Generalized linear mixed model and generalized estimating equation for binary longitudinal data

The most common analysis used for binary data is generalised linear model (GLM) with either \na binomial or bernoulli distribution using either a logit, probit, complementary log-log \nor other type of link functions. However, such analyses violate the independence assumption \nif the binary data are measured repeatedly over time at the same subject or site. Failure to \ntake into account the correlation can lead to incorrect estimation of regression parameters \nand the estimates are less efficient, particularly when the correlations are large. Therefore, \nto obtain the most efficient estimates that are also unbiased the methods that incorporate \ncorrelations (McCullagh and Nelder, 1989) should be used. Two of the statistical methodologies \nthat can be used to account for this correlation for the longitudinal data are the \ngeneralized linear mixed models (GLMMs) and generalized estimating equation (GEE). \nThe GLMM method is based on extending the fixed effects GLM to include random effects \nand covariance patterns. Unlike the GLM and GLMM methods, the GEE method is based \non the quasi-likelihood theory and no assumption is made about the distribution of response \nobservations (Liang and Zeger, 1986). The main objective of the study is to investigate the \nstatistical properties and limitations of these three approaches, i.e. GLM, GLMMs and GEE \nfor analyzing longitudinal data through use of a binary data from an entomology study. The \nresults reaffirms the point made by these authors that misspecification of working correlation \nin GEE approach would still give consistent regression parameter estimates. Further, the \nresults of this study suggest that even with small correlation, ignoring a random effects in \na binary model can lead to inconsistent estimation.