Measurement invariance of binary outc...
Message/Author
 Xu, Man posted on Friday, November 04, 2011 - 1:33 pm
Dear Dr. Muthen,

I was wondering if you could give some advice regarding a measurment invariance issue. I have got binary indicators of a latent variable. I would like to test invariance both across time and across gender.

The Mplus manual has descriptions on how to do measurement invariance on categorical variables. Should I fowllow the same for the binary variables that I have? ie.

1. configural model
3. metric + residual invariance.

Thanks very much!

Kate
 Bengt O. Muthen posted on Friday, November 04, 2011 - 8:49 pm
The Mplus UG describes how to test measurement invariance for binary/categorical variables.
 Xu, Man posted on Tuesday, November 15, 2011 - 6:25 am
Thank you. I have had a look and did it accordingly with the theta paremeter. As I have repeated measures at T1 and T2. I first did measurement invariancet (MI) on the T1 and T2 in the whole sample, but the MI procedure is exactly the same according to the steps in UG; secondly, I did multiple group MI in males and females with T1; thirdly, I did MI in males and females with T2. The three steps all look fine in terms of RMSEA, TLI and CFI, so I did not look at partial invariance and moved to the forth step, where mutliple group analysis MI is done with both T1 and T2.

In the last step, the mutiple group configural model converged with T1 & T2 fully equivelent including means(0=T1=T2), loading(T1=T2), threshold(T1=T2), uniquess(1=T1=T2), and with male and female loading, threshold, uniquess (=1 in male group) free estimated.

However, when I move to the next step, where the female group factor loading, threshold, and uniqueness got freely estimed, there was a problem.

The model did converge but the degree of freedom are somehow 6 degrees lower (512 vs. 506) than the configural model. I checked the output and the results seem reflect the parameter specification in the input files. So I was confused. Do you think there are something done wrongly?

I have got 2 constructs at each wave, 6 binary items repeatedly measured twice.

Thanks a lot!

Kate
 Xu, Man posted on Tuesday, November 15, 2011 - 6:38 am
sorry, in the previous post, third paragraph, I meant:

However, when I move to the next step of strong MI, where the female group factor loading & threshold constrained = the male group, but uniqueness and means got freely estimed, there was a problem.
 Linda K. Muthen posted on Tuesday, November 15, 2011 - 8:02 am
Please send the relevant outputs and your license number to support@statmodel.com.
 Xu, Man posted on Tuesday, November 15, 2011 - 8:14 am
I am really sorry for the "much ado over nothing", After a hard look at the TECH1, It turned out that I forgot to put the longitudinal uniqueness constraint in the free group.

Thanks for your time to read my posts. Please point out if there is something obviously wrong still...
 Xu, Man posted on Tuesday, November 15, 2011 - 9:13 am
Could I ask a follow up question? Say if I got my two group model up and running after Mi tests, and I want to create a latent difference score factor (T2-T1) in each group, is it possible to do? I figured that this would not be able to do, as any means in the reference group would have to be fixed to 0 for the means to be estimated in the free group. In order to get the latent difference scores in males and females, I suppose I will have to run the model by selecting observations seperately for each group, right?

Kate
 Linda K. Muthen posted on Tuesday, November 15, 2011 - 9:45 am
With repeated measures, you should not use multiple group analysis because the groups do not contain different individuals. You should compare across time. See the Topic 4 course handout under multiple indicator growth. Factor means can be zero at one timepoint and free at the others when intercepts are held equal across time. With two timepoints, the difference is the timepoint that is free.
 Xu, Man posted on Tuesday, November 15, 2011 - 2:59 pm
Thanks! I did not mean to use T1 as group 1 and T2 as group 2. I want to have T1 & T2 (with strict or strong MI) in male group and T1&T2 (with strictu or strong MI) in female group. But since I have binary items with theta, I think (with strict or strong MI cross groups), the means at T1 and T2 in the male group are 0 by default. So I would not be able to estimate a latent difference score in the male group (or the female since the model would not converge).

In other words, if I had 3 time points, I'd like to run growth model in males and females as seperate groups. Is this possible in binary indicators under theta?
 Xu, Man posted on Wednesday, November 16, 2011 - 5:54 am
I just tried my two time points model(binary indicators, theta) in a growth model setting (constraining the time level variances to 1 to converge). Results of this model are identical to another setup where I had it as a latent difference score model. Both setups have strict measurement invariance across T1 and T2.
Then I add one line to each of the two model: GROUPING IS sex2 (1 = male 2 = female);

This time the latent growth multiple group model converged, but not the latent difference model:
T1 by
i1_1 @1
i1_2 (2)
i1_3 (3)
i1_4 (4);
T2 by
i2_1 @1
i2_2 (2)
i2_3 (3)
i2_4 (4);
[i1_1 i2_1](5);
[i1_2 i2_2](6);
[i1_3 i2_3](7);
[i1_4 i2_4](8);
i1_1 @1;i1_2 @1;i1_3 @1;i1_4 @1;
i2_1 @1;i2_2 @1;i2_3 @1;i2_4 @1;

T2@0;
T2 ON T1@1;
LC by T2;
LC*;
[LC*];
LC with T1;

Do you think I need to change my syntax on latent change model if I want to get it run as mulitple group model? I'd like to use the latent change model as I want to have have the latent change score predicted and to predict other variables of subsntative interests. Thanks!
 Bengt O. Muthen posted on Wednesday, November 16, 2011 - 3:31 pm
I don't master the latent difference model with two time points. Maybe a question for SEMNET.
 Xu, Man posted on Wednesday, November 16, 2011 - 6:27 pm
Thanks. I just posted to the SEMNET. But then afterwards, I found I could mimic the key thing in latent change model from the latent growth set up, that is, the regression coeffecient leading from baseline (or intercept factor) to the growth factor (or the "beta" cofficient in the typical latent change models):

i s | T1@0 T2@1;
s ON i; !the "beta" cofficient in latent change models

I wanted to control for initial time point in asesssing the other predictors effect on the change score. And this works in multigroup as well. So I think this is probably what I need. But still it would be great to know exactly why I could not get the multiple group model to run in the latent change set up. I just posted to SEMNET. Maybe someone is gonna answer...

Kate