# Comparing importance of predictors in different datasets in GLM

I want to compare the importance or 'predictive power' of the same feature/covariate in 2 different datasets. Specifically let $$[\bf{y}_1,\bf{V}_1]$$ be my output & design matrix of dataset 1 & $$[\bf{y}_2,\bf{V}_2]$$ be the same for dataset 2.

I want to see if predictor X (which is a column of V) is more important in dataset 1 or 2.

To complicate matters:

1) X is expanded on a set of 10 basis functions, so $$\bf{X}$$ makes up columns 1-10 of $$\bf{V}$$.

2) y has other predictors besides X. Thus $$\bf{V}$$ has 22 columns, of which only the first 10 are $$\bf{X}$$

3) the output variable y is count data so I am doing Poisson regression (GLM with log link)

So far my thought is to compare the mean partial residuals (Pearson or Deviance) of $$\bf{r=y-Xc}$$ where c are the estimated coefficients of the columns of X. Then, I would conclude that the dataset with the lower mean residuals is the dataset where X is more important. Is this correct? One issue I see is if the mean of $$y_1$$ and $$y_2$$ are different (I would need a Poisson version of standardized coefficients?).