Can gam.vcomp be used to estimate partial deviance explained in a GAM with gaulss family?

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I am fitting a GAM using R package mgcv to estimate both a mean and SD:

b <- gam(list(Y ~ s(X1)+s(X2)+s(X3), ~ s(X1)+s(X2)+s(X3)),
         family=gaulss(), data=somedata)

Can I use the gam.vcomp() function to estimate the partial deviance explained, or at least the relative importance of each predictor?

If yes: As this is a special case modeling both mean and variance, how can I normalize relative importance? Do I have to do:

a <- gam.vcomp(b)
relative_importance <- a[ , 1] / sum(a[ , 1])

or do I have to split this for mean and variance components, i.e.:

a <- gam.vcomp(b)
mean_importance <- a[1:3, 1] / sum(a[1:3, 1])
sd_importance <- a[4:6, 1] / sum(a[4:6, 1])

as the variance components also have uncertainty given in the CI intervals, is there a robust test to apply to see if the difference in relative importance is statistically significant?

mgcv gam variance r
1 Answers

gam.vcomp returns the variance of the random effect. This random effect is like a random slope term, not a random intercept term. The partial deviance explained will thus depend both on the variance returned by gam.vcomp, as well as the variability of the predictor. This is similar to mixed-effect models, where the ICC is easy to compute if there are only random intercepts in the model, but not when there are random slopes.

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