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Bias‐corrected maximum likelihood estimator of the intraclass correlation parameter for binary data
Author(s) -
Saha Krishna K.,
Paul Sudhir R.
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2197
Subject(s) - statistics , intraclass correlation , mathematics , estimator , maximum likelihood , binary data , restricted maximum likelihood , estimation theory , score test , binary number , arithmetic , psychometrics
A popular model to analyse over/under‐dispersed proportions is to assume the extended beta–binomial model with dispersion (intraclass correlation) parameter ϕ and then to estimate this parameter by maximum likelihood. However, it is well known that maximum likelihood estimate (MLE) may be biased when the sample size n or the total Fisher information is small. In this paper we obtain a bias‐corrected maximum likelihood (BCML) estimator of the intraclass correlation parameter and compare it, by simulation, in terms of bias and efficiency, with the MLE, an estimator Q 2 based on optimal quadratic estimating equations of Crowder and recommended by Paul et al . and a double extended quasi‐likelihood (DEQL) estimator proposed by Lee. The BCML estimator has superior bias and efficiency properties in most instances. Analyses of a set of toxicological data from Paul and a set of medical data pertaining to chromosomal abnormalities among survivors of the atomic bomb in Hiroshima from Otake and Prentice show, in general, much improvement in standard errors of the BCML estimates over the other three estimates. Copyright © 2005 John Wiley & Sons, Ltd.