PCA of the random-effects covariance (lme4's rePCA())

For each grouping factor, the singular values and left singular vectors of the relative covariance factor (the block-diagonal Cholesky factor of the random-effect covariance divided by the residual variance, lme4's Lambda), returned as prcomp objects. Near-zero standard deviations flag a random-effect structure that is over-parameterised (singular). summary() gives each component's proportion of variance.

Usage

rePCA(x)

# Default S3 method
rePCA(x)

# S3 method for class 'mm_lmm'
rePCA(x)

# S3 method for class 'mm_glmm'
rePCA(x)

Arguments

x

A fitted mm_lmm or mm_glmm (for GLMM families without a dispersion parameter the covariance itself is used, as in lme4).

Value

An object of class c("mm_prcomplist", "prcomplist"): a named list (one entry per grouping factor) of prcomp objects.

Details

Singular values match lme4::rePCA(); the rotation columns are eigenvectors of the same matrix and may differ from lme4's in sign.

Examples

set.seed(1)
d <- data.frame(g = factor(rep(1:10, each = 6)), x = rep(0:5, 10))
d$y <- 1 + 0.5 * d$x + rnorm(10)[d$g] + rnorm(10, sd = 0.3)[d$g] * d$x +
  rnorm(60)
fit <- lmm(y ~ x + (x | g), d, control = mm_control(verbose = -1))
summary(rePCA(fit))
#> $g
#> Importance of components:
#>                          [,1]    [,2]
#> Standard deviation     1.0550 0.29653
#> Proportion of Variance 0.9268 0.07322
#> Cumulative Proportion  0.9268 1.00000
#>