I was looking at the online technical appendix and happened upon the formula used to compute factor scores for CFA/SEM models. After looking at this, I came up with two questions.
1.) It appears that Mplus takes the posterior moment approach, which uses the posterior disttribution or conditional distribution of the latent factors (Y) given the observed data (X): f(Y|X)
Furthermore, the means of the posterior distribution are used as estimates of the factor scores. Am I correct in my assumption here?
2.) I know that SPSS uses Bartlett's method and the Anderson-Rubin method to compute factor scores. Are these methods different from what is used in Mplus because they use the alternative solution as opposed to the posterior moment or Bayesian solution?
1) For continuous outcomes and for categorical outcomes with weighted least squares estimation, Mplus uses the maximum a posteriori method. For continuous outcomes, this is also called the regression method - probably the most commonly used method for factor score estimation. For categorical outcomes this is also called MAP (e.g. in IRT).
For ML with categorical and other non-normal outcomes, Mplus uses EAP, the expected a posterio method.
2) Those methods are different.
RDU posted on Tuesday, December 02, 2008 - 9:31 am
Thank you for the quick response. As a follow-up question, for ML with continuous outcomes, does Mplus use EAP, MAP, or something different?
I have estimated factor scores for a measurement model with 7 indicators. All load a common factor (i. e. F1 BY a b c d e f g;). Additionally, I have established a nested factor for four indicators (i. e. F2 BY d e f g;) with F1 and F2 not being correlated (F1 WITH F2@0;).
When I correlate the factor scores for F1 and F2, the correlation amounts to .289. Why would that happen? Is there a way to specify that their correlation is 0?
Hello, I have been provided with factor scores for my categorical variable factors, whose items were all measured on 5-point likert scales. While I appreciate the utility of these and will be using them for the correlational analyses I need to perform, I'm also expected to provide raw means and standard deviations for these factors. Can you please tell me how I rescale these factor scores to have the same Ms and SDs as my original scale? Thanks, Heather
You won't get factor scores coming out scored as 5-point Likert scales. Factors are specified as continuous normal variables. With continuous outcomes the mean of the factor is also different from the mean of the factor indicators due to the inclusion of measurement intercepts which pick up the indicator means. Also, means and variances of estimated factor scores are not the same as those of the estimated model parameters. Furthermore, the estimated factor score do not have the same correlations with other variables as the true factors do. These are some of the reasons behind the need to do a 1-step SEM instead of the multi-step procedure it appears you have in mind. Only if you have many good indicators would the estimated factor scores work like true factor scores. It doesn't help to rescale the estimated factor scores.
It sounds like you have categorical factor indicators which adds another layer of complexity - you can't put a continuous factor score into a categorical scale.
I am using multilevel data (students nested in classrooms nested in teachers) and have computed the factor score of a classroom-level scale using TYPE=COMPLEX. I am hoping to use these factor scores as independent variables in an HLM model.
I understand from reading Linda's response to others that the factor scores MPLUS generates are not standardized but do have a mean of zero.
I am wondering how to interpret any significant results for this scale in my HLM models because I am not sure what the units of the factor score are and whether it would be correct to say that they are standardized around the grand mean. For example, can I say that a score that is 1 standard deviation above the grand mean is associated with an X standard deviation change in my dependent variable (this variable is standardized around the grand mean)?