Understanding Scale factors
Message/Author
 mikew posted on Friday, September 01, 2000 - 1:57 pm
I have a specific question regarding the use of scale factors when analyzing longitudinal data.

*Background* - Data consist of 200 kids who responded to a 10 item rating scale at 3 points in time. The 10 items form 2 latent factors. All 10 items are dichotomous.

*Goal* - I want to estimate a longitudinal CFA, such that the 10 items are represented by 2 latent factors at all 3 points in time.

*Question* - Given dichotomous items, I intend to analyze a tetrachoric correlation matrix with the WLSM estimator. Since the same items are included in the model at 3 time points, I intend to impose equality constraints on the thresholds for each item across time. My question concerns the scale factors. Based on what I can gather from the manual, I think that I should set the scale factor for each item at the first timepoint to 1 and freely estimate the scale factors at subsequent time points (eg., {item1_t1@1 item1_t2 item1_t3}). First, would you confirm this?

Second, would you elaborate on why this is necessary? I understand that the tetrachoric corr matrix has 1's along the diagnol and does not communicate info about the variance of individual items. However I'm not sure how scale factors address this.

Third, can you offer advice on the substant. interpretation of the scale factors that are estimated?

Thank you.
 Linda K. Muthen posted on Saturday, September 02, 2000 - 12:48 pm
Just a point of clarification--WLS and WLSMV require raw data for analysis. Both a correlation matrix and weight matrix are required for correct standard errrors and chi-square test of model fit. I just want to be sure you aren't planning on using a tetrachoric correlation matrix as input.

For total measurement invariance, not only the thresholds but also the factor loadings need to be held equal across time.

Scale factors should be fixed to one at the first timepoint and be free at the others. For a relevant discussion of scale factors, see Multiple group analysis with categorical variables under the Mplus Discussion topic of Cateogircla Data Modeling.