## Technote (troubleshooting)

## Problem(Abstract)

What is confirmatory factor analysis (CFA)? Can CFA be performed with the SPSS FACTOR procedure? If not, is CFA available from any other SPSS procedure or product?

## Resolving the problem

The Factor procedure that is available in the SPSS Base module is essentially limited to exploratory factor analysis (EFA). The solution you see will be the result of optimizing numeric targets, given the choices that you make about extraction and rotation method, the number of factors to retain, etc. Suppose that you have a particular factor model in mind. For example, variables X1 to X4 load on factor 1; X5 to X8 on factor 2; X9 to X12 on factor 3. With exploratory factor analysis, you can request 3 factors and a particular rotation and look at the results to see if they match your model. If you choose maximum likelihood (ML) or generalized least squares (GLS) as your extraction method, you would get a chi-square measure of goodness of fit, which is a test of the null hypothesis that 3 factors were adequate to explain the covariances among your variables. You would not get a test of whether the factor loading matrix conformed to your model.

In confirmatory factor analysis (CFA), you specify a model, indicating which variables load on which factors and which factors are correlated. You would get a measure of fit of your data to this model. (You don't really confirm the model so much as you fail to reject it, adhering to strict hypothesis testing philosophy.) Until the early to mid 1970's, there were a handful of ways to approach CFA, but many of these seem to have fallen by the wayside. (See Technote #1476881, "Multiple Group Factor Analysis in SPSS") for a discussion of multiple group factor analysis, an approach to CFA that could be addressed in part through SPSS). The predominant CFA approach today is to consider CFA as a special case of structural equation modeling (SEM). You specify factor loadings as a set of regression statements from the factor to the observed variables. Loadings which are not specified are assumed to be fixed at 0. Goodness of fit tests and measures are provided, along with diagnostic information to help you determine weak points in the model. Some good introductory sources are:

Brown, T.A. (2006). Confirmatory Factor Analysis for Applied Research. New York: Guilford Press.

Kline, R.B. (2005). Principles and Practice of Structural Equation Modeling (2nd Ed.). New York: Guilford.

Loehlin, John C. (2004). Latent Variable Models: An Introduction to Factor, Path, and Structural Analysis (4th Ed.). Mahwah NJ: Erlbaum.

To provide our customers with SEM capability (including CFA), SPSS distributes AMOS, a SEM program developed by James Arbuckle at AMOS Development Corp. (http://www.amosdevelopment.com/ ). AMOS will read several data file formats, including SPSS data files. AMOS is a separate program and would be stored in a separate directory from SPSS. It has a graphical user interface that makes it fairly straightforward to express your CFA model on the screen. See more information on acquiring AMOS at http://www.ibm.com/software/analytics/spss/support/spss_license.html .

There is also a recent book which focuses on SEM with AMOS and includes several CFA examples:

Byrne, Barbara M. (2010). Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Programming (2nd Ed.). New York: Routledge.

## Historical Number

20837