What does warning in glmmTMB mean? "failed to invert Hessian from numDeriv"

Question

I am running a big GLMM with glmmTMB and am wondering what this warning means? I did not see any info about it in the package troubleshooting. Warning:

In finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old) : failed to invert Hessian from numDeriv::jacobian(), falling back to internal vcov estimate

Would it be bad to proceed and ignore this issue, proceeding with a drop1?

This large GLMM has quadratic terms and their interactions. Taking out some interactions and or/ terms helped solve this.

Answer 1

tl;dr drop1() should be fine, although this warning should alert you to the fact that the fit may be numerically unstable/computed standard errors may be unreliable.

There are (at least) two ways to compute the covariance matrix of the estimated coefficients (which is used to get the standard errors, p-values, etc. of the individual coefficients). In either case we have to estimate the Hessian, the matrix of second derivatives of the negative log-likelihood with respect to the parameters, then find its inverse.

Internally, the TMB package uses the base-R function optimHess(), which computes finite differences of the gradient function (see here). glmmTMB tries to use numDeriv::jacobian() instead, which uses Richardson extrapolation, which should in theory be more accurate.

The warning is saying that inverting the Hessian computed by numDeriv::jacobian() failed, and that the optimHess version is being used instead.

drop1() is using the likelihood ratio test to compare nested models; it is independent of the estimate of the covariance matrix.