Measurement invariance depedent samples
Message/Author
 Steven De Laet posted on Wednesday, June 06, 2012 - 4:45 am
Hello,

I'm investigating the measurement invariance of perceived relationship dimensions across parent-child and teacher-child relationship; do children perceive dimensions such as control equally in parent-child and teacher-child relationships.
My question is whether I may considered the relationship dimensions in their relationships with parents and teachers as two groups and thus conduct multi-group confirmatory factor analyses, since the same children rate the different relationships (1 sample of children, 2 'groups', dependent samples). If not, how would you go about it?

Thank you very much,

Steven De Laet
 Linda K. Muthen posted on Wednesday, June 06, 2012 - 10:53 am
You would run a single-group analysis where you compare the parent-child versus the teacher-child factor loadings and intercepts. See the Topic 6 course handout under multiple indicator growth where we show how to do this for multiple time points. The issues are the same.
 Oliver Rizmanoski posted on Monday, November 17, 2014 - 7:59 am
Hi, I have a question regarding this.

I tried this with two different factors, resulting in 4 different factors since I have two dependent groups of raters. According to 6.14 it should look like that:

Hilf_m4 BY ob1m4 ! Rater mothers
ob11m4 ob16m4 ob21m4 ob6m4 (10-13);
Hilf_fk BY ob1fk ! Rater fathers
ob11fk ob16fk ob21fk ob6fk (10-13);

Pf_m4 BY ob10m4 ! Rater mothers
ob15m4 ob20m4 ob25m4R ob5m4 (14-17);
Pf_fk BY ob10fk ! Rater fathers
ob15fk ob20fk ob25fkR ob5fk (14-17);

1. Question: Is the syntax correct? Or do I need to specify and add something like in the example?

i s | Hilf_m4@0 Pf_m4@0 Hilf_fk@1 Pf_fk@1;

2. Question: Assuming that the syntax is correct are there any ways to get any information regarding specific parameters? As far as I can see it, this way it is only possible to evaluate the global fit and not differences like different factor means or different correlation coefficients?

3. Question: Assuming that the syntax is correct, would you still call that a growth modell?

I hope my request makes sense.

Best regards,
Oliver
 Oliver Rizmanoski posted on Monday, November 17, 2014 - 8:01 am
I should add that it's a dyadic analysis with no time component.
 Bengt O. Muthen posted on Monday, November 17, 2014 - 2:38 pm
1. Yes, correct. No need for the growth model part.

2. You can estimate factor mean differences if you apply scalar invariance instead of the metric invariance you use (add intercept invariance). Any parameter difference for fathers vs mothers can be expressed as NEW parameter in Model Constraint and thereby get tested.

3. No.
 Oliver Rizmanoski posted on Monday, November 17, 2014 - 2:54 pm
I will try that. Thank you very much!