We consider the estimation of the intra-cluster correlation for the one-way random effects model in the case of balanced and unbalanced cluster sizes. It is well-known that the standard variance component methods, such as the ANOVA method, can produce zero and negative estimates of the intra-cluster correlation, which is inherently a strictly positive parameter. In this paper, we present an adjusted maximum likelihood estimator for the intra-cluster correlation coefficient. The adjustment is chosen such that the adjusted likelihood function is quasi-convex. We compare the proposed estimator with the commonly used ANOVA estimator using a Monte Carlo simulation for normal and beta-binomial distributed variables.
This paper is based on preovious work by Lahiri and Li (2009) and Li and Lahiri (2010).
Lahiri, P. and Li, H. (2009). Generalized Maximum Likelihood Method in Linear Mixed Models with an Application in Small-Area Estimation. Proceedings of the Federal Committee on Statistical Methodology Research Conference
Li, H. And Lahiri, P. (2010). An adjusted maximum likelihood method for solving small area estimation problems. Journal of Multivariate Analysis, 101, 882-892
Keywords: intracluster correlation coefficient; variance component model; strictly positive estimator
Biography: Siegfried Gabler is chief statistician at GESIS, Mannheim. He is a member of the sampling expert panel of the European Social Survey and a Privatdozent at the University of Mannheim. His current research areas cover sampling designs, especially for telephone surveys and for cross-cultural surveys, weighting for nonresponse, design effects, decision theoretic justification of sampling strategies.