Longitudindal invariance analysis PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 JM posted on Tuesday, May 26, 2009 - 12:58 pm
Hi, when examining longitudinal measurement invariance, comparing equal form, factor loading, and indicator intercept models, I understand that chi-sq diff testing is done to check as to whether the nested models differ compared to the comparison model; however, should I also be looking at estimates in the output to check for specific changes or non-changes in standardized or understandarized (not sure which) co-efficients?

 Linda K. Muthen posted on Wednesday, May 27, 2009 - 11:23 am
I would look at modification indices.
 Sean Tucker posted on Wednesday, August 26, 2009 - 8:46 pm
Dear Linda,

I have a three wave longitudinal dataset with equal time intervals. Following Chan (1998) I am trying to test for measurement invariance but I canít seem to find an applied example that shows the relevant MPlus syntax (including setting free vs. equal factor loadings, free vs. fixed error variances, etc) and guide to understanding the related output. Would you be so kind as to direct me to a simple applied example or provide the syntax in a reply? Iím relatively new to MPlus and I have a weak background in stats.

Many thanks,
 Linda K. Muthen posted on Thursday, August 27, 2009 - 6:50 am
See the Topic 4 course handout starting with slide 77.
 Sean Tucker posted on Thursday, August 27, 2009 - 11:14 am
Many thanks, Linda.

I received an error message (i.e., "*** ERROR in MODEL command
Unknown variable(s) in a BY statement: (1)- ") when running the model with factor loading invariance:

V1 BY v11
v12 v13 v14 v15 v16 v17 (1)-(6);
V2 BY v21
v22 v23 v24 v25 v26 v27 (1)-(6);
V3 BY v31
v32 v33 v34 v35 v36 v37 (1)-(6);

Pages 532-533 of the user manual describe the syntax for fixing parameter values. Would you be so kind has to describe what (1) Ė (6) means in expanded form. Should I be using different command for fixing the parameter values?

Thank you for your help.

 Linda K. Muthen posted on Thursday, August 27, 2009 - 11:38 am
It should say (1-6).
 Sean Tucker posted on Thursday, August 27, 2009 - 1:21 pm
Thank you, Linda.

Should I be concerned about this message?

*** WARNING in MODEL command
There are more equality labels given than there are parameters.
Some equality labels will not be used.
Equality: 1-6

When testing for partial intercept invariance some items do not appear in the commands on slide 90 (Topic 4). How do I determine which items are not subject to the equality constraint?

Thank you,
 Linda K. Muthen posted on Thursday, August 27, 2009 - 2:12 pm
Please send your output and license number to support@statmodel.com regarding the error message.

Partial measurement invariance requires relaxing the equality constraints of some items which. Modification indices were used to determine which items. The Topic 1 course video covers testing for measurement invariance. You should listen to that and then the Topic 4 course video for a full explanation.
 Pamela May posted on Thursday, August 14, 2014 - 3:14 pm

I am testing measurement invariance for a latent difference model. I have the same construct, activity frequency, being tested at two time points. I am confused by the fact that I have the same degrees of freedom, for when I fix the factor loadings (chi-square = 27.30, df = 18), as well as when the factor loadings and the intercepts are fixed (chi-square = 350.02, df = 18). Would there be any reason that these two models have the same degrees of freedom?

!Fixing factor loadings
CA08 BY dv
kv (1)
lv (2)
pv (3);
CA12 BY Ev
Mv (1)
Nv (2)
Rv (3);
dv with Ev;
kv with Mv;
lv with Nv;
pv with Rv;
CA08 with CA12;

!Fixing factor loadings and intercepts (same syntax as before plus this below)
!Indicators are categorical, with five levels

[dv$4 Ev$4] (4);
[kv$4 Mv$4] (5);
[lv$4 Nv$4] (6);
[pv$4 Rv$4] (7);
{dv@1 kv@1 lv@1 pv@1 Ev Mv Nv Rv};

Thank you,
 Bengt O. Muthen posted on Thursday, August 14, 2014 - 3:27 pm
If you have fixed scale factors at time 2 for the equal loading run, the equal loading+threshold run restricts 4 thresholds but frees 4 scale factors, so ends up with the same number of parameters.

Now, in the second model you want to have the factor mean free at time 2.
 Pamela May posted on Thursday, August 14, 2014 - 3:42 pm
Thank you, Bengt, for your prompt and helpful reply!
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