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I am attempting to create a model which looks at the effect that age, supplementary food use, and nest initiation date (converted to Julian days) is having on female reproductive success (success =1 and failure=0). Unfortunately I have a very small sample size of only 17 individuals. I believe that my data does include perfect separation in that the majority (seven of the eight) females that used supplementary food initiated nesting before a specific date, while the majority of individuals (seven of the nine) that did not use supplementary food initiated after that date. Will this prevent me from being able to run a logistic regressions on my data?

I received the error message, warning message: glm.fit: fitted possibilities numerically 0 or 1 occurred, when I ran the regression using the glm function with the family specified as binomial but not when I specify the family as quasibinomial. Does the use of quasibinomial somehow account for perfect separation or is this an unexpected side effect of accounting for overdispersion in my data?

Also, when I compare the two models' results the model where I used family = binomial produces non-statistically significant results (z-value of 0 and p-value of 1) where as the model that I use family = quasibinomial produced statistically significant results for all variables.

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    $\begingroup$ You may well have separation (based on the warning, & possibly on the z / p values), but it is not what you describe in your 1st paragraph. Since supplementary food use & nest initiation date are both covariates, the implication is that you have some collinearity / confounding. Separation pertains to the response variable. (Nb, collinearity also expands your SEs & reduces power.) $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 26, 2013 at 19:05

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That sounds strange, I would guess it is a numerical coincidence. The only difference in R's glm between binomial and quasibinomial family is in the calculation of standard errors, the estimation process is exactly the same. Or, it might be that the difference in calculation of standard errors cause differences in the criteria for declaring convergence. Anyhow, you should not trust the model for hypothesis testing, the standard errors (for both binomial and quasibinomial case) is bogus. See my answer here Why does logistic regression become unstable when classes are well-separated? for some ideas of what to do in this case of separation.

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