Is it appropriate to analyze the relationship between a proportional explanatory variable and a proportional response variable (as cbind(option 1, option 2), or as a proportion with weights) using logistic regression? If so, is there a way to weight the proportional explanatory variable to account for different sample sizes for each trial?
Here are the details of my study:
I would like to evaluate whether individual insect preferences for pairs of host plants are correlated. Insect preference was tested using three separate choice assays:
1: plant A vs. plant B, 2: plant A vs. plant C, and 3: plant A vs. plant D.
In each assay, we recorded the number of eggs laid on the two available plants. Each individual was tested on all three assays. Assay 1 was diagnostic, so all insects started on that assay, after which they were moved onto assays 2 and 3 in random order. A total of 79 individuals laid eggs in all three assays. The total number of eggs laid in assay 1 ranged from 2 to 126; in assays 2 and 3, from 2 eggs to 178.
My main questions are, is preference (proportion of eggs laid on plant A) in assay 1 correlated with preference in assay 2 and/or with preference in assay 3?
Possible solutions (and associated concerns):
Use logistic regression with proportion of eggs laid on plant A in assay 1 as an explanatory variable, including only those females that meet a minimum threshold for total eggs laid in assay 1 (>15). This both reduces my total sample size (down to n = 53), and does not take into account the greater confidence I have in the preference of an insect that lays 30/75 eggs on plant A in assay 1 compared to an insect that lays 6/15 eggs on plant A in assay 1.
Use a negative binomial mixed model (glmer.nb) with the rough form: plant A eggs ~ log(total eggs) * Assay + (1|insect ID). While this can tell me whether the eggs laid on plant A as a function of total eggs laid differs between the three assays, I don't believe it is informative about how similar the preferences are. I also looked at poisson and quasipoisson, but these models had worse fits than the negative binomial model.