ci.reliability {MBESS}R Documentation

Confidence Interval for a Reliability Coefficient

Description

A function to calculate the confidence interval for a reliability coefficient using the factor analytic approach or the normal theory approach.

Usage

ci.reliability(S = NULL, data = NULL, N=NULL, model = "True-Score Equivalent", type = "Factor Analytic", conf.level = .95)

Arguments

S symmetric covariance or correlation matrix
data the data set that the reliability coefficient is obtained from
N the total sample size
model the type of measurement model (e.g., "parallel items", "true-score equivalent", or "congeneric model") for a homogeneous single common factor test
type the type of method to base the formation of the confidence interval on, either the "Factor Analytic" (McDonald, 1999) or "Normal Theory" (van Zyl, Neudecker, & Nel, 2000)
conf.level the confidence level (i.e., 1-Type I error rate)

Details

This function calculates a reliability coefficient for a set of scores based on the measurement model chosen. Thus, coefficient alpha is calculated for parallel items and true-score equivalent; and coefficient omega is calculated for congeneric items. See McDonald (1999) for the assumptions of each of these models. Under the Normal Theory method the asymptotic distribution of the maximum likelihood estimator of coefficient alpha is used for the true-score equivalent model (van Zyl et al., 2000). Note that this model is not optimal for small samples (Yuan & Bentler, 2002), for instance with N<20.

Value

ci.lower the lower bound of the computed confidence interval
ci.upper the upper bound of the computed confidence interval
Estimated.reliability the estimated reliability coefficient
SE.reliability the standard error of the reliability coefficient
Conf.Level the confidence level (i.e., 1 - Type I error rate)

Author(s)

Keke Lai (University of Notre Dame); Leann J. Terry (Indiana University; ljterry@Indiana.Edu); Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

References

McDonald, R. P. (1999). Test theory: A unified approach. Mahwah, New Jersey: Lawrence Erlbaum Associates, Publishers.

van Zyl, J. M., Neudecker, H., & Nel, D. G. (2000) On the distribution of the maximum likelihood estimator of Cronbach's alpha. Psychometrika, 65 (3), 271-280.

Yuan, K. & Bentler, P. M. (2002) On robustness of the normal-theory based asymptotic distributions of three reliability coefficient estimates. Psychometrika, 67 (2), 251-259.

See Also

CFA.1; sem

Examples

# library(sem)

## Forming a hypothetical population covariance matrix
# Pop.Cov.Mat <- matrix(.3, 9, 9)
# diag(Pop.Cov.Mat) <- 1

# ci.reliability(S=Pop.Cov.Mat, N=50, model="True-Score", type="Normal Theory")

[Package MBESS version 2.0.0 Index]