I am analyzing fruit-set data (a binary response, so 1's and 0's only) from a pollination experiment. Five treatments were applied to flowers, one of which (pollinator exclusion) yielded no fruit-set in any of the manipulated flowers (i.e., the response was all 0's); all other treatments had varying levels of fruit-set (but not exclusively 0). I am using a binomial generalized linear model (with clog-log link function) to analyze the effect of the treatments (a categorical variable) on fruit-set, but the inclusion of 'pollinator exclusion' as a level in my treatments factor in the model produces results that are obviously erroneous. Omitting 'pollinator exclusion' as a treatment level produces expected model results.
Am I justified in excluding this '0's-only' factor level from my model, even though it was part of the original experimental design? If not, how can I overcome the havoc it wreaks on linear models?
Thank you for that interesting information. To my (non-expert) opinion, it might then make sense to use a binomial model to estimate the lower limit of the probability that it is "incapable of autonomous selfing". This information would stand aside from the comparison of the (other) treatments.
Would it be theoretically possible to get a fruit-set without pollination?
If yes, the data is informative and I think it should be used, although I have to admit that I don't know how. Using a Bayesian model with a small but non-zero prior would possible work.
If not, I wonder why this treatment was applied and what one should be able to learn by comparing the probabilities of fruit-sets of this treatment to the other treatments.
Jochen Wilhelm It is theoretically (and biologically) possible to get fruit-set without direct pollination (i.e. without a pollinator or hand-pollination). The comparison of fruit-set from the 'pollinator-exclusion' treatment with other treatments shows whether or not the plant species is capable of autonomous or facultative selfing (i.e. can it produce fruit through autonomous input of pollen from the same plant, or can it produce fruit through hand-pollination with pollen from the same plant?). A comparison with the control (completely unminipulated flowers) indicates the importance of pollinators for pollen transfer in the plant species. In this case, the complete lack of fruit-set in the 'pollinator-exclusion' treatment indicates that the plant species is dependent on pollinators for pollen transfer, and that it is incapable of autonomous selfing.
Thank you for that interesting information. To my (non-expert) opinion, it might then make sense to use a binomial model to estimate the lower limit of the probability that it is "incapable of autonomous selfing". This information would stand aside from the comparison of the (other) treatments.
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