```
if (interactive()) {
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
## 1. decrease stopping tolerances
strict_tol <- lmerControl(optCtrl=list(xtol_abs=1e-8, ftol_abs=1e-8))
if (all(fm1@optinfo$optimizer=="nloptwrap")) {
fm1.tol <- update(fm1, control=strict_tol)
}
## 2. center and scale predictors:
ss.CS <- transform(sleepstudy, Days=scale(Days))
fm1.CS <- update(fm1, data=ss.CS)
## 3. recompute gradient and Hessian with Richardson extrapolation
devfun <- update(fm1, devFunOnly=TRUE)
if (isLMM(fm1)) {
pars <- getME(fm1,"theta")
} else {
## GLMM: requires both random and fixed parameters
pars <- getME(fm1, c("theta","fixef"))
}
if (require("numDeriv")) {
cat("hess:\n"); print(hess <- hessian(devfun, unlist(pars)))
cat("grad:\n"); print(grad <- grad(devfun, unlist(pars)))
cat("scaled gradient:\n")
print(scgrad <- solve(chol(hess), grad))
}
## compare with internal calculations:
fm1@optinfo$derivs
## compute reciprocal condition number of Hessian
H <- fm1@optinfo$derivs$Hessian
Matrix::rcond(H)
## 4. restart the fit from the original value (or
## a slightly perturbed value):
fm1.restart <- update(fm1, start=pars)
set.seed(101)
pars_x <- runif(length(pars),pars/1.01,pars*1.01)
fm1.restart2 <- update(fm1, start=pars_x,
control=strict_tol)
## 5. try all available optimizers
fm1.all <- allFit(fm1)
ss <- summary(fm1.all)
ss$ fixef ## fixed effects
ss$ llik ## log-likelihoods
ss$ sdcor ## SDs and correlations
ss$ theta ## Cholesky factors
ss$ which.OK ## which fits worked
}
```

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