# Confirmatory factor analysis

Confirmatory factor analysis

In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis. 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). 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. CFA has built upon and replaced older methods of analyzing construct vailidity such as the MTMM Matrix as described in Campbell & Fiske (1959).

A typical example of a CFA on a 50 item personality test that claimed to be measuring the "Big Five" Personality Traits, might assess the fit of the proposed model. A model could be developed that assumed structure, where each item loads on only one factor. The correlations between latent factors could be free to vary or they could be constrained to be zero. Model fit measures could then be obtained to assess how well the proposed model captured the covariance between all the items on the test. 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 hypothesis 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 & Muthén, 2009).

CFA is commonly used in social research (Kline, 2010). CFA is frequently used when developing a test, such as a personality test, intelligence test, or survey.[citation needed]

Structural equation modeling software is typically used for performing the analysis. LISREL[1], EQS,[citation needed] AMOS[2] and Mplus[3] are popular software programs. CFA is also frequently used as a first step to assess the proposed measurement model in a structural equation model. Many of the rules of interpretation regarding assessment of model fit and model modification in structural equation modeling apply equally to CFA. CFA is distinguished from structural equation modeling by the fact that in CFA, there are no directed arrows between latent factors. In other words, while in CFA factors are not presumed to directly cause one another, SEM often does specify particular factors and variables to cause one another. In the context of SEM ,the CFA often is called 'the measurement model', while the relations between the latent variables (with directed arrows) are called 'the structural model'

## References

• Asparouhov, T.;Muthén, B. (2009). "Exploratory structural equation modeling". Structural Equation Modeling, 16, 397-438.
• Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford.
• Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York, New York: Guilford Press.

## External sources

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