In our thesis, we have used a mixed-effects logistic regression and now we want to present it as a formula, however, we are not sure how to present a mixed-effects logistic regression?
Our binary outcome is if the calf of a specific age group is sick (yes/no) and we have two explanatory variables. The first one is a continuous variable (Cq-values) made to a dichotomous one (true/false under a certain Cq cut-off). The second explanatory variable is a categorical one called age group with four levels = 1, 3, 5, and 7. We also have a random effect that is a combination between herd number (from where a calf is from) and age group (where the calf belongs to) called GroupID.
We have tried to make a formula but it does not seem right when we compare it to others. It is as follows:
logit(p_ij )=intercept+A_ij+slope*x_ij+G_kij where p_ij = is the probability for a calf j in an age group i, being scored as sick given the explanatory variables A_ij is the fixed effect, age group, i = 1, 3, 5, 7 for calf j x_ij is the fixed effect, Cq values being ≤ cutoff, i = true, false for calf j G_kij is the random effect, herd number, k =1…36, in combination with age group, i = 1, 3, 5, 7 for calf j