Comparing importance of smoothers and other covariates

[seananderson]

Question via email:

In the models that I am working on, I standardise the covariates to alleviate computational issues but also to be able to compare the effect strength of each covariate. I do extract the p-values to find which covariates are statistically significant (following Github instructions), but I would like to know which of these covariates are more important. While I can compare the coefficient estimates of non-smoothed covariates, the problem of course arises when I pass some of the used covariates as smoothers. Essentially, what I want to ask if there is a way to compare the strength and importance of smoothed versus non-smoothed covariates given that, as an end goal, I would like to know which covariates are more important than others.

[seananderson]

I was working on a version of an R2 statistic that could be relevant here. That's in a branch still. It's not quite finished and I can't guarantee there aren't bugs or flaws in logic at this point. If anyone wants to help me get that finished, I'd welcome help.

The basic idea is to compare how much variance is explained by the various parts of the model following the approach in the Nakagawa et al. papers as referenced. With respect to the smoothers, that part is here:

sdmTMB/R/r2.R

Line 131 in b845a14

varSmooths <- stats::var(r$eta_smooth_i)

You could always split that up by smoother (eta_smooth_i is the sum of all smoothers in link space).

In a more qualitative sense, you can look at how the predicted values change across a sequence of predictor values holding all other predictors at constant values. You can do that with linear or smoother terms. The R2 above is effectively doing that and taking the variance of the predictions. You could also do that plotting their predictions spatially if that's of interest.