I'm doing a study using generalized linear models to investigate effect size and direction of species whose presence/absence were found to be affected by the presence of drought (tested by a Fisher's Exact Test). To do the results easy to interpret, I did the following:
1) I produced a binomal GLM.
2) For presence and absence of a particular species, I converted the non-standardized logistic regression coefficients given by the GLM for the intercept-only model (the null model) and the intercept + drought presence and absence model (the alternative model) to the log-odds probability (using the logit function, where β0 represents the intercept and β1x1 represents drought presence/absence). I did this for drought and for non-drought separately.
3) I converted log-odds probability to probability of detection for drought and non-drought (using the inverse of the logit function), and compared these probabilities of detection within each species during drought and non-drought.
The equations used are as follows:
for (2) logit (α) = β0 + β1x1
for (3) logit^-1 (α) = e^α / (1 + e^α)
The issue is that a couple species do not at all represent reality, even if the patterns are correct. For example, a bird that is detected 60% of the time during drought and 25% of the time during non-drought (from the raw data), after running the GLM, and converting to probability, the model said there's a 58% chance of detecting the bird (instead of somewhere near 25%) during non-drought and a 96% chance of detecting the bird (instead of 60%) during drought. The true probability can't be anywhere near 96%, right? This bird is not that common. Should I not be interpreting these values as true probabilities? How should I be interpreting this 96%? Did I do something wrong? Thank you for any and all help!