

EFA with categorical indicators 

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Hello. I was running an EFA using oblique rotation (I believe Oblimin rotation is the default) for three ordinal, Likertscale items, and 2 questions came up when I examined the output, which had 0 degrees of freedom since the model is just identified. 1.) I changed the default estimation method and used ML estimation because I wanted my results to relate to the overall population and not just to my data. Is OK to use ML estimation in Mplus when running an EFA with 3 ordinal indicators? 2.) Since factor loadings are often interpreted as regression coefficients, could I interpret both my unrotated and rotated factor loadings as I would a logisitic or even an ordinal probit model (e.g., regressing the observed ordinal variable on the latent factor)? Thanks. 


With three factor indicators, only one factor can be extracted. This means that there can be no rotation. I'm not sure what you mean by "relate to the overall population and not just my data". All estimators do this. It is okay to use ML with ordinal indicators. The factor loadings with ML and categorical outcomes are logistic regression coefficients unless LINK=PROBIT is used. Then they are probit regression coefficients. 


Dear Mplus team I have a question about WLSMV estimation ; I hope that you can offer me some guidance. It has been asserted to me that WLSMV is a least squares EFA on on polychoric correlations. In contrast, My understanding was that with WLSMV estimation, factors are linked to categorical variables (questionnaire items in my case) based on probit regressions. As such, is it the case that *only* the polychoric correlation matrix goes into the calculations of parameter estimates ? If not, can you direct me to a better understanding of this issue ? I have reviewed the Mplus manual, but I am wanting to better understand the way in which WLSMV calculates parameter estimates as compared with some of the alternative estimators. If you can direct me to some further information and reading on WLSMV, I would be grateful. Warm wishes Jamie Griffith 


Yes, WLSMV for ordered categorical items is least squares estimation on polychoric correlations. The probit model is used for the regressions of the items on the factors which together with normality for the factors implies that underlying continuous latent response variables are multivariate normally distributed and the correlations of these latent response variables are therefore relevant statistics to fit the model to. Research has shown that higherorder moments than the secondorder moments used by WLSMV do not carry that much more information. For a recent article showing the advantage of the WLSMV approach, see the paper on our website: Barendse, M.T., Oort, F.J., & Timmerman, M.E. (2014). Using exploratory factor analysis to determine the dimensionality of discrete responses. Structural Equation Modeling: A Multidisciplinary Journal, 00: 115. Note also that Mplus can use ML and Bayes estimators in addition to WLSMV. 

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