Effect size & slope var for multiple ...
Message/Author
 Bruce A. Cooper posted on Saturday, October 01, 2011 - 5:16 pm
I haven't been able to figure out (or find a reference) for how to estimate a simple latent growth model with multiple indicators (2 times, 8 indicators at each time), and obtain an intercept for the latent factor on the same scale as the original items, and obtain the standard error (STDY) for the slope, so I can calculate a standardized effect size for the significant slope. I have only two times, but I'm using the LGM approach to keep all the observations via FIML, and to estimate a latent variable (factor) rather than just compute a scale score from the items. Also, MANOVA isn't appropriate because the items are left skewed, and I lose too many cases due to missing items at each or both times. My basic setup is from Ex6.14 in the manual. Can you point me to additional references?
Thanks! Bruce
 Bengt O. Muthen posted on Saturday, October 01, 2011 - 6:53 pm
With only two time points, why don't you put aside growth modeling and just do a "longitudinal factor analysis" like on slide 165 of Topic 1, simplified to one factor? You still benefit from "FIML".

In the typical setup you let the factor mean at time 1 be the reference point, fixing it at zero. I don't know why you want this mean in the scale of the items - but you can have it free and instead fix one of the item intercepts at zero to achieve this wrt this item. Then you have to have that item intercept fixed at zero at time 2 as well (with equality across time of the other intercepts).

Perhaps you want a standardized slope of the time 2 factor on the time 1 factor - which is then the same as their correlation. You get that by STDY.

Hope that helps.
 Bruce A. Cooper posted on Sunday, October 02, 2011 - 1:37 pm
Thank you for your blazingly fast response and suggestions, Bengt! I have run the longitudinal FA, and it is essentially the same as the FA part of the LGM model I ran previously. Basically, I dropped the LGM portion of the analysis and just estimated the factors at T1 and T2. The corr between the factors was about the same for the longtdnl FA model as for the corr between factors in the LGM, both about .93. I'm concerned about the interpretation of the correlation between factors, however. It isn't the same as a stdzd diff between factor means at T1 compared to T2, such as a stdzd LGM slope would represent. My colleagues are interested in the mean change from before to after an event (raw s = .180 in the LGM, p = .015), and the correlation doesn't capture that. I tried your suggestion about setting the same item's intercept to 0 at T1 and T2. I get variances that appear to be on the original item scale, but factor means still = 0, and now the corr = .996.

Additional guidance would be great! - bac
 Bruce A. Cooper posted on Sunday, October 02, 2011 - 1:39 pm
Follow-up to my just previous post: Here's the setup for the model setting the first item's intercept to 0.
- bac

MODEL:
prehas BY prehas1 prehas2 prehas3 prehas4 (1-4)
prehas5 prehas6 prehas7 prehas8 (5-8) ;
posthas BY posthas1 posthas2 posthas3 posthas4 (1-4)
posthas5 posthas6 posthas7 posthas8 (5-8) ;
[ prehas1@0 ] ;
[ posthas1@0] ;
[prehas2 posthas2] (9) ;
[prehas3 posthas3] (10) ;
[prehas4 posthas4] (11) ;
[prehas5 posthas5] (12) ;
[prehas6 posthas6] (13) ;
[prehas7 posthas7] (14) ;
[prehas8 posthas8] (15) ;
 Bruce A. Cooper posted on Monday, October 03, 2011 - 11:48 am
Another follow-up! I saved the factor scores from the model and created a Stata file. The posthas factor mean is equivalent to the slope, the prehas mean is zero. I compared these to raw scale scores as means of the items using unit weights for items (allowing <=3 missing items) and grand mean centered the scores. I see that the factor scores have about the same min/max and SD as the scale scores, but a bit narrower. I'm guessing then, that the factor scores are on the same scales as the items (1-10, before centering) and can be used to get my standardized effect size. That is, the mean of the posthas factor is equivalent to the slope, and divided by its SD gives an EBE of the effect size. Does that work? - bac
 Bengt O. Muthen posted on Monday, October 03, 2011 - 8:32 pm
If by factor scores you mean estimated factor scores, I would not use them in this context. Instead, get the SD as the square root of the factor variance, which is a parameter that is estimated in the model.
 Bengt O. Muthen posted on Monday, October 03, 2011 - 8:53 pm
On your 10/2 question, you have to make sure that your factor mean at the second time point [posthas] is free - check TECH1. If not, mention it.
 Bruce A. Cooper posted on Tuesday, October 04, 2011 - 4:02 pm
Perfect! Thanks very much, Bengt. - bac