by Isabella Ghement
Last Updated March 14, 2019 20:19 PM - source

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 mortality count (MORTALITY) collected yearly for a number of different facilities where an animal is known to die.

The model predictors are both dynamic and consist of YEAR and REGIME, where REGIME keeps track of whether or not a facility adopted mitigation measures in a given year to reduce the mortality count. REGIME will have the value 0 in all years which precede the adoption of the mitigation measures and 1 in all years when the measures were put in place. (Once the measures are adopted at a facility, they stay in place.)

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 = MORTALITY ~ YEAR * REGIME,
random = ~ 1 + YEAR | FACILITY_ID,
data = DATA,
family = poisson())
```

The function marginal_effects() 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
REGIME 1.2335 0.6905 1.7864 0.0740308
YEAR:REGIME -0.3668 0.1218 -3.0127 0.0025894
```

**My first question is:**

What is the scale used by marginal_effects() for reporting marginal effects: log scale or natural scale of the MORTALITY response?

**My second question is:**

How should the marginal effect of REGIME 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 MORTALITY across all facilities when YEAR = 0 (i.e., first year) associated with changing from no mitigation measures to mitigation measures at those facilities?

**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 1.2335)? Should it be interpreted as the average change (on what scale?) in the expected value of MORTALITY across all facilities with no mitigation measures in place associated with moving from one year to the next?

Thank you for any clues you can provide!

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