gradient.check: how does it work?

[gerverska]

Hi folks!

It's mostly in the title, but I guess I was just trying to consult the documentation about what's going on when gradient.check = T.

As a follow-up question, is it inherently problematic to have a converged with large gradients (>0.05) warning? I'm currently in the process of fitting smaller and smaller reltol, and I keep getting the warning. It seems possible that some datasets could just have large gradients along LVs or covariates, right?

Here are the model details:

model <- gllvm(Y,
               family = 'tweedie',
               Power = NULL,
               num.lv = 2,
               offset = offset,
               gradient.check = T,
               control = list(reltol = 1e-25,
                              max.iter = 12000),
               control.start = list(n.init = 3))

[BertvanderVeen]

gradient.check uses the gradient, I.e. The vector of first derivatives to the likelihood, to check if the model has converged. At the maximum the surface is flat, so the gradient should be zero.

If the gradient is not zero (by some tolerance) for some parameters, the model has not properly converged. This can happen due to a variety of reasons, for example, due to a poor model fit in one way or another.

With many parameters it tends to be difficult to get the gradient for all parameters below some tolerance, and whether it really is problematic or not (in my experience) depends on the (number and type) of parameters that this applies to.

You can check with parameters are not playing nice by checking model$TMBfn$gr() while using the names from the model$TMBfn$par object.

Reltol values lower than machine accuracy as indicated in your post will not achieve anything.

[gerverska]

Excellent, this is good to hear. What do you think is triggering the gradient warning then? Are the ePower and sigmaLV terms capable of triggering the warning, or are the couple of stray gradient values from lambda and u the culprits? I guess I'm assuming that absolute values > 0.05 trigger the warning--is this actually the case, or are only positive values considered?

[BertvanderVeen]

Yes, absolute values.

[gerverska]

Gotcha, and what affects which parameters are included with model$TMBfn$gr() and model$TMBfn$par? Below is the figure whenever I changed the method to LA, and it seems some of the terms from before are no longer included.

[BertvanderVeen]

The VA method includes additional parameters for the approximation; in LA something similar happens but they are not (explicitly) available, and do not show up in the gradient.

[gerverska]

Thanks Bert!