| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 92 === In many scientific follow-up studies, repeated observations of several response variables, along with other covariate variables, are taken from a fixed sample of clusters, resulting in multivariate longitudinal clustered data. It is often of interest in these studies to develop appropriate multivariate regression models for investigating the relationships between the
response variables and the covariates while taking into account the association among multiple responses.
In the thesis, we propose a multivariate regression model for analyzing longitudinal clustered data of multivariate binary responses. Normally distributed latent variables with unit variance are assumed to generate the observed binary response variables via a common threshold. The expectations of the latent variables are determined from the marginal regression of the observed binary variables. Based on the clustering structure for the data at hand, the random error of the latent variable is further decomposed into several random effect terms to identify the source of correlation for each binary response. Regression models of pairwise latent correlation for any two binary response variables are considered to study the association among the multivariate binary response variables.
Using this latent variable approach, one can easily construct the working covariance matrix for parameter estimation using the generalized estimating equation (GEE) approach.
To illustrate the utility of the proposed model, we analyzed a longitudinal data set on metabolic disorders that was collected from a sample of families in Taiwan. Not only the risk assessments of these disorders were conducted but also sources of within-disorder and between-disorder correlations were identified which might be informative to epidemiologists.
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