Factor Analysis II

• Main Authors: Ke-Chin Chen, 陳可芹
• Other Authors: Fu-Chang Hu
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/09894515994453335121

碩士 === 國立臺灣大學 === 流行病學研究所 === 87 === 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.