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Mplus Discussion > Structural Equation Modeling >
 Xu, Man posted on Saturday, April 09, 2011 - 8:40 am
Dear Drs Muthen,

I have items for a latent variable measured twice in the same individuals. I am also interested in how this construct is invariant across gender. So I fit a multigroup model with two latent variables. For both gender groups, I fixed the factor loadings and threshholds to be equal for the repeated items. I think the default is also to constrain these factors and threshhold to be equal across gender. I was wondering if it is sensible to assess invariance this way and how I should best use the modification index for the factor loadings and threshholds. Many thanks! Kate
 Linda K. Muthen posted on Sunday, April 10, 2011 - 10:20 am
You should assess invariance across time as a first step. The steps to do this are shown in the Topic 5 course handout under Multiple Indicator Growth. Then you can assess measurement invariance across groups using the inputs shown in the Topic 1 handout under Multiple Group Analysis.
 Xu, Man posted on Monday, April 11, 2011 - 6:34 am
Thank you! I will read these handouts. Just a quick follow up question: Do you mean that I should first assess time invariance in a single group, free any item showing time related differential item functioning. Then in the next step, I keep the time specific partial invariance model constraits, in order to assess the gender invariance using multiple group analysis?
 Linda K. Muthen posted on Monday, April 11, 2011 - 9:17 am
I would look at each group separately. If both groups show the same non-invariance across time, I would include this when I test over groups.
 Xu, Man posted on Tuesday, April 12, 2011 - 6:51 am
Thank you! I did see this is done in a paper, although they separeted factor loading and threshold as two steps when testing invarance - the manual says they should be relaxed/constrained in one model for categorical outcomes.

If both men and women showed the same non-invariance across time, then I can be more confident in the mutiple group analysis that any non-invariance should be coming from the group, right?
 Linda K. Muthen posted on Tuesday, April 12, 2011 - 9:22 am
It is likely the paper is concerned with continuous outcomes.

Your logic sounds correct.
 Xu, Man posted on Wednesday, April 13, 2011 - 2:39 am
Thanks :-)

I think it was categorical variables in this paper, because they tested also scale factor invariance...
 Kerry Lee posted on Saturday, September 29, 2012 - 4:31 am
Dear Drs Muthen,

My colleague and I are running some data from a cohort-sequential design. For one particular analysis, we are focusing on data that fall into two grades. Data for each grade come from two age groups. For the younger children, we have data from Cohort A collected at Wave 3 and Cohort B collected at Wave 1. For the older children, we have data from Cohort B collected at Wave 3 and Cohort C from Wave 1.

At this stage, we are just using age group as a covariate in a SEM containing data from both age groups. The problem is that the two age groups are not independent. Cohort B contributed data to both groups. How should the partial repeated measures be specified? We are thinking of using TYPE=COMPLEX in conjunction with ANALYSIS=CLUSTER to correct for the potential reduction in variance that results from the repeated measures. Is the use of these two commands appropriate and sufficient for this problem?

 Linda K. Muthen posted on Monday, October 01, 2012 - 10:48 am
I am having a hard time understanding the structure of your data. Can you make a chart similar to the one in Example 6.18.
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