This research proposes to address several issues in modelling longitudinal data. Previously, the investigators have performed comparative studies of different longitudinal models on cardiopulmonary data, and have concluded that in most instances the best fit is achieved by models in which the error term has a damped autoregressive correlation structure. One issue in fitting such models is the development of efficient approaches for detecting outliers. It is important to detect outlying subjects or outlying data values for an individual subject, since, failure to do so can seriously affect type I and type II errors. The second specific aim is concerned with modelling bivariate longitudinal data, using the joint distribution of the component random variables. Specifically, the investigators consider an extension of the damped autoregressive correlation model to the bivariate case. The third specific aim focuses on measurement error in longitudinal models. The effects of measurement error on regression coefficient estimates and standard errors will be studied for two types of modelling structures : (i) where reproducibility study data are available, and (ii) where reproducibility study data are not available. Measurement error model for bivariate longitudinal data will also be considered that will allow for correlated measurement error between the individual responses.
The final aim i s to investigate relative advantages of fitting marginal and conditional AR-1 models to the cardiopulmonary data, and to compare interpretations of parameters. Marginal models are easy to interpret, but conditional models allow a time varying covariate to explicitly affect later responses.
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