alphaIRT

Predict coefficient alpha from a set of IRT parameters.

Description

Predicts coefficient alpha from a set of IRT parameters. If a data set X is provided, then an estimate of the standard error of sample coefficient alpha is also computed. For now, only the dichotomous three-parameter logistic model (3PLM) of IRT parameters, and the normal distribution with supplied mean and sd values, are supported.

Usage

alphaIRT(pars, X = NULL, mean = 0, sd = 1, MaydeuOlivares = FALSE)

Arguments

Argument	Description
pars	𝑘 × 3 matrix of item parameters for the 3PLM.
X	𝑁 × 𝑘 matrix of binary responses of 𝑁 examinees to 𝑘 items.
mean	Mean of the normal distribution of the population of trait values.
sd	Standard deviation of the normal distribution of the population of trait values.
MaydeuOlivares	If TRUE, then compute the standard error originally described by Maydeu-Olivares and Coffman (2007). This computation does not use item parameters.

Value

Returns a list containing some or all of the following objects:

• alpha — Classical Cronbach's alpha coefficient;
• alpha.IRT — IRT-based sample coefficient alpha;
• SE.IRT — IRT-based standard error of sample coefficient alpha;
• SE.MaydeuOlivares — Standard error originally described by Maydeu-Olivares and Coffman (2007).

References

Maydeu-Olivares, A. & Coffman, D. L. (2007). Asymptotically distribution-free (ADF) interval estimation of coefficient alpha. Psychological Methods, 12(2), 157–176. doi:10.1037/1082-989X.12.2.157