Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 896082, 10 pages
http://dx.doi.org/10.5402/2012/896082
Research Article

Alternatives to Mixture Model Analysis of Correlated Binomial Data

1Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529-0077, USA
2Department of Biostatistics, Virginia Commonwealth University, 830 East Main Street, Richmond, Virginia 23298-0032, USA
3Department of Mathematical Sciences, Indiana University-Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, USA

Received 28 February 2012; Accepted 29 March 2012

Academic Editors: P. D'Urso, A. Hutt, and M. Scotto

Copyright © 2012 N. Rao Chaganty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

While univariate instances of binomial data are readily handled with generalized linear models, cases of multivariate or repeated measure binomial data are complicated by the possibility of correlated responses. Likelihood-based estimation can be applied by using mixture distribution models, though this approach can present computational challenges. The logistic transformation can be used to bypass these concerns and allow for alternative estimating procedures. One popular alternative is the generalized estimating equation (GEE) method, though systematic errors can lead to infeasible correlation estimates or nonconvergence problems. Our approach is the coupling of quasileast squares (QLSs) method with a rarely used matrix factorization, which achieves a simplified estimation platform—as compared to the mixture model approach—and does not suffer from the convergence problems in GEE method. A noncontrived example is provided that shows the mechanical breakdown of GEE using several statistical software packages and highlights the usefulness of the QLS approach.