[R-sig-ME] Checking Model Assumptions for Poisson Mixed Effects Model

[Sol Vitkin]

Hello!

tldr; Aside from equidispersion, what are the model assumptions I should be
checking for a poisson mixed effects model that has a random intercept,
group mean centered transformations of its explanatory variables, and group
means included as variables?

I have a county-year dataset with 21 counties that each have 8 years of
data (N = 168). I am attempting to model the number of prescription opioid
related hospitalizations for this data using the number of prescription
opioid pills supplied to each county in a year, the prescription rate of
each county in a year, and demographic and economic (unemployment rate,
median household income) variables also at the county-year level. I am
using a poisson distribution (with a log link) and the lme4 package to
estimate this model with a random intercept, group mean centered
transformations of each variable, and the group mean of each variable in
line with the specification found in Bell and Jones, 2015
<https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0334A27557D15848549120FE8ECD8D63/S2049847014000077a.pdf/explaining_fixed_effects_random_effects_modeling_of_timeseries_crosssectional_and_panel_data.pdf>
. Additionally, I have been using the DHARMa package to visually examine
the relationships between my explanatory variables and the randomized
quantile residuals from the model and to test for overdispersion. I am not
formally trained in mixed effects modeling and want to be as sure as one
can be that the estimates from my model are not biased. What are the
assumptions of a poisson mixed effects model and is there a rigorous set of
steps for testing these assumptions (either by looking at residuals or any
other part of the model output)?

Thank you in advance for any help!

-Sol

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