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.)
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 126.96.36.199.
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: