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 Anonymous posted on Friday, September 03, 2004 - 1:49 pm
I have a few questions about FIML when fitting a multigroup CFA with binary items.
1. Is the distribution of the residuals logistic or normal?
2. Can cross-group constraints be imposed on theta/delta?
3. Can the measurement intercept be used with across-group constraints?
 bmuthen posted on Saturday, September 04, 2004 - 5:08 pm
1. When you use the ML estimator, the residuals are logistic, and when you use the WLSMV estimator they are normal.

2. Yes

3. Yes. If by this you mean that you want intercepts instead of the standard thresholds, you would have to specify a factor behind each item to capture the intercept in the factor intercept.
 Anonymous posted on Thursday, September 16, 2004 - 10:51 am
I had understanding the robust ML estimator was to be used with models that included a covariate (x values) and that WLSMV was appropriate for models that did not (like a CFA with categorical indicators). But, based on the previous message, is this thinking correct?

Can the robust ML estimator be used with categorical indicators? IF so, would this estimator be more computationally intensive than WLS (due to the full-information ML technique), especially when larger models are used?

If so, do we know the limitations of MLMV in terms of model size and fit indices for this technique? And if a requirement for the ML estimator is normally distributed data, is MLMV as sensitive to distributional nonnormality (e.g., item or parcel level skew/kurtosis) as ML or does the mean/variance adjustment help to accommodate this problem?
 Anonymous posted on Friday, September 17, 2004 - 2:43 pm
When the ML estimation technique is used with ordinal/Likert data, is this estimator operating under full information (as under conditional probability formulation)?
How does this differ from limited information, which is what is conducted with WLS, correct?

Is limited information (latent variable formulation) an option with the ML technique?
 bmuthen posted on Wednesday, September 29, 2004 - 4:36 pm
Re: September 16. Both maximum likelihood and weighted least squares can be used with categorical outcomes with or without covariates. Yes, the robust ML can be used with categorical indicators. Yes, it can be more computationally intensive than weighted least squares depending on the model. MLMV is not used for categorical outcomes. Numerical integration is used with ML and the computational work increases with the number of factors.
 bmuthen posted on Wednesday, September 29, 2004 - 4:39 pm
Re: Sept 17. ML always implies full information. Limited info using WLSM implies that first- and second-order moment information is used. ML uses as high-order moments as there are observed variables. Limited-information ML is sometimes referred to as quasi- (or pseudo-) ML but is not available in Mplus in this context.
 Jason Bond posted on Wednesday, October 30, 2013 - 9:57 am

I'm trying to implement the DIF analyses in (Muthen, Kao, and Burstein, 1991) and had a couple of questions.

1) The first sentence at the top of the right column of page 11 says "In these formulas, the trait has been standardized to mean zero and variance one" which I take as meaning that Var(Equation(1)) = 1 but that would appear to cause problems if Var(x) or Var(z) was large. Also, sigma_nu_nu in formulae 4 and 5 would also be 1...that sentence was quite confusing.

2) Related, I take it that the formulation in this paper uses the delta parameterization, where Psi is estimated as part of the model and theta is obtained from Psi and Lambda.

Thanks for any input,

 Bengt O. Muthen posted on Friday, November 01, 2013 - 3:54 pm
1) This sentence was meant to imply that the a and b that you get correspond to a latent ability scale with mean zero and variance one. So like IRT parameters. I don't mean that sigma_{eta,eta} is 1 or that mu_eta is 0.

2) Yes, Delta.
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