conditional_moments: Conditional moments of scores

In mcbeem/giftedCalcs: Psychometrics for Gifted Program Identification

Conditional moments of scores

Description

This function calculates the conditional mean and variance of scores. The user specifies a value for the confirmatory test true score, the confirmatory test observed score, or the nomination observed score. The moments of the conditional distribution of the other two scores are calculated.

Usage

conditional_moments(t.true = NA, n.obs = NA, t.obs = NA, relyt, valid = 1e-07)

Arguments

t.true	The confirmatory test true score on a standardized (z-score) metric. Only one of t.true, t.obs, or n.obs should be specified
n.obs	The nomination observed score on a standardized (z-score) metric. If n.obs is specified, a value for valid must also be given.
t.obs	The confirmatory test observed score on a standardized (z-score) metric.
relyt	Confirmatory test reliability coefficient. Range (0, 1). Must not be exactly 0 or 1.
valid	Nomination validity coefficient. Controls the relatedness of the nomination scores and the confirmatory test scores. Range (0, 1). Must not be exactly 0 or 1, and must be less than the square root of the test reliability. If provided, the two-stage version of the computation is performed. @return A list containing the following: conditional.mean: For one-stage systems, the mean of the confirmatory test scores. For two-stage systems, the mean vector of the bivariate normal distribution of the observed nomination and confirmatory test scores, in that order. conditional.cov: For one-stage systems, the variance of the observed confirmatory test scores. For two-stage systems, the covariance matrix of the bivariate normal distribution of the observed nomination and confirmatory test scores, in that order.

Details

In a two-stage identification system, there is a test true score, a test observed score, and a nomination observed score. (In principle there is also a nomination true score, but it is irrelevant and may be ignored). In a one-stage system, there is a test true score and observed score.

The joint distribution of these three variables is assumed to be multivariate normal. Therefore, the conditional distribution is also normal.

If the argument valid is supplied, the two-stage conditional moments are returned. Otherwise the one-stage moments are returned.

Examples

# one-stage system
conditional_moments(t.true = 2, relyt = .9)

# two-stage system
conditional_moments(t.true = 2, relyt = .9, valid = .6)

mcbeem/giftedCalcs documentation built on May 3, 2022, 3:34 a.m.