Interaction Terms in LTA
Message/Author
 the_statistician posted on Tuesday, April 04, 2017 - 11:40 am
Hi Dr. Muthen,

In example 8.14 of the MPLUS Version 7 user's guide, there is a section in the output (just before the 'results in probability scale' section) which says:

Latent Class Pattern 1 1

C2#1 ON
X -0.689 0.327 -2.106 0.035

C2#2 ON
X -1.708 0.630 -2.711 0.007

Latent Class Pattern 2 1

C2#1 ON
X -1.659 0.863 -1.921 0.055

C2#2 ON
X -2.353 0.734 -3.208 0.001

Latent Class Pattern 3 1

C2#1 ON
X 0.522 0.384 1.360 0.174

C2#2 ON
X 1.316 0.424 3.101 0.002

My question is: What would be the proper way of interpreting the numbers in the first column?

The way I look at it is that, for example, 1.316 would be the effect of the covariate X on the log odds of a participant transitioning to class 2 over class 3 at time 2, given that the participant was in class 3 at time 1.

Similarly, for example, -0.689 would be the effect of the covariate X on the log odds of a participant transitioning to class 1 over class 3 at time 2, given that the participant was in class 1 at time 1.
 Bengt O. Muthen posted on Thursday, April 06, 2017 - 5:30 pm
You should ignore the second digit in

Latent Class Pattern xy

(y is deleted in Version 8).

So, 1.316 is simple the log odds in the regression of c2 on x for c1=3.
 the_statistician posted on Friday, April 07, 2017 - 9:24 am
Hi Dr. Muthen,

Thank you for the clarification.

As I understand, in the above example, we actually have several regression equations estimated. One of which is:

c2#1 = intercept + (beta1)c1#1 + (beta2)c1#2 + X + (beta3)(c1#1)*X + (beta4)(c1#2)*X

where c2#1 is a binary response variable equal to 1 if a participant is classified in category 1 at the second time point and zero if the participant is classified in category 2 or 3 at the second time point (the example assumes 3 latent classes only per time point), and c1#1 and c1#2 are defined analogously (with class 3 as the reference class). In the above, beta1-beta4 are regression coefficients.

Thus the output of MPLUS I posted previously actually do NOT include beta3 and beta4, but rather, they are estimates of contrasts -- is this correct?

If so, how do I obtain beta3 and beta4, and their corresponding standard errors and p-values?

Thank you.
 Bengt O. Muthen posted on Saturday, April 08, 2017 - 3:28 pm
See Mplus Web Note 13 on our website for different parameterizations.
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