# Commonality analysis in negative binomial regression?

I am new to negative binomial regression and am using Generalized Linear Models in SPSS to analyze some highly skewed count data (it is not zero inflated and the variance is much higher than the mean so I'm not using Poisson regression).

I'm interested in the extent to which shared variance among the predictors may be causing some predictors to be non-significant in the final model. My supervisor has used commonality analysis to address this in linear regression and I'm curious whether there is something comparable that I could use given that R square is not available for negative binomial regression. Any suggestions for SPSS or other programs? Thanks!

I haven't used SPSS in a long time, but in R there is the simple vif() function that you can apply to a regression model. Or you can use the above equation to calculate a variance inflation factor.
• You can always calculate the variance inflation factor for any particular regression coefficient ($\beta_j$) directly using: $VIF = \frac{1}{1-R^2}$ Where $R^2$ is the R-square value associated with an ordinary least squares model regressing $X_j$ on all other covariates in your data. You can also calculate the correlation between all variabels in your dataset to see if variables you have are highly correlated. Just a question when you say shared variance do you mean correlated? – Alejandro Ochoa Jun 25 '15 at 4:15