Correlated data arise naturally in many different ways in scientific disciplines such as the biological, health or social sciences. Liang and Zeger (1986) presented the generalized estimating equations (GEE) approach to analyzing this type of data which do not require assumptions about the complete joint distribution of the response vector. Their approach relies on estimating functions and provides a natural extension of quasilikelihood to the multivariate response setting. Standard GEE require only correct specification of the univariate marginal probabilities while adopting some working assumptions about the association structure. Model checking is an important aspect of regression analysis. Therefore GEE approach also needs diagnostic procedures for checking the model's adequacy and for detecting outliers and influential observations. Graphical diagnostic displays can be useful for detecting and examining anomalous features in the fit of a model to data. For correlated binary data, Tan et al. (1997) proposed several graphical methods. Oh et al. (2008) proposed residual plots to investigate the goodness-of fit of the GEE approach for discrete data. They investigated Pearson, Anscombe and deviance residuals for Poisson and binary responses. In this work, we propose to generalize these plots using a family of residuals based on the ϕ-divergence measures which contains the Pearson and Deviance residuals. The graphical methods are illustrated with a real life example.
Keywords: correlated data; generalized estimating equations; graphical diagnostic; residuals based on divergences
Biography: María del Carmen Pardo is Associate Professor at the Complutense University of Madrid. Her research interests nowadays is Biostatistics, Survival Analysis and Longitudinal Data Analysis. She has published more than 50 papers in JCRSC journals. She has been a visiting scientist at McMaster University in Hamilton, Canada, Miguel Hernández University in Elche, Spain and for several times at the Institute of Information Theory and Automation, Czech Academy of Sciences, Prague.