Bayesian evaluation of inequality constrained hypotheses of means for ordered categorical data

Abstract

本研究利用了多群組離散型驗證性因素分析模型來分析多群組的有序分類數據，主要目的在於利用貝氏估計在最小限制式的條件下，來估計模型中的閾值、潛在因子的平均與變異數等參數，我們利用了資料擴張與Gibbs抽樣的方式來估計這些參數的聯合分配。並利用貝氏因子來檢驗潛在因子的平均是否滿足不等限制的假說。而藉由模擬與實徵資料的分析，貝氏因子已被驗證在檢驗不等限制的假說上是可行的。

The main purpose of this study is to use Bayesian estimation and Bayes factor to test for inequality constrained hypotheses of means for ordered categorical data among multiple groups using categorical confirmatory factor analysis model. Joint Bayesian estimates of the thresholds, the factor scores and the structural parameters subjected to some minimal identification constraints are obtained by using data augmentation and Gibbs sampling. By the simulation and real data analysis, Bayes factor is shown useful in testing hypotheses involving inequality constraints of means for ordered categorical data.