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



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.

Source : Link , Question Author : Jin-Dominique , Answer Author : Community

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