A Comparison Between Estimation Methods in Semiparametric and Ordinary Poisson Regression Models for Clustered Count Data

Abstract

Abstract. Clustered data are considened one of the most common model in applied studies because of it contrase within-cluster variability. In this regard, A semiparametric Poisson regression model was a dopted to analyze this type of  data , throughout mergine the nonparametric procedune to represent the nonlinear relations between independent variables and the parametric procedune that models the random effects specific to each cluster. The two estimation methods were considered. The first method involves simultaneous estimation of both the parametric and nonparametric parts using the Penalized Least Squares (PLS) and. The second method estimates the nonparametric parts first, followed by the parametric parts  using the Backfitting algorithm. These two methods were compared with the classical Maximum Likelihood Estimation (MLE) method used to fit the ordinary Poisson regression model, based on the Mean Absolute Percentage Error (MAPE) as the evaluation criterion.  Simulation were done with several , considering three different values for the number of clusters: k = 3,5,10. Also Two types of cluster sizes were used:

• In the first, clusters had equal sizes: nₖ = 10,30,50
• In the second, clusters had unequal sizes, drawn from total sample sizes of n = 50,100,250,500 resulting in varying cluster sizes.

The results indicated that the Backfitting algorithm superior the other methods in both experimentaly and practicly