I would like to carry out inference on a binomial LASSO model, but take into account the fact that my data are overdispersed and use the quasibinomial family instead.
selectiveInference, which does inference for LASSO models, only seems to support the binomial family though and not quasibinomial.
To get around this, I was wondering if it would be correct to adjust the z scores and p values returned by
fixedLassoInf called using
family="binomial" for overdispersion by dividing the z scores by the square root of the estimated dispersion coefficient of a quasibinomial GLM with the selected variables included? (or perhaps all variables included??)
Any thoughts if this would be a correct procedure? If it is, I was also wondering then how I should recalculate/adjust the returned confidence intervals? Any thoughts?
hdi, which has a similar aim, also doesn't support
quasibinomial, and I also couldn't readily see how that package could be interfaced with package
glmmLasso - if that would be possible then overdispersion could perhaps be taken into account using an observation-level random effect; if anyone would know how to do this then let me know too]
The output I had for my data right now was
fixedLassoInf(x, y, beta, lambda, family = "binomial", intercept=TRUE, alpha=0.1, type="partial") # Var Coef Z-score P-value LowConfPt UpConfPt LowTailArea UpTailArea # 2 2.596 10.710 0 2.194 2.995 0.048 0.050 # 3 1.224 16.400 0 1.101 1.348 0.049 0.050 # 5 2.608 17.219 0 2.356 2.857 0.049 0.050 # 7 0.776 10.588 0 0.655 0.897 0.048 0.050 # 8 -1.857 -5.103 0 1.229 2.462 0.050 0.048