Calculate scale-separation reliability

Calculate conventional SSR as 1 - mean(se^2) / stats::var(theta) and expose its variance components. The observed variance uses the sample denominator n - 1. Estimates and SEs must use the same scale and item order.

Usage

scale_separation_reliability(theta, se)

Arguments

theta

Real numeric vector of finite item estimates, with at least two entries and positive sample variance.

se

Real numeric vector of finite, nonnegative standard errors, in the same order and of the same length as theta. Names are not used to align the vectors.

Value

A list with observed_variance, mean_squared_se, true_score_variance (observed variance minus mean squared SE), ssr, n_items, n_finite, valid, and status. Successful calculations have valid = TRUE and status "ok" or "negative_true_score_variance". Invalid inputs or nonfinite calculated components raise an error; no items are dropped and no coefficient is returned for an undefined calculation.

Details

Negative SSR and negative estimated true-score variance are retained, not clipped. They indicate that mean squared uncertainty exceeds observed score variance. SSR depends on the estimator, its SE convention, and the estimated score variance; it is not an estimator-free measure of recovery or accuracy.

See also

fit_bt_model(), integrated CJ workflow

Other frequentist models: bootstrap_bt_model(), build_bt_data(), build_elo_data(), fit_bt_model(), fit_elo_model(), predict.pairwiseLLM_bt_alpha(), predict.pairwiseLLM_bt_firth(), predict.pairwiseLLM_bt_lapse(), summarize_bt_fit()

Examples

scale_separation_reliability(c(-1, 0, 1), c(0.2, 0.3, 0.4))
#> $observed_variance
#> [1] 1
#> 
#> $mean_squared_se
#> [1] 0.09666667
#> 
#> $true_score_variance
#> [1] 0.9033333
#> 
#> $ssr
#> [1] 0.9033333
#> 
#> $n_items
#> [1] 3
#> 
#> $n_finite
#> [1] 3
#> 
#> $valid
#> [1] TRUE
#> 
#> $status
#> [1] "ok"
#>