check.reliability {mokken}

Computation of reliability statistics

Description

Returns a list of reliability statistics: Molenaar Sijtsma (MS, 1984, 1988) statistic (a.k.a rho; also see, Sijtsma & Molenaar, 1987; Van der Ark, 2010), Cronbach's (1951) alpha, Guttman's (1945) lambda 2, and the latent class reliability coefficient (LCRC; Van der Ark, Van der Palm, & Sijtsma, 2011).

Usage

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

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: the number of items minus 1.

irc

Boolean.If TRUE, the item-rest correlation (a.k.a. corrected item-total correlation) is computed.

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).

Value

MS

Molenaar Sijtsma statistic (a.k.a. rho).

alpha

Cronbach's alpha

lambda.2

Guttman's Lambda 2

LCRC

LCRC

Author(s)

L. A. van der Ark [e-mail]

References

Cronbach, L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. doi:10.1007/BF02310555

Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10,255-282. doi:10.1007/BF02288892

Molenaar, I. W., & Sijtsma, K. (1984). Internal consistency and reliability in Mokken's nonparametric item response model. Tijdschrift voor onderwijsresearch, 9, 257–268. Retrieved from https://pure.uvt.nl/ws/portalfiles/portal/1030704/INTERNAL.PDF

Molenaar, I. W., & Sijtsma, K. (1988). Mokken's approach to reliability estimation extended to multicategory items. Kwantitatieve methoden, 9(28), 115-126. Retrieved from https://pure.uvt.nl/ws/portalfiles/portal/1030575/MOKKEN__.PDF

Sijtsma, K., & Molenaar, I. W. (1987). Reliability of test scores in nonparametric item response theory. Psychometrika, 52,79-97. doi:10.1007/BF02293957

Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software. doi:10.18637/jss.v020.i11

Van der Ark, L. A. (2010). Computation of the Molenaar Sijtsma statistic. In A. Fink, B. Lausen, W. Seidel, & A. Ultsch (Eds.), Advances in data analysis, data handling and business intelligence (pp. 775-784). Springer. doi:10.1007/978-3-642-01044-6_7

Van der Ark, L. A., Van der Palm, D. W., & Sijtsma, K. (2011). A latent class approach to estimating test-score reliability. Applied Psychological Measurement, 35, 380-392. doi:10.1177/0146621610392911

Van der Palm, D. W., Van der Ark, L. A. & Sijtsma, K. (2014). A flexible latent class approach to estimating test-score reliability. Journal of Educational Measurement, 51, 339-357. doi:10.1111/jedm.12053

See Also

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

Examples

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