## Confirmatory factor analysis, Applied Statistics

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Confirmatory factor analysis (CFA) seeks to determine whether the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the basis of pre-established theory. Indicator variables are selected on the basis of prior theory and factor analysis is used to see if they load as predicted on the expected number of factors. The researcher first generates one (or a few) model(s) of an underlying explanatory structure (i.e., a construct) which is often expressed as a graph. The researcher's ri priori assumption is that each factor (the number and labels of which may be specified hpriori) is associated with a specified subset of indicator variibles. A minimum requirement of confirmatory factor analysis is that one IiypotheSize beforehand the number of faCtors in the model, but usually also the researcher will posit expectations about which variables will load on which factors (Kim and Mueller, 1978b: 55). The researcher seeks to determine, for instance, if measures created to represent a latent variable really belong together. The correlations between the dependent variables are fitted to this structure. Models are evaluated by comparing how well they fit the data. Variations over CFA are called structural equation modelling (SEM), LISREL, or EQS.

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