起伏變遷型長期追蹤資料的分析方法研究

Abstract

許多社會科學及醫學上的長期追蹤研究上，常會根據研究之需要，而針對某一群人在一段時間內重覆地收集其有關變項（包括類別型反應變項及解釋變項）的資料。這種重覆觀察的資料在統計的文獻上稱為長期追蹤研究資料。在這些長期追蹤研究上，研究者常利用迴歸模型建構的技巧來探討反應變項及解釋變項之間的關係。 一般常用的模型，著重於評估解釋變項對反應變項的當時及短期效應，當解釋變項比反應變項更頻繁地被觀測時，這些模型則不適用。當反應變項可在不同類別間變動時，我們通常有興趣去探討解釋變項如何去影響反應變項的演變或未來走向的趨勢，這種研究可稱之為類別型長期追蹤研究資料的未來趨勢分析。本論文提出了以馬可夫離散時間過程來建立類別型長期追蹤研究資料的模型。此模型不但可以捕捉到解釋變項對反應變項的未來趨勢效應；而且當解釋變項較反應變項更頻繁地被觀測時，本模型也可以利用解釋變項的完整訊息來做出更正確的統計推論。

Many longitudinal studies in social science and medical science take repeated observations of an categorical outcome, along with several covariates, from follow-up subjects over a certain period of time. Such repeated observations are called longitudinal or panel data in the statistical literature. It is often of interest in these studies to investigate the relationship between the outcome and the covariates through regression modeling techniques. Commonly used models often focus on assessing the contemporary or short term effect of the covariate on the outcome, and can`t incorporate time-varying covariates that are observed more or less frequently than the rate we observe the outcome. When the outcome fluctuates among different categories, it is often of interest to assess how covariates effect the evolution or trend of the underlying outcome process. Such assessment can be termed trend analysis of categorical panel data. In this thesis, we propose a Markov chain based regression model for analyzing nominal categorical panel data that are generated by a discrete time outcome process. The proposed model focuses on assessing the trend effect of the covariate on the categorical outcome, and is able to utilize the complete information of the covariates that are observed more or less frequently than the outcome.