# Lasso on Negative Binomial Regression Model

Is there anyway that I can perform LASSO with Negative Binomial Regression on R? I am performing a negative binomial regression on my dataset because the data are too dispersed to impose poisson regression. Meanwhile, I am also facing some multicollinearity problem. I already tried using glmnet with family = poisson, but the data is not fitting very well (for both alpha = 0 and alpha = 1).

EDIT: here is variance-covariance table of the negative binomial fit

       8.392729e+18  1.239178e+06  -3.624090e+05  1.896258e+17  -3.702521e+17
1.239178e+06  1.119052e-04   5.201989e-06 -1.877590e+05  -2.558095e+05
-3.624090e+05  5.201989e-06   5.179343e-06 -8.021543e+04  -1.436381e+05
1.896258e+17 -1.877590e+05  -8.021543e+04  2.193290e+17   6.413947e+16
-3.702521e+17 -2.558095e+05  -1.436381e+05  6.413947e+16   2.142183e+17


• I think you'll want to take this one to Stack Overflow. Dec 31, 2013 at 22:19
• To be honest, I'm not sure if this question will even be on-topic on SO; you may want to ask on the r-help listserv. Dec 31, 2013 at 23:13
• This question appears to be off-topic because it is about whether a particular analysis can be run in R. Dec 31, 2013 at 23:14
• it's also going to get hammered on SO because it's just a "how can I?" question, rather than a specific programming question ... Can you give a little more context? I would be tempted to do a quasi-Poisson fit (i.e., fit the model as a Poisson lasso, e.g. with the glmnet package, then make a post hoc adjustment to the standard errors of the parameters based on the estimated residual deviance ...) Dec 31, 2013 at 23:41
• Have you tried a quasipoisson model then? Based on the very vague description, I think your substantive problem probably has to do with a singularity issue. Show us what the vcov(fit) gives, fit being your glm object. Dec 31, 2013 at 23:59

LASSO and other penalized methods for negative binomial and zero-inflated negative binomial are provided by the mpath package in R, as has been noted on a more recent Cross Validated page. One answer on that page, however, indicates some difficulty in using mpath. A recent publication illustrates an application of the mpath package; a vignette in the R package reproduces the data analysis of that publication.