic regression mode, to investigate the behaviour of this statistic under the wrong model. Moreover, we are interested to examine the behaviour of the dispersion matrix under wrong logistic model and compute alternative formula of variance, empirical variance of IMT and examine it by simulation.