I employed a software package on binary data thats takes a long time to run (e.g. a week) that used a multilevel mixed model (linear) instead of a logistic model; the significance is very similar between the models, and the software says its appropriate for binary data as outcome, but it doesn't give the right estimates you would get from a logistic regression.

Is it possible to correctly convert linear regression coefficients to coefficients you get from logistic regression?

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    $\begingroup$ Actually a crude rule of thumb says that you can divide logit estimates by 4 to make comparable to their OLS counterparts. But really there is no substitute for the real thing, espcially not if the model is complicated. $\endgroup$ – Repmat Mar 10 '16 at 22:20

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