coefH: Scalability coefficents H

Description

Computes item-pair scalability coefficents Hij, item scalability coefficents Hi, and scale scalability coefficent H (Loevinger, 1948; Mokken, 1971, pp. 148-153; Molenaar and Sijtsma, 2000, pp. 11-13; Sijtsma and Molenaar, chap. 4; Van der Ark, 2007; 2010), as well as their standard errors (Kuijpers, Van der Ark, and Croon, 2011; also see Van der Ark, Croon, and Sijtsma, 2008). It is possible to compare scalability coefficients across groups using the item-step ordering of the entire sample (cf. CHECK=GROUPS option in MSP; Molenaar and Sijtsma, 2000).

Usage

coefH(X, se = TRUE, nice.output = TRUE, group.var = NULL)

Arguments

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

Logical: If TRUE, the standard errors of the scalability coefficients are given

nice.output

Logical: If TRUE, scalability coefficients and standard errors are combined in an a single object of class noquote

group.var

vector of length nrow(X) or matrix with number of rows equal to nrow(X) to be used as grouping variable

Value

Hijscalability coefficients of the item pairs (possibly with standard errors; see details)
Hivector containing scalability coefficients of the items (possibly with standard errors; see details)
Hscalability coefficient of the entire scale (possibly with standard error; see details)
se.Hijstandard errors of the scalability coefficients of the item pairs (only if nice.output = FALSE and se = TRUE; see details)
se.Histandard errors of the scalability coefficients of the items (see details)
se.Hstandard error of the scalability coefficient of the entire scale (see details)
GroupsScalability coefficient for subgroups (see details)

Details

May not work if any of the item variances equals zero. Such items should not be used in a test and removed from the data frame. If nice.output = TRUE and se = TRUE, the result is a list of 3 objects of class noquote; if nice.output = FALSE and se = TRUE, the result is a list of 6 matrices (3 for the scalability coefficients and 3 for the standard errors); and if se = FALSE, the result is a list of 3 matrices (for the scalability coefficients. if group.var = Y with Y having K values, an additional element named Groups is added to the list. Element Groups shows the scalability coefficients per group ordered by means of sort (see Sys.getlocale for details). group.var returns coefficients for groups containing at least two case. Computation of standard errors can be slow for a combination of a large sample size and a large number of items.

References

Kuijpers, R. E., Van der Ark, L. A., and Croon, M. A. (2011). Standard errors and confidence intervals for scalability coefficients in Mokken scale analysis using marginal models. Manuscript submitted for publication. Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of `scale analysis' and factor analysis. Psychological Bulletin, 45, 507-530. Mokken, R. J. (1971) A Theory and Procedure of Scale Analysis. Berlin, Germany: De Gruyter. Molenaar, I.W. and Sijtsma, K. (2000) User's Manual MSP5 for Windows [Software manual]. Groningen, The Netherlands: IEC ProGAMMA. Sijtsma, K., and Molenaar, I. W. (2002) Introduction to nonparametric item response theory. Thousand Oaks, CA: Sage. Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software, 20 (11), 1-19. http://www.jstatsoft.org/v20/i11 Van der Ark, L. A. (2010). Getting started with Mokken scale analysis in R. Unpublished manuscript. http://cran.r-project.org/web/packages/mokken/vignettes/mokken.pdf Van der Ark, L. A., Croon, M. A., and Sijtsma (2008). Mokken scale analysis for dichotomous items using marginal models. Psychometrika, 73, 183-208.

Examples

Run this code

data(acl)
Communality <- acl[,1:10]
coefH(Communality)

coefH(Communality, se=FALSE)

subgroup <- ifelse(acl[,11] < 2,1,2)
coefH(Communality, group.var = subgroup)

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