Basic random effect structures and non-convergence in lmer()

random-effects.R

library(lme4)
library(nlme)
library(ggplot2)

data(Oxboys)
head(Oxboys, 12)

ggplot(aes(y=height, x=age), data=Oxboys) +
    geom_point() + geom_path(aes(group=Subject))

## random intercepts only
m1 <- lmer(height ~ age + (1|Subject), data=Oxboys)

## uncorrelated random intercepts and random slopes
m2 <- lmer(height ~ age + (1|Subject) + (0+age|Subject), data=Oxboys)
## m2 <- lmer(height ~ age + (1+age||Subject), data=Oxboys) ## alt syntax for uncorr. slope/int. Note double "|".

## random intercepts, random slopes, and their correlation
m3 <- lmer(height ~ age + (1+age|Subject), data=Oxboys)

summary(m1)
summary(m2)
summary(m3)


## In our work, a major reason for using less than a maximal random effect structure is 
## the presence of convergence issues in models that include rich random effects. So, if 
## if a model with maximal raneff does not converge, our typical first step is to retry with 
## orthogonal slopes and intercepts (e.g., m2 above). If that fails, then we will try 
## different optimizers as proposed here 
## https://rstudio-pubs-static.s3.amazonaws.com/33653_57fc7b8e5d484c909b615d8633c01d51.html
## and here (pp14-15)
## https://rstudio-pubs-static.s3.amazonaws.com/33653_57fc7b8e5d484c909b615d8633c01d51.html
##
## In the second case, pay particular attention to this advice:
## "try all available optimizers (e.g. several different implementations of BOBYQA and 
## NelderMead, L-BFGS-B from optim, nlminb, . . . ) via the allFit() function, see ‘5.’ in 
## the examples. While this will of course be slow for large fits, we consider it the gold 
## standard; if all optimizers converge to values that are practically equivalent, then we 
## would consider the convergence warnings to be false positives."


## ** Sub-optimal random effects

## In LMMs, sub-optimal handling of random effects can lead to shrinking of SEs
## for fixed effects with the end result being increased liklihood of type 1
## error (Barr et al., 2013; Mirman, 2014, p62).