OR and CI for latent interaction PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Ilya Yaroslavsky posted on Monday, August 27, 2012 - 9:24 pm

I am modeling the effects of a latent-manifest variable interaction on a 2-category outcome. The interaction term is significant and I am trying to calculate the OR and 95% CI for +/-1 SD of the interactionís components. Based on previous posts in this forum, it is my understanding that logits for combinations of the interactionís components could be calculated and compared via the following formula through Model Constraint:

Logit1 = threshold + b1 * [+1SD predictor1 * +1SD predictor 2];
Logit2 = threshold + b1 * [-1SD predictor1 * +1SD predictor 2];
Difflogit12= logit1-logit2;

If my understanding is correct, Difflogit12 is the log odds ratio. If so, could the standard error of this parameter produced through Model Constraint be used to calculate the 95% CI?

For example, would the following be correct?

Difflogit12 = 0.305,
Difflogit12 _SE= .17;
OR=exp(Difflogit12) = 1.36
low_OR_CI= exp(.305 -1.96* .17) = .97
high_OR_CI = exp(.305 +1.96* .17) = .1.89

Thank you for your assistance.
 Bengt O. Muthen posted on Saturday, September 01, 2012 - 4:02 pm
I think you are correct about difflogit's relationship to OR and the CI limits of the OR. But the logit1 and logit2 equations look suspect to me. First, the sign of the threshold should be changed to give a logit intercept. Second, I would express the interaction as a moderation like:

b*(gamma1 + gamma2*mod)*x,

where mod moderates the influence of x. Here, mod*x is the interaction.
 Ilya Yaroslavsky posted on Friday, September 14, 2012 - 10:02 am
Dr. Muthen,

Thank you for your helpful feedback, and please excuse this delayed reply. Based on your handouts, it was my understanding that the moderator function is (b_eta2 + b_intercept*eta1)*eta2. Can you clarify what the "b" parameter represents in b*(gamma1 + gamma2*mod)*x?

Thank you,

 Bengt O. Muthen posted on Friday, September 14, 2012 - 6:26 pm
Sorry, the b comes from a mediation model (Y ON M), which I guess you don't have.
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