comparing marginal probabilities and calculating contrast of a contrast

[Sule Yaylaci]

Dear Statalist Users,

I use Stata version 14 on a Mac OS.
The dataset I use come from a pre-test/post-test study. The main dependent variable is racial attitudes, measured before and after the experiment, and the treatment is receiving a genetic ancestry test.
Time variable is called 'wave.' Each individual observation has a unique number under variable 'ID'.

We are trying to see first whether individuals’ racial attitudes changed for the treatment group after receiving the ancestry test. The hypothesis is that the treatment group will change while the control group will not.
Secondly, we want to see if this change is dependent on the Knowledge of Biology or not (measured with 4- category ordinal variable).

I use the following commands to run the interaction model and calculate the margins afterwards:

mixed DV i.Treatment##i.wave##i.BiologyKnowledge i.Male i.Age i.Educ  i.region ideology || ID:, var 
 
margins BiologyKnowledge#Treatment, at (wave=(1 2)) contrast(atcontrast(r._at) effects marginswithin)

I find that for people who have no Biology knowledge, the change between two waves is significant for both the Control and Treatment Groups. Participants in the Control group with no knowledge has the ‘contrast’ coefficient 0.47 (std. error is .094, z=-5.05) between the waves, and those in the Treatment group with no knowledge has the ‘contrast’ coefficient -0.59 (std.error is .111, z=-5.42).
0.59 looks quite a bit higher than 0.47 on the probability scale of 0-1.
I would like to know whether the predicted decrease in the probability of DV for Treatment group with no knowledge (.59) is significantly higher than the predicted decrease in the probability of DV for the Control group with no knowledge (.47).

Basically, I am trying to find the contrast of a contrast: Control#wave2 vs. Control#wave1 with Treatment#wave2 vs. Treatment#wave1

I used the command:

contrast r.wave#r.Treatment@BiologyKnowledge,  effects

I think it gave me what I want but want to make sure.
It shows the following results for ‘No Knowledge,’ and repeats these contrasts for each category of Knowledge:

Contrast coefficient
Wave#Treatment@BiologyKnowledge = -.126 (std. error= .144, z=-0.87, p-value is 0.384)
(2 vs 1) (Treatment vs Control) No Knowledge


Basically from this result should I conclude that the difference between the .59 and .47 is not statistically significant because p-value is 0.38 for the difference of -.12?
Or is there an additional test I need to run?

[Clyde Schechter]

Your interpretation appears correct to me.

One small thing: when you first state the results, you give value of -0.59, although all future references to that parameter are 0.59. I'm assuming that the initial report of -0.59 is a typo. But if the -0.59 is actually correct then something is wrong with the rest of the figures you report.

[Sule Yaylaci]

Perfect! The sign of both coefficients is actually negative. So, it is -0.59 and -0.47.