Transitional models for multivariate longitudinal binary responses with an application to behavioral data of Canadian children
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In longitudinal studies, observational units (commonly referred to as individuals) drawn from some population of interest are followed prospectively over time, and measurements from each individual are taken repeatedly at different points in time with the ultimate goal of characterizing the important features of the population. Longitudinal data naturally arise in many areas of study, where the characterization of the population may be achieved by investigating the effects of covariates on a response. Two or more correlated responses from each individual are also common in longitudinal studies, giving rise to multivariate longitudinal data. For example, the National Longitudinal Survey of Children and Youth (NLSCY) is a long-term study to observe the development of Canadian children. In this survey, measurements about factors influencing a child's social, emotional and behavioral development are collected over time; anxiety and aggression reported for each child in this study may be considered as two response variables to characterize the emotional and behavioral development of children. Since in longitudinal studies, information is collected repeatedly from each individual over time, the occurrence of an event at a particular time point may increase/decrease the likelihood of the occurrence of another event in future. Failure to take into account this phenomenon in analyzing longitudinal data may lead to erroneous conclusion. Moreover, repeated responses (e.g., anxiety and aggression) from an individual may exhibit correlation over time. Separate analyses of such multivariate longitudinal responses ignore this correlation, and as a result, cannot reveal the potential association among the responses which could be of paramount importance in many applications. Therefore, analysis of multivariate longitudinal data requires substantial extension of the standard longitudinal methods. In this thesis, we describe a methodology based on the transition models for multivariate longitudinal binary data to address the transitional behavior between two states characterized by binary responses for two different responses (i.e., two processes). Transitional analysis of multivariate longitudinal binary data can address the longitudinal association within processes and enable marginal interpretation of covariate effects. In addition, estimation and inference of the association between the processes can also be achieved via such models. We illustrate this approach with an application to the NLSCY data, where anxiety and aggression (two correlated responses) are modeled as a function of covariates (gender, depression of person most knowledgeable, number of siblings and family status) to identify their effects on behavioral development of Canadian children. In addition, the extent and direction of the association between two responses are estimated. Gender of the child is found statistically significant for both directions of transition, i.e., from low to high and high to low, of aggression. On contrary, gender of the child is found statistically not significant for both transitions of anxiety. Meanwhile, depression of person most knowledgeable is found marginally significant in the high to low direction for aggression. For association parameters, all four directions of associations between anxiety and aggression are found statistically significant.
DegreeMaster of Science (M.Sc.)
DepartmentSchool of Public Health
SupervisorKhan, Shahedul A.; Bickis, Mik G.
CommitteeMuhajarine, Nazeem; Roy, Chanchal
Copyright DateApril 2014