emreliability (version 1.0.0)

rel_test: Test Reliability and CSEMs for IRT Scores

Description

Compute test reliability for raw scores (and optionally scale scores), along with associated conditional standard errors of measurement (CSEMs), for a unidimensional IRT model.

Usage

rel_test(ip, ct = NULL, nq = 11, D = 1.702)

Value

A list with three components:

fx

A data frame containing the estimated marginal score distribution for raw scores (and scale scores if ct is provided).

rel

A data frame with overall error variance, true score variance, observed score variance, and reliability for raw scores, and additionally for scale scores if ct is provided.

csem

A data frame with theta, weights, expected raw scores and corresponding CSEMs. If ct is provided, expected scale scores and scale-score CSEMs are also included.

Arguments

ip

A data frame or matrix of item parameters. Columns are interpreted in order as:

• 3 columns: b, a, c (3PL; a on the D metric),

• 2 columns: b, a (2PL; c internally set to 0),

• 1 column: b (1PL/Rasch; a = 1, c = 0).

ct

Optional. A data frame or matrix containing the score conversion table. If supplied, it must have ni + 1 rows (for raw scores 0:ni) and a column named ss giving the corresponding scale scores. If ct = NULL (default), only raw-score reliability and CSEMs are computed.

nq

Integer. Number of quadrature points used to approximate the standard normal ability distribution. Defaults to 11.

D

Numeric. Scaling constant for the logistic IRT model. Defaults to 1.702.

Examples

data(ip.u)
data(ct.u)
rel_test(ip.u)
rel_test(ip.u, ct.u)