Estimation using penalized quasilikelihood and quasi-pseudo-likelihood in Poisson mixed models

Area of Science:

• Statistics
• Biostatistics
• Statistical Modeling

Background:

• Poisson mixed models are widely used in various scientific fields.
• Penalized quasilikelihood (PQL) is a common estimation method for these models.
• Understanding the bias of PQL estimators is crucial for accurate statistical inference.

Purpose of the Study:

• To investigate the asymptotic bias of PQL estimators in Poisson mixed models.
• To compare the bias of PQL estimators for Poisson versus binomial data.
• To propose and evaluate unbiased estimating equations using quasi-pseudo-likelihood.

Main Methods:

• Asymptotic analysis of bias for regression coefficients and variance components.
• Development of unbiased estimating equations based on quasi-pseudo-likelihood.
• Simulation studies to compare finite sample performance of PQL and quasi-pseudo-likelihood.

Main Results:

• PQL estimators in Poisson mixed models exhibit a smaller order of bias compared to those for binomial data.
• Unbiased estimating equations based on quasi-pseudo-likelihood provide consistent estimators under regularity conditions.
• Simulation results demonstrate the finite sample performance of the proposed methods.

Conclusions:

• PQL is a viable estimation method for Poisson mixed models with reduced bias compared to binomial models.
• Quasi-pseudo-likelihood offers a promising approach for obtaining unbiased and consistent estimators.
• The study provides valuable insights for selecting appropriate statistical methods in mixed model analysis.