Background The Poisson regression model is useful to analyze count data, but, when the observations are correlated the Poisson estimate will be biased. Whereas, when the over-dispersion and heterogeneity problems occur the imposition of the Poisson model underestimate the standard error and overestimate the significance of the regression parameters. Therefore, the objective of this paper was to develop a test statistic to model and predict clustered count response data via application and

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... tion data. Methods This paper concentrated on the clustered count data model to take into account heterogeneity. Accordingly, we developed a score test based on the multilevel Poisson model for testing heterogeneity with the alternative Poisson regression model. In addition, for the model application, we used the EDHS children's data. Therefore, to evaluate the proposed model, we used both simulation and application data. Results Simulation results showed that the proposed score test has high power to predict and used to control heterogeneity between groups. Oromia, Amhara, and SNNPR are among the regions with the highest child mortality rates (Table 1). The results indicated that women who made marriage a mean age of 16 years and gave birth for the first child a mean age of 18 years and 8 months. Table 1 showed that 81% of all child deaths have recorded in rural areas. 78% of child families were illiterate, as a result, 75% of children don't have access to latrines and drinking water. Rivers and open-sources waters are the common sources of drinking water which comprised 79% of the total water supply. Therefore, from the research finding, it is possible to conclude that most child mortality is due to scarcity of water. Conclusion The Power of test estimates indicated that the proposed method was better than the existing models. All covariant and dummy explanatory variables have a significant effect on the deaths of children. Hence, the multilevel Poisson model results indicated that there exist high variability among regions for the deaths of children. Therefore, this work suggested that the applications of the random-effects model provided a simple and robust means to predict the count response data model.