Multigroup Analysis in a within design
Message/Author
 Marko Vidakovic posted on Friday, March 22, 2013 - 11:51 am
Hey everyone,

I hope you can help me. I'd like to do something similar to multigroup analysis. I want to test for psychometric invariance in one sample with three different forms of one scale. The first measure is the standard scale and the second and third measures are variants of the first one I adapted myself. Most of the items remained exactly the same but some items are completely new. Now I am facing two problems running a multigroup analysis: (1) In fact there is no actual second (or third) group, it is simply one sample. (2) The scale's items are not identical. Can anyone help me?

Thanks a lot!
 Bengt O. Muthen posted on Friday, March 22, 2013 - 2:17 pm
It sounds like you have one sample which takes 3 test forms. You want to test measurement equality across items for this one sample. That is easy in Mplus. With 2 forms and 3 items per form (item y1-y3 for form a and y4-y6 for form b) where the 3rd item is the same:

MODEL:
fa by y1
y2-y3 (lama2-lama3);
fb by y4
y5-y6 (lamb2 lama3);
[y1-y2] (nu1-nu2);
[y4-y5] (nu4-nu5];
[y3] (nu3);
[y6] (nu3);

and then you can test equalities of the other labelled parameters using e.g. MODEL TEST.

Or, if you believe the forms are measuring the same dimension, you can use a single factor for them all.
 Marko Vidakovic posted on Wednesday, March 27, 2013 - 9:48 am
Hi Bengt,

thank you very much for your response. Though I tried to look it up in the manual I cannot find an explanation for some of the things you've written and since I'm pretty new to MPLUS and SEM I simply have to ask again:

1. What to the brackets () and [] mean?
2. lam certainly means lambda but what is nu?

Maybe I should become more explcit with my special case. I would like to test equal loadings. I thought this could be done like e.g.

f1 by y1 y2;
f1 by y3 (1);
f2 by y4 y5;
f2 by y6 (1);

or isn't this possible?

Then I would like to test equal intercepts. How do I specify that? I've found that equal error variances are specified like

y1 y2 (1);

These constraints are all that I need to specify: equal loadings, equal intercepts and equal error variances.

And which commands can I use for MODEL TEST?

Could you maybe give me the pages in the manual where my questions are addressed or could you please answer them?

Best
 Linda K. Muthen posted on Wednesday, March 27, 2013 - 11:03 am
See Chapter 17 of the current user's guide where brackets statements and all options in the MODEL command are discussed including MODEL TEST.