臺灣博碩士論文加值系統

在此研究中，我們考慮了因素分析模式中外生變數的影響效果。進而提出了修正的新方法「因素分析方法II」來調整這類變數的影響效果。因素分析是一種很常用的方法，它利用可觀測變數間的相關來幫助我們探索變數背後隱藏的測量結構，例如：我們可以透過學生的學科表現來瞭解學生的智力。大多數的因素分析都不考慮性別、年齡、種族、治療等外生變數，然而這類的變數是可能會影響因素分數的平均值或因素負荷值的估計。標準的因素分析存在著一個隱藏的假設，即若這類的外生變數具影響效果，則它們只作用在潛藏因素上，因此變數只影響潛藏因素分數的平均值。在本研究中，我們發現：（1）假若外生變數的影響效果只作用在潛藏因素上，則因素負荷值及殘差變異數的估計結果會與忽略外生變數的傳統因素分析所得結果相同。（2）假若外生變數的影響效果只作用在某些可觀測的測量變數上，則因素負荷值的估計結果會與忽略外生變數的傳統因素分析所得結果相同，但是該殘差變異數的估計結果將會與忽略外生變數的傳統因素分析所得結果不同。（3）假若外生變數的影響效果同時作用在潛藏因素及某些可觀測的測量變數上，則因素負荷值及該殘差變異數的估計結果均會與忽略外生變數的傳統因素分析所得結果不同。因此，我們發展了較一般性的因素分析方法（稱作「因素分析方法II」），其中包括了分層因素分析，來調整外生變數所造成的兩種可能的不同影響。

In this study we considered the effects of exogenous variables on a factor analysis model first, and then modified the standard factor analysis method (called the "Factor Analysis I") to adjust for the covariates' effects. Factor analysis is one of the most popular statistical methods for discovering or examining the latent measurement structure. It extracts the information from the correlations between the observed indicator variables to identify the latent variables of interest. For example, one may be interested in studying students' intelligence through their grades in various courses. Notice that most of the factor analyses conducted before ignored exogenous variables such as sex, age, race, treatment, and so on. Yet, those covariates might affect the mean of the factor scores and/or the estimation of the factor loadings of a factor analysis model. The standard factor analysis method implicitly assumes that the covariate has an effect, if any, only on the latent variable so that it would just affect the mean of the factor scores. In this study, we found that (1) if the covariate has an effect only on the latent variable, then the estimated factor loadings and error variances are the same as ignoring the covariate; (2) if the covariate has an effect only on some of the observed indicator variables, then the estimated factor loadings are the same as ignoring the covariate but some of the estimated error variances are different; and (3) if the covariate has effects both on the latent variable and on some of the observed indicator variables, then the estimated factor loadings and error variances are different from ignoring the covariate. Hence, we developed a general factor analysis method (called the "Factor Analysis II"), which includes the stratified factor analysis as a special case, to account for the dual effects of exogenous variables.

1. Introduction
2. Review
3. Discovering the Effects of Exogenous Variables
4. Factor Analysis II
5. Simulations
6. An Example
7. Discussion
8. Appendices
9. References
10. Tables
11. Figures

Amemiya, T. (1985). Advanced Econometrics. Cambridge, MA:Harvard University Press.