Measurement Invariance Syntax Confirm...
Message/Author
 Dylan John posted on Thursday, July 27, 2017 - 9:27 am
If I am looking to assess measurement invariance, across three timepoints, and I have identified a best fit model of 4-profiles at each timepoint, does the following syntax look correct? Is there anything missing? Many thanks!

knownclass = cg(time = 1 time = 2 time = 3);
classes = cg(3) c(4);
missing = all(-999);
analysis: type = mixture;
processor = 10;
starts = 1000 50;
model: %overall%
c ON cg;
 Linda K. Muthen posted on Thursday, July 27, 2017 - 9:57 am
You can't use multiple group analysis to check measurement invariance across time. In multiple group analysis, the observations in each group must be different. See the Topic 4 course handout and video under Multiple Indicator Growth. The first part of this example shows how to test measurement invariance across time.
 Dylan John posted on Thursday, July 27, 2017 - 12:55 pm
Is it okay to use this method if it is not necessarily repeated measures. This is a national survey so there is a fair amount of dropouts across time.

So time 1 n=10,000;
time 2 n=9,000,
time 3 n=6000.
 Linda K. Muthen posted on Thursday, July 27, 2017 - 2:46 pm
If it is repeated measures, you should not use multiple group.
 Dylan John posted on Saturday, July 29, 2017 - 11:17 am
Thank you. Could you please point me to the part of the Topic 4 video that you are referring to?
 Dylan John posted on Saturday, July 29, 2017 - 11:23 am
For me, the first example that I am seeing is DATA TWOPART which I don't think it what I am looking for.
 Dylan John posted on Saturday, July 29, 2017 - 11:59 am
Sorry for the continuous posting. I managed to find the section that you referred to and have watched it.

For your example, you use a latent variable of aggression with 7 indicators. Can I view this the same way as what I have done:

- First I conducted a latent profile analysis at each of three timepoints, with three indicator variables at each timepoint

- Next I used fit indices and identified a best fit model of 4 profiles on my latent variable: problem behaviour

So my questions are as follows:

1. Can I use my latent variable of problem behaviour the same way as you have used aggression?
2. If my sole goal is to be able to say that my latent profile structures do or do not vary, across time, do I want to carry out all levels of measurement invariance modelling:

i) measurement non-invariance
iv) factor loading and partial intercept invariance with a linear growth structure

Thank you very much, I have found all of your feedback quite informative!
 Bengt O. Muthen posted on Saturday, July 29, 2017 - 1:37 pm
I think you want to do a Laten Transition Analysis (LTA). See UG ex 8.13 where c1 refers to the time 1 latent class variable and x2 to the time 2 latent class variable. That example has a predictor as well which you can ignore (it is the cg variable). The example refers to binary latent class indicator, so you should change e.g. the threshold

[u11\$1] (1);

to the mean

[u11] (1);
 Dylan John posted on Saturday, July 29, 2017 - 2:12 pm
My plan was to do a latent transition analysis after testing measurement invariance. I have identified a 4-profile model at each of the three timepoints, but before carrying out the latent transition analysis, I wanted to test whether or not the profiles at timepoint 1 are structurally the same as timepoint 2, and timepoint 3.
 Dylan John posted on Sunday, July 30, 2017 - 8:37 am
How do you recommend I proceed with such a goal?
 Bengt O. Muthen posted on Sunday, July 30, 2017 - 5:10 pm
If you want to test measurement invariance you analyze all time points jointly and let all 3 latent class variables be correlated using WITH in the Loglinear parameterization (see p. 559-560 in the V8 UG on our website).

But an LTA is almost the same thing except the usual lag-1 assumption means that c3 is influenced by c1 only indirectly via c2, not directly. That's why most invariance testing is done in the LTA context.
 Dylan John posted on Monday, July 31, 2017 - 6:57 am
I am sorry, but this is a bit confusing. I thought that latent transition analyses was used to tell you the probability of class belongingness, for example, at timepoint 2 based on timepoint 1.

Say I have identified a 4-class model at timepoint 1 and a 4-class model at timepoint 2, how does an LTA inform me that the structure of these classes at each timepoint is the same/a similar construct? Don't I need at test of measurement invariance for this?
 Bengt O. Muthen posted on Monday, July 31, 2017 - 5:58 pm
Take the factor analysis analogue. To test measurement invariance over time you analyze both time points jointly where you let the factors correlate freely over time because that's not the part you want to test.

Same for latent class analysis at two or more time points. Let the latent class variables be freely associated and test measurement invariance. And LTA does that if you have

c1 with c2;
c1 with c3;
c2 with c3;

This is the same at LTA with

c2 on c1;
c3 on c2 c1;

Assuming c1 with c3 is insignificant, this is the same as the usual lage-1 LTA:

c2 on c1;
c3 on c2