Evaluate the proportional recovery rule with an artefact guard

Tests whether recovery follows the proportional recovery rule \(\Delta \approx p \,(\mathrm{max} - \mathrm{initial})\) (default \(p = 0.7\)), classifies fitters vs non-fitters, handles ceiling effects, and runs two diagnostics against the known statistical artefact: a mixture-vs-single-line comparison and a regression-to-the-mean (label-shuffle) control.

Usage

proportionalRecoveryRule(
  initial,
  followup,
  max_score,
  expected_prop = 0.7,
  fitter_tol = 0.2,
  ceiling_frac = 0.9,
  n_shuffle = 999,
  seed = NULL
)

Arguments

initial

Numeric baseline scores.

followup

Numeric follow-up scores (same length).

max_score

Scalar maximum attainable score (the recovery ceiling).

expected_prop

Expected recovery proportion (default 0.7).

fitter_tol

Half-width around expected_prop for a "fitter" (default 0.2).

ceiling_frac

Subjects with initial >= ceiling_frac * max_score are treated as ceiling cases (default 0.9) and excluded from the slope fit.

n_shuffle

Label-shuffles for the regression-to-the-mean control (default 999).

seed

Optional RNG seed.

Value

An AnalysisResult (type "proportional_recovery") whose result holds the fitted slope (+ CI and test vs expected_prop), per-subject classification, the mixture_preferred flag, and artefact_suspected.

Details

A genuine proportional rule implies the follow-up regresses on the initial score with slope \(1 - p\); a pure regression-to-the-mean / coupling artefact instead reproduces the \(\Delta\)-vs-potential slope when the follow-up scores are shuffled across subjects. When the observed slope is not distinguishable from that shuffled null, artefact_suspected is set.

References

Prabhakaran 2008; Winters 2015; Hawe, Scott & Dukelow 2019 (proportional-recovery artefact).

See also

recoveryTrajectoryLME(), latentClassGrowth()

Examples

set.seed(1)
init <- runif(60, 5, 55)
fu <- init + 0.7 * (66 - init) + rnorm(60, 0, 3)   # genuine 0.7 rule
proportionalRecoveryRule(init, fu, max_score = 66)
#> <AnalysisResult> proportional_recovery 
#>   estimate: 0.7098355 
#>   method: proportional_recovery_rule 
#>   fields: slope, slope_ci, expected_prop, p_vs_expected, followup_on_initial_slope, n, n_ceiling, n_fitter, classification, observed_prop, mixture_preferred, mixture_bic, shuffle_slope_ci, artefact_suspected