Parsimonious Selection of a Working Correlation Matrix in Generalized Estimating Equations
Robert Nyamao Nyabwanga *
Department of Mathematics and Actuarial Science, Kisii University, Kenya.
Kepher Makambi
Department of Biostatistics, Bioinformatics, and Biomathematics, Georgetown University Cancer Center, USA.
Fred Monari
Department of Mathematics and Actuarial Science, Kisii University, Kenya.
Lewis Keter
Department of Mathematics and Actuarial Science, Kisii University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
The quasi-likelihood information criteria (QIC) developed based on the Kullback-Leibler cross-entropy principles is famously used in generalized estimating equations modelling to select a working correlation structure that is vital in improving efficiency of estimates. However, many studies have shown that its use favors over-parameterized correlation structures. In this paper, we suggest a modification to the penalty term of the original QIC by adding a weighting factor built using the number of correlation and regression parameters as cost components. This is aimed at improving its selection rates of a parsimonious correlation matrix structure. Using a simulation study, the performance of the modified QIC was established to be better than that of the original QIC, EAIC and EBIC. Further, it was found out that as the number of repeated measures and degree of correlation became larger, the proposed method gained more power in choosing the correct matrix. The new method was illustrated using the data for Mother’s Stress and Children’s Morbidity study.
Keywords: Generalized estimating equations, weighted euclidean squared distance, working correlation matrix, parsimony, quasi-likelihood information criteria