The behaviour of the distribution of goodness-of-fit tests is an important statistical problem especially in dichotomous data. Many authors, discussed methods to examine and compare between different goodness-of-fit tests, where they show the Information matrix test (IMT) and the Information Matrix Diagonal test (IMTDIAG) statistics have reasonable power even for a logistic model with very sparse data. However, many issues related to the elements of the log-likelihood functions and covariance matrix which may be quite close to zero, these elements leading to singularity and have an effect on the behaviour of the distribution of statistics. In this paper, we are interested to investigate the behaviour of the distribution of the $IMT$ statistic and IMTDIAG statistic, by using different levels of elements of the matrix. Moreover, the mean and the variance of the distribution of statistics should be examined, by the simulation to compare between different levels of elements of the matrix to find a reasonable new form of $IMT$ to avoid the Singularity Problem forecasting.
Keywords: binary outcome, goodness-of-fit tests, information matrix test, logistic model, singularity problem
