Hierarchical screening

A location and spread criterion whose centre and spread are shrunk towards the values pooled over all groups, rather than estimated from each group alone.

Usage

rule_hierarchical(
  n_sd = 2.5,
  n0 = 20,
  center = c("mean", "median"),
  scale = c("sd", "mad")
)

Arguments

n_sd

Multiplier applied to the shrunk spread.

n0

Trials at which a group is weighted equally between its own estimate and the pooled one. Larger values shrink harder. Inf gives one criterion for every group.

center

Location statistic, "mean" or "median".

scale

Spread statistic, "sd" or "mad".

Value

An object of class c("rtprep_rule_hierarchical", "rtprep_rule").

Details

Experimental. No published convention exists for it, so it has no conventional setting to cite, and it is not a recommendation.

A per-participant criterion is estimated from the very data it is meant to clean. A participant with a handful of very slow trials has a mean and a standard deviation pulled outward by exactly those trials, so the criterion widens to admit them: the more contaminated a participant is, the less their own criterion removes. Estimating one criterion for everyone instead trades that for a different error, since participants really do differ in speed and variability.

Shrinkage sits between the two. Each group's centre is w * centre_group + (1 - w) * centre_pooled with w = n / (n + n0), and its spread is shrunk the same way on the log scale, which keeps it positive. n0 is the number of trials at which a group is weighted equally between its own estimate and the pooled one: n0 = 0 gives each group its own criterion, exactly as rule_sd() under the same grouping, and n0 = Inf gives every group one common criterion. A group whose own spread cannot be computed pools completely, which is the case the method exists for.

Grouping

.by in rt_screen() names the units that are shrunk towards each other, normally participants. Everything in one call is pooled, so a .by that crosses participants with an experimental condition pools across conditions as well, and a condition that is genuinely slower drags every centre towards it. Screen one condition at a time.

See also

rules for the criteria estimated within each group.

Examples

rule_hierarchical()
#> <rtprep rule> hierarchical(2.5, n0 = 20, mean, sd) 
#>  Exclude trials more than 2.5 x sd from the mean, both shrunk towards the pooled value at n0 = 20 (experimental).

# what shrinkage changes, against the same criterion estimated per group
screen_compare(
  rt_example$rt,
  list(
    per_group = rule_mad(2.5),
    shrunk = rule_hierarchical(
      2.5,
      n0 = 20, center = "median", scale = "mad"
    )
  ),
  .by = rt_example$id
)
#> <rtprep comparison> 800 trials, 2 rules
#> 
#>   per_group                    dropped  11.0%
#>   shrunk                       dropped  11.0%
#> 
#>   least agreement: per_group vs shrunk, 100.0% of decisions (Jaccard 1.00)