|
In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis, most commonly used in social research.〔Kline, R. B. (2010). ''Principles and practice of structural equation modeling (3rd ed.).'' New York, New York: Guilford Press.〕 It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct (or factor). As such, the objective of confirmatory factor analysis is to test whether the data fit a hypothesized measurement model. This hypothesized model is based on theory and/or previous analytic research.〔Preedy, V. R., & Watson, R. R. (2009) ''Handbook of Disease Burdens and Quality of Life Measures''. New York: Springer.〕 CFA was first developed by Jöreskog〔Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183-202.〕 and has built upon and replaced older methods of analyzing construct validity such as the MTMM Matrix as described in Campbell & Fiske (1959).〔Campbell, D. T. & Fisk, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. ''Psychological Bulletin'', ''56'', 81-105.〕 In confirmatory factor analysis, the researcher first develops a hypothesis about what factors s/he believes are underlying the measures s/he has used (e.g., "Depression" being the factor underlying the Beck Depression Inventory and the Hamilton Rating Scale for Depression) and may impose constraints on the model based on these a priori hypotheses. By imposing these constraints, the researcher is forcing the model to be consistent with his/her theory. For example, if it is posited that there are two factors accounting for the covariance in the measures, and that these factors are unrelated to one another, the researcher can create a model where the correlation between factor A and factor B is constrained to zero. Model fit measures could then be obtained to assess how well the proposed model captured the covariance between all the items or measures in the model. If the constraints the researcher has imposed on the model are inconsistent with the sample data, then the results of statistical tests of model fit will indicate a poor fit, and the model will be rejected. If the fit is poor, it may be due to some items measuring multiple factors. It might also be that some items within a factor are more related to each other than others. For some applications, the requirement of "zero loadings" (for indicators not supposed to load on a certain factor) has been regarded as too strict. A newly developed analysis method, "exploratory structural equation modeling", specifies hypotheses about the relation between observed indicators and their supposed primary latent factors while allowing for estimation of loadings with other latent factors as well.〔Asparouhov, T. & Muthén, B. (2009). Exploratory structural equation modeling. ''Structural Equation Modeling'', 16, 397-438〕 == Confirmatory factor analysis and exploratory factor analysis == Both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) are employed to understand shared variance of measured variables that is believed to be attributable to a factor or latent construct. Despite this similarity, however, EFA and CFA are conceptually and statistically distinct analyses. The goal of EFA is to identify factors based on data and to maximize the amount of variance explained.〔Suhr, D. D. (2006) - “Exploratory or confirmatory factor analysis?” in ''Statistics and Data Analysis'', ''31'', Retrieved April 20, 2012, from http://www2.sas.com/proceedings/sugi31/200-31.pdf〕 The researcher is not required to have any specific hypotheses about how many factors will emerge, and what items or variables these factors will comprise. If these hypotheses exist, they are not incorporated into and do not affect the results of the statistical analyses. By contrast, CFA evaluates ''a priori'' hypotheses and is largely driven by theory. CFA analyses require the researcher to hypothesize, in advance, the number of factors, whether or not these factors are correlated, and which items/measures load onto and reflect which factors.〔Thompson, B. (2004). ''Exploratory and confirmatory factor analysis: Understanding concepts and applications.'' Washington, DC, US: American Psychological Association.〕 As such, in contrast to exploratory factor analysis, where all loadings are free to vary, CFA allows for the explicit constraint of certain loadings to be zero. EFA is sometimes reported in research when CFA would be a better statistical approach.〔Levine, T. R. (2005). Confirmatory factor analysis and scale validation in communication research. ''Communication Research Reports'', ''22''(4), 335-338.〕 It has been argued that CFA can be restrictive and inappropriate when used in an exploratory fashion.〔Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. ''Multivariate Behavioral Research'', ''36'', 111-150.〕 However, the idea that CFA is solely a “confirmatory” analysis may sometimes be misleading, as modification indices used in CFA are somewhat exploratory in nature. Modification indices show the improvement in model fit if a particular coefficient were to become unconstrained.〔Gatignon, H. (2010). ''Confirmatory Factor Analysis in Statistical analysis of management data''. DOI: 10.1007/978-1-4419-1270-1_4〕 Likewise, EFA and CFA do not have to be mutually exclusive analyses; EFA has been argued to be a reasonable follow up to a poor-fitting CFA model.〔Schmitt, T. A. (2011). Current methodological considerations in exploratory and confirmatory factor analysis. ''Journal of Psychoeducational Assessment'', ''29''(4), 304-321.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「confirmatory factor analysis」の詳細全文を読む スポンサード リンク
|