並列摘要
Based on cluster measurements, our research interest mainly focuses on seriating the uncertainty in the degree of health or functioning of the body for collected subjects. For this problem, a latent variable is used to represent an unobserved seriation. In this thesis, some adequately and widely used joint models of a latent variable and cluster measurements are proposed to predict the most possible occurring value of a latent variable, which is taken in our seriation procedure. Since a latent variable is considered in modeling, a popular expectation and maximization (EM) algorithm is implemented for the estimation of parameters in the observed likelihood function. Moreover, a parametric bootstrapping method is considered to generate latent values and bootstrap samples, which are used to estimate seriation indices such as the correlation and concordance proportion in the evaluation of seriation. To examine the performance of the developed procedures, a class of simulations is conducted. From the numerical studies, we further detect that the evaluation indices computed based on the maximum likelihood estimators or the true parameters are very close although the accuracy of estimators relies on the sample size. Thus, a computationally efficient approach is proposed to estimate seriation indices. Finally, the seriation and evaluation procedures are applied to a CD4 depletion study.