Solved – Lasso on Negative Binomial Regression Model

generalized linear modelrregression

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

Best Answer

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.

Related Solutions

Solved – Selecting regression model for a non-negative integer response

Your model is fully saturated, because you have indicators for every possible combination of categories. As such you have correctly specified the conditional expectation.

Any MLE estimate based on a distribution in the linear exponential family is consistent when the conditional expectation is correctly specified. Therefore you can use Poisson or a number of other distributions.

As whuber implies though, this problem reduces to estimating means and testing for their differences, which could conveniently be done in a regression framework.

Solved – Overdispersed poisson or negative binomial regression

Instead of overdispersed (or quasi-)poisson regression you can use the NB1 distribution, which has the same linear variance function as ODP and a full-fledged likelihood function instead of the quasilikelihood of ODP. NB1 is implemented in the gamlss package as family=NBII, whereas regular Negative Binomial can be called through family=NBI. All credit for this part of the answer goes to @Achim Zeileis for helping me with a similar question here: Why is the Quasipoisson in glm not treated as a special case of Negative Binomial? , see his post for more info regarding NB/NB1 (and the confusing naming conventions).

Regarding ANOVA, I have not been able to find a built-in method for gamlss objects, but it is not hard to write your own implementation of the chi-squared test statistic. An example:

set.seed(123)
data = rNBII(100,mu = 6,sigma=0.5)  #generate NB1 data with mean mu=5 and variance (1+sigma)*mu = 9
h0 = gamlss(data~1,family=PO) #null model: poisson
h1 = gamlss(data~1,family=NBII) #alternative model: NB1/ODP

df = h1$df.fit - h0$df.fit
deviance = as.numeric(-2*logLik(h0) + 2*logLik(h1))
p.value = pchisq(deviance,df,lower.tail=F)
> p.value
[1] 0.01429169 #reject the null model at > 95% confidence

Best Answer

Related Solutions

Solved – Selecting regression model for a non-negative integer response

Solved – Overdispersed poisson or negative binomial regression

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