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Marginal reliability of an item response theory scale

Source: R/subpop_psychometrics.R
morie_irt_marginal_reliability.Rd

\(1 - \bar{SE}^2 / \sigma^2_\theta\), the share of trait variance not attributable to measurement error, averaged over the trait distribution. Reporting this separately by group is the reliability counterpart of a DIF analysis: a scale can be adequately reliable in one group and not in another, and pooling conceals it.

Usage

morie_irt_marginal_reliability(se, var_theta = 1)

Arguments

se

Standard errors of the trait estimates, one per respondent.

var_theta

Variance of the trait in the population. Default 1, the usual identification convention.

Value

A single numeric reliability. Values at or below 0 indicate error variance at least as large as trait variance and are returned as such rather than truncated.

See also

morie_irt_theta_se, CttAlpha

Examples

morie_irt_marginal_reliability(c(0.3, 0.35, 0.4, 0.5))
#> [1] 0.844375