emreliability (version 1.0.0)

csem_binomial: CSEM and CSSEM with Binomial Model

Description

Compute the conditional standard error of measurement (CSEM) and conditional standard error of scaled scores (CSSEM) under the binomial model.

Usage

csem_binomial(ni, ct = NULL)

Value

A list with:

x

A vector of raw scores from 0 to ni.

csem

A vector of CSEM values (on the raw-score metric) for each raw score.

cssem

If ct is provided, a vector of CSSEM values for the scale scores corresponding to each raw score.

Arguments

ni

A single numeric value indicating the number of items.

ct

An optional data frame or matrix containing a conversion table with two columns: the first column as raw scores (0 to ni) and the second column as scale scores.

Details

Under the binomial model, for a test with \(n_i\) items and a true-score proportion \(\pi\), the distribution of raw scores is assumed to be \(\mathrm{Binomial}(n_i, \pi)\). This function treats each possible raw score \(k = 0, 1, \ldots, n_i\) as the true-score value (i.e., \(\pi_k = k / n_i\)) and computes:

• the CSEM of the raw scores; and

• if ct is provided, the CSSEM of the scale scores defined in the conversion table.

Examples

csem_binomial(40)
csem_binomial(40, ct.u)