Backward elimination of random and fixed effects (lmerTest's step())

step() for mm_lmm fits follows lmerTest::step(): it first removes random-effect terms one at a time while the least significant has p > alpha.random, then removes fixed-effect terms (respecting marginality: a term is only dropped when no higher-order term contains it) while the least significant has p > alpha.fixed, refitting after every removal.

Usage

# S3 method for class 'mm_lmm'
step(
  object,
  ddf = c("Satterthwaite", "Kenward-Roger"),
  alpha.random = 0.1,
  alpha.fixed = 0.05,
  reduce.fixed = TRUE,
  reduce.random = TRUE,
  keep,
  ...
)

Arguments

object: A fitted mm_lmm.
ddf: Denominator degrees of freedom for the fixed-effect F tests.
alpha.random, alpha.fixed: Elimination thresholds.
reduce.fixed, reduce.random: Whether to eliminate fixed / random terms.
keep: Character vector of fixed-effect terms never to remove.
...: Unused.

Value

An object of class mm_step with the elimination tables random and fixed and the final model in $model (also returned by lmerTest::get_model() when lmerTest is loaded).

Details

Differences from lmerTest, by design: random terms are tested with test_random_effect()'s boundary-corrected likelihood-ratio test (a chi-bar-square mixture, so p-values are about half of lmerTest's ranova() naive chi-square); only whole random terms are removed (lmerTest's ranova() also tries reducing (x | g) to (1 | g) – write the reduced term as its own term, e.g. (1 | g) + (0 + x | g), to make that reduction available); and the last random term is never removed (a model without random effects is not an LMM). Fixed terms are tested with test_effect() (ddf = "Satterthwaite" or "Kenward-Roger").

Examples

set.seed(1)
d <- data.frame(g = factor(rep(1:10, each = 6)), x = rep(0:5, 10),
                z = rnorm(60))
d$y <- 1 + 0.5 * d$x + rnorm(10)[d$g] + rnorm(60)
fit <- lmm(y ~ x + z + (1 | g) + (0 + x | g), d,
           control = mm_control(verbose = -1))
s <- step(fit)
s
#> Backward reduced random-effect table:
#>         term statistic   p_value                          method eliminated
#>  (0 + x | g) 0.4933364 0.2412214 boundary_lrt_self_liang_mixture          1
#> 
#> Backward reduced fixed-effect table (ddf: Satterthwaite):
#>  term num_df   den_df     F_value      p_value eliminated
#>     z      1 48.60119  0.03294079 8.567331e-01          1
#>     x      1 48.99997 49.89804401 5.282960e-09          0
#> 
#> Model found:
#> y ~ x + (1 | g)
s$model
#> Linear mixed model fit by REML
#> Formula: y ~ x + (1 | g)
#> Fit status: converged_interior
#> Optimizer: pattern_search; iterations: 24; objective: 170.46
#> nobs: 60, sigma: 0.793663, logLik: -85.2301
#> Fixed effects:
#> (Intercept)           x 
#>    1.677290    0.423798 
#> Audit verbs: audit(), diagnostics(), inference_table(), model_report()