Interpretation of multilevel negative binomial output

Question

I am wondering how to interpret the coefficients returned in a multilevel (repeated measures nested within person; random intercepts-only) negative binomial regression. Output is pasted below conducted in R and utilizing the glmmTMB package.

Some background on this dataset: I am predicting the number of comments made on a digital platform posted by a user each week over a ~3 month period. I am particularly interested in the effect that "taskgoal_gm," which represents a centered and continuous measure of the perceived alliance with the digital platform, has on the number of comments made over time - thus I've introduced an interaction term "time*taskgoal_gm." The other variables in the equation - age (centered, continuous), gender (dichotomized 0/1), and race (dichotomized 0/1) - are control variables. All variables in the model have meaningful 0s, so the intercept should be interpretable.

glmmTMB::glmmTMB(comments_made ~ age_gm + gender + poc + time*taskgoal_gm + (1|id), data = engagelong_complete, ziformula = ~0, family = "nbinom2")

Questions:

1. I've limited training in interpreting the coefficients in nonlinear models but my understanding is that continuous main effects like age_gm (aside from the presence of the significant interaction) could be interpreted as: 1 unit change in Age is associated with a .13 change in the log-odds of the number of comments made, controlling for the other variables in the model. This would mean that a unit increase in Age is associated with a 100 x (exp(.13) - 1) = ~14% increase in the number of comments. Is this interpretation correct? How would a coefficient associated with a dichotomous variable like gender be interpreted?

2. How would the interaction term of time * taskgoal_gm = .017 be interpreted? My understanding is that the RR for this is calculated to be 1.02 but I'm not sure if we can say, like with Age, that a 1 unit change is associated with a (X)% increase in the DV. I've plotted the predicted values using ggeffects() package to try to visualize (see below) and this leaves me more confused. Are we essentially seeing that at higher values of taskgoal_gm the rate of decrease in the number of comments made over time is slower relative to other levels of the moderator variable?

Appreciate anyone's advice. Thank you.

Answer 1

This UCLA web page provides a good introduction to interpreting results from negative binomial models. The coefficients represent the change in the log of the number of counts per unit change in the predictor.

I'd recommend against reporting results as percentage changes. See Frank Harrell's post on "Why I Don't Like Percents.

Other than that, the interpretations are straightforward. An increase of 1 year of age leads to a factor of $\exp(0.133)=1.14$ change in the number of counts. The female/male comment ratio, other things equal, is $exp(0.83)=2.29$. You can think about a coefficient for a dichotomous predictor as being the association of outcome when only a change of 1 unit from baseline is allowed.

Interaction terms are tricky. They are the extra change in log of counts beyond what you would predict based on the individual coefficients for the interacting predictors. It's seldom helpful to try to interpret such an interaction on its own, particularly when two continuous predictors are involved. It's best instead to display and evaluate predictions at defined values of variables, as you have done with your plot. Tools from the emmeans package can help you evaluate the statistical significance of differences between scenarios, if that's important for your application.