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I am calculating a generalized linear mixed model (GLM) with a two-column (n successes/failures) binomial response using the the lme4 package in R. The link function used is the default logit link. The model itself works perfectly and the results obtained are reasonable. I was just wondering two things:

(i) how does the logit-link handle 0 and 1 (i.e. when 100% success or failure) as the logit of 0 and 1 is -Inf and Inf. Is here also a remapping (to 0.025, 0.975) applied as in the logit::car function?

(ii) if so, to which range are the values remapped and is there an inverse logit function that considers also this remapping range? This is of special interest when using the model coefficients for predictions of responses (without using the predict function of lme4).

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  • $\begingroup$ Why should it that 0 and 1 as special cases and not return inf's? It would be inconsistent since after back-transforming you'd receive something else then on input... $\endgroup$
    – Tim ♦
    Feb 15, 2017 at 9:28

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In GLMs the data are not transformed via the link function; it's the model for the mean that is transformed. You wouldn't normally encounter a situation where the fitted mean in a logistic regression is 0 or 1, (except perhaps with complete separation).

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