Maximum likelihood EFA with categoric... PreviousNext
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 yang posted on Sunday, September 08, 2013 - 5:40 am
I noticed that now we can do EFA analysis with categorical indicators using estimator = ML. My question is: Which parameterization is used when estimating the model, standardized or unstandardized? (By standardized I mean the loading-threshold parameterization which is typically encountered in item factor analysis literature; by unstandardized I mean the slope-intercept parameterization which is often used in IRT literature.)
 Bengt O. Muthen posted on Sunday, September 08, 2013 - 3:08 pm
The use of the Mplus parameterization in IRT modeling is exemplified in the Cai et al. (2011) Psych Methods article on item bi-factor analysis. Page 224 talks about the binary item case and page 225 the graded case. The article refers to the Mplus parameterization as “slope-intercept” where the intercept is the negative threshold in Mplus. The article refers to the a(theta- b) IRT parameterization as the “slope-threshold” parameterization where the “threshold” is the b difficulty parameter, not what Mplus calls threshold. The authors find that the slope-intercept parameterization (used by Mplus) is more general, saying on page 224:

Unfortunately, the slope-threshold form
does not generalize well to truly multidimensional models, so we
adopt the slope–intercept parameterization for this model and all
remaining IRT models.

The slope-intercept parameterization is also used in the Reckase (2009) book “Multidimensional IRT”; see section
 yang posted on Sunday, September 08, 2013 - 4:22 pm
Thanks. So Mplus uses slope-intercept parameterization even for the ML exploratory item factor analysis (type = EFA, estimator = ML)? Then I guess that Mplus computes the SEs for rotated factor loadings via delta-method following this chain:

slopes --> unrotated factor loadings --> rotated factor loadings

Am I correct?
 Bengt O. Muthen posted on Sunday, September 08, 2013 - 4:52 pm
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