

Odds ratios with probit latent regres... 

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Dear Pr Muthen, I wish to calculate the odds ratios of responses to four ordinal 3level items, u1, u2, u3, u4, depending on the values of two covariates, x and z, with the hypothesis that the effect is completely mediated through a latent construct eta. eta is linked to u1u4 via probit functions. We have eta BY u1*u4* (load1load4); eta@1; ! scale eta residual variance eta ON x (bx) z (bz); I would like to compute an odds ratio for u1=2 vs u1=0 or 1, depending on the covariate x, such as: OR(x=1/x=0) = [ P(u1=2  x=1) / P(u1=0 or 1 x=1) ] / [ P(u1=2  x=0) / P(u1=0 or 1 x=0) ] A. If the link between eta and u1u4 was logit, do we have OR(x=1/x=0) = load1 . bx ? B. If the link is probit, the probabilities depend on the value of the other covariate z. Does it make sense to express an OR(x=1/x=0) with z fixed to some reference value, say 0 (or its mean if z is continuous)? Are there any studies expressing results in this way ? Odds ratios are more commonly reported (and compact) than probabilities, but I also need probit to benefit from WLSMV estimation (faster, and simpler to get indirect effects). Thank you very much for any guidance, Mô 


A. OR(x=1/x=0) = exp(load1 . b) B. With probit you have to actually express the probabilities that go into the OR. You can't just work with exp(coeff). But if you express probabilities, you can certainly condition on various z values. 


Thank you very much for your fast answer, Pr Muthen! A. Yes, I had indeed forgotten exp(.) (or ln OR), thank you for correcting my error. B. This is actually what I had in mind: computing the probabilities in the OR, conditioned on a given value of z. If z is binary, with z=0 the "normal" reference value (e.g. "no pain"): OR(x=1/x=0)_{z=0} = [ P(u1=2  x=1, z=0) / P(u1=0 or 1 x=1, z=0) ] / [ P(u1=2  x=0, z=0) / P(u1=0 or 1 x=0, z=0) ] Since the resulting OR for x depends on the chosen value for z, does it still make sense to give the result in terms of one odds ratio? Or do you mean that several odds ratios should be given for several values of z ? As OR_{"no pain"} and OR_{"pain present"}? 


He means that several odds ratios should be given for several values of z. 

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