Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias

This paper deals with joint estimation of the mean and dispersion parameters in the analysis of proportions. We consider a parametric model, namely the extended beta‐binomial model, and several semiparametric procedures. We study large‐sample efficiency and small‐sample bias and efficiency properties of the estimates of the mean and intraclass correlation parameters. Estimation and efficiency calculations are présentés for the regression model. However, for simplicity, numerical large‐sample efficiency and small‐sample bias and efficiency calculations are performed for the two‐parameter model only. Numerical efficiency results are présentés in terms of graphs. Estimated asymptotic efficiencies of various estimates are also compared for two data sets. Our findings suggest that for the estimation of the mean (regression) parameters the quasilikelihood procedure performs best. However, for the joint estimation, the Gaussian likelihood estimates perform best.