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I am running a nested 3-block logistic model. In block 1, the odds ratio for Variable 1 (V1) is 2.0 but in block 2 when I enter other variables (demographics) it jumps up to 4.0 which is odd (pun intended). When I run the full model with vars in block 3, the odds ratio returns to the normal values I see in block 1. Something in block 2 is amiss. I've tried systematically removing variables in block 2 to figure out which one is the offender thinking it's a violation of linearity of logit assumption, but several different variables seem to be the issue albeit inconsistently. For example, I figured out V2 was the issue by removing vars one by one from the model. Then I reran without v2 and the effect was still there. Repeat and ID another variable, reran without v3, the effect is still there. I think the issue is some sort of suppressor or interaction effect between the variables in block 2. So 1) how problematic is my issue in block 2? It sets my spidey sense off. 2) any suggestions on how to fix it or what's going on? Also, my hosmer is significant though I know that that isn't always indicative of bad model fit.

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It's hard to diagnose what's going on in a particular data analysis from afar, but in principle it's expected that adding covariates (or adding suitable random effects) to a model would make an odds-ratio further away from 1.

The odds ratio is not collapsible. I.e. if you omit covariates that matter (more than to a non-negligible extent), you end up (on average) shrinking the odds-ratio towards 1 (or equivalently the log-odds-ratio towards 0). So, would a non-collapsible effect measure be better? Not necessarily, because they cannot possibly be constant across different risk levels (while an odds ratio could be - which doesn't mean that it is) so that you end up getting interactions in your model when they might not have been needed (if only you'd used an odds ratio).

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Agree with noncollapsibility being why the OR increases (i.e. the added variable is prognostic for the outcome) but it could also happen if one of the added variables is a confounder. Neither of these options implies anything bad for the analysis or for use of the odds ratio as an effect measure as noncollapsibility simply means that outcome heterogeneity is being accounted for.

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