Drop the correlation bet. random effects to find those with small variance

I think this has been answered implicitly in some of the answers to your
other questions, but the bottom line is

The issue is the number of parameters compared to the amount of data /
information in that data. By setting the correlations to zero, you're
greatly reducing the number of parameters you have to estimate, which
leaves more information left over for estimating the other parameters.
This does impact shrinkage, but the resulting model fits are still
typically more stable (less variance across fits) than an
overparameterized model (less bias because you're not forcing any
parameter to a particular value).

In other words, it's an example of the bias-variance tradeoff. In other
words: it's often better to reduce model complexity, even at the cost of
real-world fidelity, in order to avoid overfitting.

Phillip

Dear All,

Bates, et al. (2015) <https://arxiv.org/pdf/1506.04967.pdf> mention that to
identify a mixed-model with a singular variance-covariance matrix we can:

Fit a zero correlation parameter which will identify random effects with
zero, or very small, variance

That is, going from `m0` to `m1` (see below). BUT, how come dropping all
correlations between slopes and intercepts can lead to identifying random
effects with zero, or very small, variance?

library(lme4)

dat <- read.csv('
https://raw.githubusercontent.com/WRobertLong/Stackexchange/master/data/singular.csv
')

m0 <- lmer(y ~ A * B * C + (A * B * C  | group), data = dat)
m1 <- lmer(y ~ A * B * C + (A * B * C || group), data = dat)

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