# 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!

You can look at variance inflation factors (VIFs). VIFs measure the impact of multicollinearity on standard error estimates. You should be able to do this for any type of regression model including negative binomial regression using the equation found on wikipedia:

https://en.wikipedia.org/wiki/Variance_inflation_factor

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.

• Thanks, Alejandro! I don't think VIFs are available in SPSS for Generalized Linear Models but perhaps I could run the analysis as a linear regression and examine the VIFs there (without interpreting the rest of the analysis). I'm not so much worried about multicollinearity though as lower-level shared variance among the predictors. Is there anything that would quantify this shared variance more specifically, as well as the unique variance of the predictors? – madison Jun 24 '15 at 12:41
• 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