University Publications

The fact that Hosmer-Lemeshow test is based on formation of groups for variables values poses a number of questions. One of these is how many groups should be formed? Will a different number of groups change the final result? Another is to what extent the power of the test is affected by factors such as sample size and population distribution characteristics? The main aim of this paper is to examine the performance of Hosmer-Lemeshow test when the fitted logistic model is the incorrect model under some factors such as the changing number of groups, sample size and population distribution that is expected to affect its performance to see whether its performance in case of incorrect model better than its performance in the case of correct model. This is accomplished through techniques of analysis and simulation using RStudio package.The analytical approach is composed of conduction of Hosmer-Lemeshow test, formation of groups, etc, while the simulation approach is entirely based on the ideas of data generation based on specified circumstances, sample selection steps, iterations steps and so on. The results concluded that when 10 groups are formulated the value of the test statistic is increased with sample size and when the number of groups is changed the test performance is affected by changing the number of groups especially when the sample size is small. Moreover, when the simulation technique is used to check for the effect of repeated sample and to see whether the covariate’s distribution and the sample size will affect the power of the test or not and to what extent, it has been revealed that the power of the test increases with the increase in both the sample size and the variance value and accordingly its performance in case of the incorrect model and through its interaction with the control factors is better compared to its performance in the case of the correct model