I am currently working on a GLMM model which uses a Poisson distribution and need to compute and interpret marginal effects from this model.
The model outcome consists of a count (COUNT) collected yearly for a number of different entities.
The model predictors are both dynamic and consist of YEAR and CONDITION, where CONDITION is a dynamic predictor which takes the values 0 or 1. (The CONDITION predictor can be 0 on all years, or perhaps 0 on some years and 1 on subsequent years.)
The GLMM model is fitted to the data using the GLMMadaptive package in R and has a syntax along these lines:
model <- mixed_model( fixed = COUNT ~ YEAR * CONDITION, random = ~ 1 + YEAR | ENTITY_ID, data = DATA, family = poisson())
marginal_coefs() applied to this model produces output similar to the one below:
Estimate Std.Err z-value p-value (Intercept) 9.9867 3.0754 3.2473 0.0011652 YEAR -1.0717 0.5093 -2.1040 0.0353749 CONDITION 1.2335 0.6905 1.7864 0.0740308 YEAR:CONDITION -0.3668 0.1218 -3.0127 0.0025894
My first question is:
What is the scale used by
marginal_coefs() for reporting marginal effects: log scale or natural scale of the COUNT response?
My second question is:
How should the marginal effect of CONDITION in the above output be interpreted (i.e., the one estimated as being equal to 1.2335)? Should it be interpreted on the average change (on what scale?) in the expected value of COUNT across all entities when YEAR = 0 (i.e., first year) associated with changing from CONDITION = 0 to CONDITION = 1 at those entities?
My third question is:
How should the marginal effect of YEAR in the above output be interpreted (i.e., the one estimated as being equal to -1.0717)? Should it be interpreted as the average change (on what scale?) in the expected value of COUNT associated with moving from one year to the next across all entities with CONDITION = 0?
My fourth question is:
How should the marginal interaction effect between YEAR and CONDITION be interpreted?
My fifth question is:
What if we wanted to report "simple" marginal effects for this model? Would that amount to reporting the marginal effect of YEAR when CONDITION = 0 separately from the marginal effect of YEAR when CONDITION = 1? Alternatively, would it entail reporting the marginal effect of CONDITION when YEAR = 0, the marginal effect of REGIME when YEAR = 1, etc. Not sure how people report marginal effects for dynamic predictors (one continuous, one binary) engaged in an interaction.
Thank you for any clues you can provide!