# Is it acceptable to use a relative gradient because of convergence failure in LMER/GLMER?

My research suggests that when an LMER/GLMER fails to converge due to a too-large deviance gradient...

e.g., Model failed to converge with max|grad| = 0.00297196 (tol = 0.001, component 1)

1. You should be worried.
2. Everything possible should be done to examine the data for problems and question your assumptions (i.e., get to the root of the problem), as outlined here.
3. As somewhat of a last resort, you can check the relative gradient, which has been updated here (since the changelog entry linked above) to include the Choleski Factorization e.g.,
relgrad <- with(model@optinfo\$derivs,solve(chol(Hessian),gradient)) max(abs(relgrad))

Assuming you have done a lot of work at step 2, switching to a relative gradient to solve this problem still seems post-hoc if it is motivated by convergence failure under the max|grad| framework.

I'm looking for any advice or citations you can provide that describe the conditions that could a priori motivate the calculation and use of a relative gradient as above.

With some more digging, I found that the proposal to include a relative gradient as above was not incorporated into lme4 and instead a help page ?convergence was included that suggests to use many optimizers and compare the result, which is great, but it doesn't address my main question:

Are there circumstances where it is acceptable to calculate the relative gradient as above, or, is this approach outdated/ill-advised?

Second, (and if the relative gradient is useful) when the relative gradient and the lme4 stock max|grad| results diverge, what clues might this provide to resolve the issue on the data side?