Simulates posterior distributions of parameters from a two-level normal model with heterogeneous within-cluster variances (Kasim and Raudenbush, 1998). Imputations can be drawn as an extra step to the algorithm.
kr(y, x, g, control, seed, na.action)Vector with outcome value
Matrix with predictor value
Vector with group values
A list with elements:
model: Correlation model: "argyle", "cole" or "none"
runin: Number of run-in iterations
ndraws: Number of parameter draws
par_skip: Number of iterations to next parameter draw
imp_skip: Number of iterations to next outcome draw
Seed number for base::set.seed(). Use NA to bypass
seed setting.
Not really used here
A list with components:
* `beta` Fixed effects * `omega` Variance-covariance of random effects * `sigma2_j` Residual variance per group * `sigma2` Average residual variance * `draws` A matrix with `ndraw` columns with draws for missing data
The calculation time of lme4::lmer() rapidly increases with the
number of random effects. More than 10 random effects (knots)
takes significant time, and beyond 15 knots generally impossible
to fit.
In contrast, the speed of the Kasim-Raudenbush sampler is almost
independent of the number of random effect, and foremost depends
on the total number of iterations: runin + ndraws * par_skip.
The defaults ndraws = 200 and par_skip = 1 provides a good
approximation to the variance-covariance matrix of the random
effects. Increase par_skip to 10 (better) or 20 (best) to
obtain closer approximations at the expense of a linear
increase in calculation time. Setting ndraws = 50 (or lower)
will reduce computation time, but the result should be treated as
indicative.
It is possible to subsample the parameter draws at every
imp_skip iteration, and draw one or more synthetic outcome values
from the posterior distribution of the outcome. The number of
multiple imputations is equal to floor(ndraws / imp_skip). Thus,
setting imp_skip = 20L returns 200 / 20 = 10 multiple
imputations for each missing value in the outcome. The default does
not produce imputations.
Kasim RM, Raudenbush SW. (1998). Application of Gibbs sampling to nested variance components models with heterogeneous within-group variance. Journal of Educational and Behavioral Statistics, 23(2), 93--116.