Inferences in generalized linear longitudinal mixed models

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There are many situations in socio-economic and biomedical research fields, among others, where binary and count responses along with suitable multi-dimensional time-dependent covariates are repeatedly collected over a small period of time, from the members of a large number of independent families. The analysis of this type of familial-longitudinal binary and count data may not be easy, because of the difficulties in modeling their underlying familial-longitudinal correlation structures. Furthermore, due to the complex nature of the correlation models, it may be either impossible or extremely complicated to develop the so-called likelihood approach for suitable inferences. Recently, based on a class of auto-correlation structures, Sutradhar (2003, Statistical Science), Sutradhar, Jowaheer and Sneddon (2008, The Scandinavian Journal of Statistics), and Sutradhar, Rao and Pandit (2008, Sankhya B, The Indian Journal of Statistics), among others, developed a unified generalized quasi-likelihood (GQL) approach for inferences in longitudinal and/or familial-longitudinal models for count and/or binary data. These GQL inferences are, however, developed for standard situations such as when the data are complete, and they neither contain any outliers, nor, any measurement errors. The main objective of this proposal is to develop consistent and efficient inference techniques under three non-standard and highly practical situations: (1) where familial-longitudinal data may be subject to missing at random; (2) where the covariates in the familial-longitudinal set up may be subject to contamination; (3) where the responses or covariates in the familial-longitudinal set up may contain measurement errors. Thus, the proposed research program will significantly advance the methodological developments for the analysis of complex but important societal problems in the familial-longitudinal set up for binary and count data. It is anticipated that the proposed work will have significant impact on future statistical research involving socio-economic and bio-medical data and will be of benefit to goverment statistical agencies, hospital and/or clinical researchers, and health ploicy makers in Canada and abroad.