

OR and CI for latent interaction 

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Hello, I am modeling the effects of a latentmanifest variable interaction on a 2category outcome. The interaction term is significant and I am trying to calculate the OR and 95% CI for +/1 SD of the interaction’s components. Based on previous posts in this forum, it is my understanding that logits for combinations of the interaction’s 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= logit1logit2; 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. 


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. 


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, Ilya 


Sorry, the b comes from a mediation model (Y ON M), which I guess you don't have. 

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