Initial Status by Treatment Interaction
Message/Author
 Anonymous posted on Wednesday, August 06, 2003 - 11:42 am
I have a quasi-experimental situation, where there are two groups that I want to compare over time. After reading a previous post “Specifying a reg path from inpt to slope 01/31/2001 05:19pm, I see that I can control for initial status by regressing the slope factor on the intercept factor. What is the model specification that will allow me to include the interaction term; that is, Initial Status by Treatment?
 bmuthen posted on Wednesday, August 06, 2003 - 11:48 am
One way to do that is in a 2-group analysis of treatment and control group individuals, where the regression coefficient for the slope on the intercept is different in the treatment and control groups.
 jcookston posted on Monday, July 18, 2005 - 2:55 pm
We have intervention data and are doing latent growth models with initial status estimated as the immediate post-test score and growth calculated as change after treatment. This allows us to predict immediate changes by regressing initial status on program and allows for the estimation of baseline by treatment interaction scores using the product of pretest and program. Here's my question -- let's say that the path from the product term to the slope is statistically significant. How do we interpret the effect?
 bmuth posted on Monday, July 18, 2005 - 5:39 pm
It sounds like your treatment-baseline interaction allows there to be a larger or smaller effect on the development after the immediate impact time point as a function of the observed baseline values. For a critique of using observed baseline in the model, see the 1997 Psych Methods article by Muthen & Curran.
 Christoph Weber posted on Monday, February 16, 2009 - 8:39 am
Dear Dr Muthen,
I'm working on a LG-Model with an interaction effect (intercept)X(covariate) on the slope factor (similar to web note 6). But Contrary to web note 6 I am using a latent covariate measured by 5 items.

My model input is:

MODEL: i s | soz1m@0 soz2m@1 soz3m@2;
f1 by x1* x2 x3 x4 x5;
f1@1;
i on f1;
s on f1;
s on i;
iXf1 | f1 XWITH i;
s on iXf1;

[soz1m soz2m soz3m] (1);
[i@0];

First time I did not standardise the intercept (i). The results indicate a significant interaction effect and significant main effect of f1 on the slope.

Then I did a second analysis (guided by your input from web note 6). I standardised the intercept [i@0] and constrained the intercepts of soz1m, soz2m and soz3m to be equal ([soz1m, soz2m, soz3m] (1)).

The results are almost identical, with one exception: The main effect of f1 disappears (1. analysis = 0,524 --> 2. analysis = -0,015).

Why is this so? What strategy is the correct one and do I have to standardise the intercept?

Thanks
 Bengt O. Muthen posted on Monday, February 16, 2009 - 10:10 am
I would think the 2 parameterizations give the same results in terms of how the mean of s changes as a function of changes in f and i (using standard deviation units away from their means). Then it doesn't matter if a certain main effect is significant or not.
 Amy L. Tobler posted on Friday, July 30, 2010 - 2:31 pm
Drs. Muthen,
I am running an analysis incorporating an interaction term into a binary growth model; the interaction being treatment by race. So my code is as follows:

DEFINE: rt1=trt*r1;
rt2=trt*r2;
rt3=trt*r3;
rt4=trt*r4;
rt5=trt*r5;
MODEL: i s | b1@0 b2@1 b3@2 b4@3 b5@7;
i ON sex r1 r2 r3 r4 r5;
s ON sex trt r1 r2 r3 r4 r5 rt1 rt2 rt3 rt4 rt5;

Where r1-r5 are dummy codes for racial categories. My question is: Is there a way to test the null hypothesis that all of the interaction coefficients (rt1-rt5) are equal to 0, similar to the CONTRAST statement available in SAS?
 Linda K. Muthen posted on Friday, July 30, 2010 - 4:21 pm
You can do this using MODEL TEST. See the user's guide for details.
 Wen-Hsu Lin posted on Tuesday, April 15, 2014 - 6:30 pm
Dear Drs. Muthen,
I am trying to see if the latent growth factor interacted to influence an outcome variable. My coding is as follow:
i1 s1|sup1@0 sup2@1 sup3@2;
i2 s2|fsup1@0 fsup2@1 fsup3@2;
inter1| s1 xwith s2;
i1 with i2;
i1 with s1;
i2 with s2;
s1 with s2;
esteem on i1 i2 s1 s2 inter1;
My questions are two:
(1)If I want to know whether the interaction model fitted the data, do I compare the AIC and BIC to the model without interaction?
(2)If I put two interaction terms in the model (inter1 as shown above, and inter2 is i1 xwith i2), inter1 was significant. However, if I put one by one in two separated model, the neither was significant. Which results shall I trust?
 Bengt O. Muthen posted on Wednesday, April 16, 2014 - 12:29 pm
(1) Yes.

(2) The model with both in - assuming that is the a priori model you would specify.