Longitudinal measurement invariance
Message/Author
 Matthew Fuller posted on Wednesday, November 23, 2011 - 6:10 pm
Hi Bengt and Linda,

I'd like to conduct a test of measurement invariance for daily diary data based on mood assessments. I have roughly 30 time points (although some individuals have missing data at various time points), and 200-300 participants.

I’ve seen discussion of longitudinal measurement invariance here and elsewhere. But those examples typically focus on a much smaller number of time points. I'm wondering if the following is the most appropriate approach?

*Treat each time point as a factor, allowing the factors to correlate.
*Test configural invariance first, before evaluating the change in model fit once factor loadings etc. are constrained to be equal across time points.

My concern is that as a single level analysis, I will have a lot of factors to correlate - will the model encounter problems if my sample is 200-300 participants?

Is there another way to do this analysis (e.g., MLM with time points at level 2 and a clustering effect for individuals as well?)

Kind regards,
Matthew
 Bengt O. Muthen posted on Wednesday, November 23, 2011 - 6:12 pm
How many variables do you consider per time point and how many factors?
 Matthew Fuller posted on Thursday, November 24, 2011 - 5:25 pm
Hi Bengt,

There are six items for the scale, and two factors provide a good fit for this measure.

I wasn't intending to use other variables in addition to this mood measure.
 Bengt O. Muthen posted on Friday, November 25, 2011 - 8:06 am
So you have 6 x 30 = 180 variables if you do it as a wide analysis with a longitudinal factor model. That will be heavy and won't work well with your smallish sample.

You can do it as a twolevel model, so 6 variables, 30 "cluster members", and subject as the level 2 unit, that is, using cluster=id. But then you don't get a test of measurement invariance across time as you would in a wide analysis.

So maybe you can take a wide approach and choose a few critical time points such as beginning, middle, and end in order to have fewer variables. Testing the longitudinal invariance that way.
 Matthew Fuller posted on Tuesday, November 29, 2011 - 2:02 pm
Terrific. Thank you for your help Bengt.
 J.D. Haltigan posted on Wednesday, January 21, 2015 - 10:59 pm
Hello:

In the same vein as the questions above, I am evaluating a longitudinal measurement invariance model. In short, the model is a 2-factor model with 4 indicators each across 4 time points. N = 280. When I set up the configural model, it runs fine except for the warning noted above that there may be a linear dependency etc. and to check Tech 4. None of the latent variable corrs are > .85 and the variances across time are set = 1 so there is not a negative latent variance. I have tried constraining factor covars across time to equality but this doesn't work.

Two queries: what are the implications of ignoring this warning and

is it possible that my sample size is simply too small for this longitudinal configuration?

Any thoughts would be much appreciated.

Thank you!
 Linda K. Muthen posted on Thursday, January 22, 2015 - 7:28 am
The message should not be ignored. I can't say more without seeing the output.
 J.D. Haltigan posted on Thursday, January 22, 2015 - 10:50 am
Thank you. I had been running this longitudinal invariance setup on a subset (validation sample) of a larger sample. When I run this setup on the full sample, the warning disappears. My inclination is this points to sample size issues.

A query: if I do an EFA on a calibration sample, confirm CFA on a validation sample (other half of the sample) and then do longitudinal invariance on the full sample, does this go against the grain of best practice in confirming a measurement model in an independent sample? In short, I confirm with the other half (validation sample) but would be demonstrating long. invar. with the full sample. I want to make use of the available data as best as possible while maintaining best practices.
 Linda K. Muthen posted on Thursday, January 22, 2015 - 11:46 am
This is a question more appropriate for a general discussion forum like SEMNET.
 Julia Steinhorst posted on Friday, July 22, 2016 - 12:47 am
Dear Linda and Bengt,

I am runing a longitudinal analysis with 3 timepoints and 3 groups. There is partial scalar invariance across time. For establishing invariance across groups, I would like to use the Mplus shortcut “model = configural metric scalar”. I was wondering, which model to input: (a) the partial scalar invariance model or (b) the configural model? Do I use exactly the same input? If not, how do I modify the input below (with indicatorspecific factors? Thanks a lot.
t2elIM by t2elIM1
t2elIM3 (1)
t2elIM2 (2)
t2elIM4 (3);
t3elIM by t3elIM1
t3elIM3 (1)
t3elIM2 (2)
t3elIM4 (3);
t4elIM by t4elIM1
t4elIM3 (1)
t4elIM2 (2)
t4elIM4 (3);

is3 by t2elIM3 t3elIM3 t4elIM3;
is2 by t2elIM2 t3elIM2 t4elIM2;
is4 by t2elIM4 t3elIM4 t4elIM4;

is3 with t2elIM-t4elIM@0;
is2 with t2elIM-t4elIM@0;
is4 with t2elIM-t4elIM@0;

[t2elIM1@0 t3elIM1@0 t4elIM1@0];
[t2elIM3 t4elIM3](4);
[t2elIM2 t3elIM2 t4elIM2](5);
[t2elIM4 t3elIM4 t4elIM4](6);

[t2elIM t3elIM t4elIM];
 Bengt O. Muthen posted on Friday, July 22, 2016 - 10:05 am
Try using the partial invariance model you show here and check Tech1 to see if you get the equalities you want. I think Mplus will do the metric/scalar versions on the is2-is4 factors.