Testing for "additive interaction"... PreviousNext
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 Richard E. Zinbarg posted on Tuesday, April 05, 2016 - 5:07 pm
Can one test for "additive interaction" in Mplus? I don't understand the concept terribly well but it relates to testing for group differences in risk differences (relative excess risk due to interaction) rather than risk ratios. I am doing survival analyses testing whether neuroticism interacts with stressful life events in predicting episodes of major depression - we don't get much evidence using the conventional multiplicative interaction tests (which is what I assume Mplus is giving me) but have been alerted recently to the distinction some statisticians draw between additive versus multiplicative interactions with binary outcomes and sometimes one can have additive interaction in the absence of multiplicative interaction (and vice versa).
 Tihomir Asparouhov posted on Thursday, April 07, 2016 - 11:01 am
Here is a nice paper on this topic.

On top of page 42 it states that the multiplicative interaction is simply presenting the additive interaction on a different scale. The multiplicative interaction is the exponent of the additive interaction and represents the hazard ratio. It is not a different model.
 Richard E. Zinbarg posted on Friday, April 08, 2016 - 2:37 pm
thanks very much Dr. Asparouhov - I was already familiar with that paper and it was one of the ones that alerted me to the difference between multiplicative and additive interactions. I read their paper differently than you did. On pages 36 and 37 the authors clearly state, it seems to me, that additive and multiplicative interaction can differ and that for public health it is often the additive interaction that is most relevant. And the following reference:

states that one way to test the additive interaction is through the use of linear binomial regression rather than logistic regression. I agree, though, that from pages 42-43 of the paper you provided the link to, the authors show how to derive RERI (additive interaction) from the parameters of a logistic regression but I wouldn't know how to get the standard error for an inferential test.
 Tihomir Asparouhov posted on Friday, April 08, 2016 - 9:54 pm
You can use this to get the SE

model constraint: new(Ebeta); Ebeta=exp(beta);
 Richard E. Zinbarg posted on Monday, April 11, 2016 - 10:40 am
thanks very much! Now that I am attempting to do this, though, I realize I don't know how to get the parameters needed from the logistic regression (or in my case, survival analysis) from the Mplus output - especially for my main effect of my latent variable as a time invariant covariate and for my interaction term involving the product of the time-invariant latent variable and the time-varying life stress variable.
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