Background: I have estimated a 3-factor model using 14 dichotomous indicators (residuals are not correlated and one of the 14 items is crossloaded onto 2 factors). I am using complex sample data with sample weight, strata, and cluster variables. The model was estimated using WLSMV. The model fits well, and the parameter estimates are reasonable.
In this CFA model the factor correlations are .84, .85, and .76, respectively. I subsequently created factor scores from this CFA model. When I correlate the three factors using the factor scores, I get correlations of .94, .95, and .90, respectively. [When I apply the sample weight in computing these correlations, the change is negligible].
So, my question is: Is it reasonable for there to be differences (of the order I am finding; .14 is the greatest difference) between when the factor correlations are taken from the CFA model and when they are derived from correlating the factor scores that were generated from this CFA model? Or are these differences a red flag that I made a mistake?
BMuthen posted on Saturday, July 02, 2005 - 6:22 pm
There could be this big of a difference between estimated factor score correlations and model-based factor correlations when you do not have many good indictaors for each factor. In this case, good means a high standardized factor loading. This difference is the reason for using SEM to relate factors rather than working with factor scores.
Jtte posted on Saturday, January 17, 2009 - 2:45 pm
I have estimated a 2 group CFA (3 factors & 11 indicators- each factor has 3 or 4 indicators)using WLSMV and generated factor scores which I wish to use in a subsequent twin analysis.
1. If WLSMV uses a tetrachoric correlation matrix why are my unstandardised parameter estimates different from the standardised. I thought with a correlation matrix they might be the same?
2. Factor scores were generated for every case even those that had missing values on some of the indicators. I was wondering how missing values are handled in the generation of factor scores.
3. and can I use factor scores for all cases (even those with missing) in the subsequent twin analysis ?
1. It sounds like you have used the default of fixing the first factor loading to one to set the metric of the factor. If you free the first factor loading and fix the factor variance to one, I think you will see what you expect. 2. They are generated using all available information. 3. I would not do an analysis in two steps using factor scores. Factor scores should be used only as independent variables in the model. If factor determinacy is not very high, factor scores may be poorly determined.