mokken (version 2.5.1)

check.reliability: Compaction of reliability statistics

Description

Returns a list of reliability statistics: Molenaar Sijtsma (MS, 1984, 1988) statistic (a.k.a rho), Cronbach's (1951) alpha, Guttman's (1945) lambda 2, and the latent class reliability coefficient (LCRC; Van der Ark, Van der Palm, and Sijtsma, 2011).

Usage

check.reliability(X, MS = TRUE, alpha = TRUE, lambda.2 = TRUE, LCRC = FALSE, nclass = nclass.default)

Arguments

X

matrix or data frame of numeric data containing the responses of nrow(X) respondents to ncol(X) items. Missing values are not allowed

MS

Boolean. If TRUE, The MS statistic is computed.

alpha

Boolean. If TRUE, Cronbach's alpha is computed.

lambda.2

Boolean. If TRUE, Guttman's Lambda 2 is computed.

LCRC

Boolean. If TRUE, the LCRC is computed.

nclass

Integer. Number of latent classes for the computation of LCRC. By default: half the number of items rounded to the nearest integer.

Value

• MS
  Molenaar Sijtsma statistic (a.k.a. rho).
• alpha
  Cronbach's alpha
• lambda.2
  Guttman's Lambda 2
• LCRC
  LCRC

Details

The computation of LCRC depends on the package poLCA, which in its turn depends on the packages MASS and scatterplot3d. Computation of the LCRC may be time consuming if the number of latent classes is large. The optimal number of latent classes should be determined prior to the computation of the LCRC, using software for latent class analysis (e.g., the R-package poLCA).

References

Cronbach, L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10,255-282. Molenaar, I. W. and K. Sijtsma (1984). Internal consistency and reliability in Mokken's nonparametric item response model. Tijdschrift voor onderwijsresearch, 9, 257--268. Molenaar, I. W. and K. Sijtsma (1988). Mokken's approach to reliability estimation extended to multicategory items. Kwantitatieve methoden, 9(28), 115-126. Sijtsma, K. and I. W. Molenaar (1987). Reliability of test scores in nonparametric item response theory. Psychometrika, 52,79-97. Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software. http://www.jstatsoft.org Van der Ark, L. A. (2010). Computation of the Molenaar Sijtsma statistic. In A. Fink, B. Lausen, W. Seidel, and A. Ultsch (Eds.), Advances in data analysis, data handling and business intelligence (pp. 775-784). Berlin: Springer. Van der Ark, L. A., Van der Palm, D. W., and Sijtsma (2011). A latent class approach to estimating test-score reliability. Applied Psychological Measurement.

See Also

coefH, check.iio, check.monotonicity, check.pmatrix, check.restscore

Examples

data(acl)
Communality <- acl[,1:10]
check.reliability(Communality, LCRC = TRUE)