# Justification for using zero-inflated model in GLMM

I am using GLMMs in R to examine the influence of various continuous predictor variables (x) on several biological counts variables (y). My response variables (n=5) each have a high number of zeros (data distribution), so I have tested the fit of various distributions (genpois, poisson, nbinom1, nbinom2, zip, zinb1, zinb2) and selected the best fit one according to the lowest AIC/LogLik value.

According to this selection criteria, three of my response variables with the highest number of zeros are best fit to the zero inflated negative binomial (zinb2) distribution. Compared to the regular NB distribution (non-zero inflated), the delta AIC is between 30-150.

My question is: must I use the ZI models for these variables considering the dAIC? I have received advice from a statistician that if dAIC is small enough between the ZI and non-ZI model, use the non-ZI model even if it is marginally worse fit since ZI models involve much more complicated modelling & interpretation. The distribution matters in this case because ZINB / NB models select a different combination of top candidate models when testing my predictors.

Thank you for any clarification!

Use the ZINB model over the NB. Usually a "small" $$\Delta$$AIC is of magnitude 2, not 30-150.

The R DHARMa package is a good tool to use alongside AIC selection in generalised mixed models. It can inform you of goodness of fit, patterns in the residuals etc.

• Thank you for your recommendation. Do I interpret/report the output the same way as a NB model and ignore the ZI part of the model? Or does it require different interpretation?
– Ryan
Feb 21, 2023 at 2:26
• @Ryan it's a different interpretation, overall. The ZINB model is basically the product of a Bernoulli R.V and a NB R.V. The Bernoulli is the source of the extra zeroes. Conditional on the Bernoulli = 1, then the variable has an NB distribution with some mean and variance (or however you wish to parameterise it). I would as general advice, report both the parameters of the ZI component (the Bernoulli), and the parameters of the NB component. Exactly what you will report though depends on the objective of your modelling, any relevant reporting standards etc. Feb 21, 2023 at 7:01
• Thank you for your detailed response. For each of the models that "should" include a ZI term (according to the dAIC), I have tested DHARMa::testZeroInflation() on the NB-specified model and received no significant p values to suggest ZI should be used. Despite these non-significant results, do you think that I should use ZINB based on the dAIC alone?
– Ryan
Feb 25, 2023 at 1:12
• Could you clarify what you mean? So (dummy example) if you have m1 <- zinb(data), m2 <- nb(data), you are running testZeroInflation on which model? Feb 26, 2023 at 21:55
• I have run testZeroInflation() on m2 in your example (nb model only) and received no significant results across all responses that "should" require ZI terms according to dAIC
– Ryan
Feb 26, 2023 at 22:28