Discrete outcome variable is common in public health, behavioral sciences and in many medical applications; the Poisson regression model is useful to analyze discrete random variable. For clustered discrete outcome variable where the observations are correlated among individual subjects, the number of observed discrete is sometimesgreater than the expected frequency of the Poisson distribution and the discrete random variables are over-dispersed. Overdispersion is familiar in discrete random variable models particularly within the area of ecology and biological science because of missing covariates, non-independent, aggregations of data and an excess frequency of zeros. Every cluster levels received a singular level of a random effect that models the extra Poisson variation given within the data, are usually utilized to discuss heterogeneity in discrete random variable. However, studies investigating that the power of cluster level random effects as a way to discrete random variablemodel with over-dispersion is scarce. A situation where the variance of the response variable exceeds the mean, and hence, both over- dispersion and heterogeneity problems occur, in the appropriate imposition of the Poisson model may underestimate the standard error and overestimate the significance of the regression parameters, and so, giving misleading inference about the regression