Using Zero inflated GlMM when you have too many zeros

Question

I am trying to understand the influence of several predictors (n=8) on the presence or absence of a species using generalized linear mixed models. Unfortunately, I do not have great data. I have 13000 points, of which 300 are 1 (presence) and the rest 0 (absence). After encountering problems of convergence and high eigenvalues, I now believe the problem lies in my data, specifically, there being too many 0s. I wonder if using a zero-inflated model would resolve these issues.

Post the GlmmTMB, I do model selection to choose the best model using delta AIC. Below is my code:

SP1 <- cbind(Data_scaled, 
               SP1 = Data$SP1,  
           Dist_ID = Data$Dist_ID) 

set.seed(123)

SP1_Final <- SP1 %>% dplyr::select(ProtectedAreas, TRI, 
   Water, Perc_NR, Perc_TB, Settlements, Precipitation, 
   HMI, SP1, Dist_ID)

SP1_ZIGLMM <- glmmTMB(SP1 ~ ProtectedAreas + TDF + Water + Perc_NR +
      Settlements + TRI+ Perc_TB + Precipitation + (1 | Dist_ID), 
                    data = SP1_Final, family = binomial, 
                    ziformula = ~ 1, 
                    na.action = na.fail,# Zero-inflation model (intercept-only model)
                    control = glmmTMBControl(optimizer = "nlminb",  # Changed optimizer
                                             optCtrl = list(iter.max = 100000)))
summary(SP1_ZIGLMM)
SP1model_set_sample <- dredge(SP1_ZIGLMM)
print(SP1model_set_sample)

Answer 1

I would expect the mixed-effects logistic regression to handle settings with many zeros without requiring an extra zero-part (see also here).

Perhaps the problems you experience stem from the nature of the predictors and the selected optimization and integration algorithms. You could also try fitting the model with alternative implementations (e.g., in GLMMadaptive).

Answer 2

Adding to Dimitris's excellent answer:

The issue of imbalanced data in logistic regression has been discussed here and elsewhere. In general, problems arise when there are too few cases in the smaller category, but here, you have 300 observations for only 8 predictors, and that should be fine.

I am very leery, in general, of using complex and unusual models to try to help when "the problem is in my data". Those problems are usually solved by getting better data (sorry, I know that's not what you want to hear).

Have you tried using fewer predictors?

Have you looked at collinearity? Just looking at the names of your predictors, I think that collinearity could be a problem, but I am doing a bit of guessing as to what the names mean.

Have you plotted each predictor against the dependent variable? Or looked at the mean of each predictor for each level?

Have you tried using splines of the predictors?