```
# NOT RUN {
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
## 1. center and scale predictors:
ss.CS <- transform(sleepstudy, Days=scale(Days))
fm1.CS <- update(fm1, data=ss.CS)
## 2. check singularity
isSingular(fm1)
## 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$derivs
## 4. restart the fit from the original value (or
## a slightly perturbed value):
fm1.restart <- update(fm1, start=pars)
## 5. try all available optimizers
fm1.all <- allFit(fm1)
ss <- summary(fm1.all)
ss$ fixef ## extract 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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