混合因素分析對群體異質性之探索：以國中生學業困擾二元資料為例

Abstract

本研究示範如何應用混合因素模式處理群體異質性。文中除了展示混合因素分析模式之特性，並比較該模式與類別因素分析及潛在類別分析之間的差異。本研究樣本為1,703位國中一至三年級學生，樣本資料為有關於學業困擾的議題。研究結果發現，二因素二類別之混合模式為解釋國中生五種代表性學習困擾行為之最佳模式：學習困擾可以分為「外在焦慮困擾」與「內在動機困擾」等兩種連續因素，而其困擾潛在類別可以分為「高困擾」與「低困擾」兩種。混合因素模式為近年來新興之統計技術，本研究成功地示範如何利用混合因素模式在實徵二元資料分析上，並對未來研究方向提出若干建議。

One essential assumption of traditional multivariate analysis is population homogeneity and model parameters estimated will be inaccurate if the assumption is violated. The purpose of this study was to demonstrate using factor mixture model (FMM) to explore population heterogeneity. FMM is a combination of factor analysis and latent class analysis, therefore, this study also described characteristics of FMM in comparison to categorical factor analysis (CaCFA) and latent class analysis (LCA). One thousand seven hundred and three middle school students of all grades were surveyed regarding their learning behaviors and binary data were collected and analyzed with CaCFA, LCA and FMM models. Results show that the five typical learning behaviors investigated can be explained best by a two-factor and two-class FMM model. The two factors are “external learning anxiety” and “internal lack of motivation” whereas the two latent classes are “high” and “low” disturbance groups. Factor mixture model was a newly developed statistical model and most recent studies investigating characteristics of FMM have used simulated data. This study successfully utilizes FMM to a real life data set from an empirical study of learning behaviors. From a statistical aspect, FMM produces factor scores similar to those of CaCFA. However, the results of latent classifications from FMM are somewhat different from those of LCA. Suggestions and recommendations are given for future studies.