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I just want to confirm that I am understanding this correctly. So if logistic regression models have omitted variable bias, does that mean that I should discard any logistic regression models that does not include every significant main effects and their every significant interactions, even if I need to exclude some of the potentially significant interaction terms to avoid multicollinearity or to make an MCMC-GLM algorithm converge?

In my situation: 1. I am fitting a logistic regression model for my binary response against three predictors. When I run glm(y~(A+B+C)^3) in R it does not seem to have any problem with this. However, when I try to run MCMClogit(y~(A+B+C)^3) for a Bayesian power analysis on logistic regression model, R tells me that the algorithm does not converge. The MCMClogit algorithm cannot handle the model involving full interaction, meaning the Bayesian method is subject to omitted variable bias. 2. Because I was being so cautious about the omitted variable bias in logistic regression, I added bunch of interaction terms into my logistic regression model that deem to have significant effect on the response. This causes multicollinearity, which makes the p-values to become unreliable.

Does this mean that I should abandon this Bayesian approach of conducting power analysis? and does omitted variable bias mean that I should include every significant interaction even if it causes multicollinearity?

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