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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?).

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This is a topic which has been addressed in the context of logistic regression using dominance analysis, a useful relative importance approach.

Given that the only difference between Poisson and logit regression is the link and disribution, the results from the logit model should apply in a straightforward way to Poisson.

The only software I am familiar with to estimate such a model is in Stata currently. There is an R version which could accommodate, but I have yet to try this package out myself.

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