coefH: Scalability coefficents H
In vandenman/mokken: Conducts Mokken Scale Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes item-pair scalability coefficents Hij, item scalability coefficents Hi, and scale scalability coefficent H (Loevinger, 1948; Mokken, 1971, pp. 148-153; Molenaar & Sijtsma, 2000, pp. 11-13; Sijtsma & Molenaar, chap. 4; Van der Ark, 2007; 2010), as well as their standard errors (Kuijpers, Van der Ark, & Croon, 2013; also see Van der Ark, Croon, & Sijtsma, 2008). Mokken's coefficients and standard errors can also be estimated in two-level data (Koopman, Zijlstra, & Van der Ark, 2020). It is also 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).

1	coefH(X, se = TRUE, nice.output = TRUE, level.two.var = NULL, group.var = NULL, fixed.itemstep.order = NULL)

`X`	matrix or data frame of numeric data containing the responses of `nrow(X)` respondents to `ncol(X)` items. Missing values are not allowed
`se`	Logical: If `TRUE`, the standard errors of the scalability coefficients are given
`level.two.var`	vector of length `nrow(X)` or matrix with number of rows equal to `nrow(X)` that indicates the level two variable for nested data to get appropriate standard errors (Koopman et al., 2020.
`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
`fixed.itemstep.order`	matrix with number of rows equal to the number of item steps (m) and number of columns equal to the number of items (J). The matrix should consis the integers 1 : (m * J), indicating a predefined order of the items steps with respect to popularity. Value 1 indicates the easiest (most popular) item step, value (m * J) indicates the most difficult item step.

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 level.two.var is not null the standard errors are adjusted to take the nesting into account. 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.

`Hij`	scalability coefficients of the item pairs (possibly with standard errors; see details)
`Hi`	vector containing scalability coefficients of the items (possibly with standard errors; see details)
`H`	scalability coefficient of the entire scale (possibly with standard error; see details)
`se.Hij`	standard errors of the scalability coefficients of the item pairs (only if `nice.output = FALSE` and `se = TRUE`; see details)
`se.Hi`	standard errors of the scalability coefficients of the items (see details)
`se.H`	standard error of the scalability coefficient of the entire scale (see details)
`Groups`	Scalability coefficients for subgroups (see details)

L. A. van der Ark L.A.vanderArk@uva.nl L. Koopman

Koopman, L. Zijlstra, B. J. H, & Van der Ark, L. A. (2020). A two-step procedure for scaling multilevel data using Mokken's scalability coefficients. Manuscript submitted for publication.

Kuijpers, R. E., Van der Ark, L. A., and Croon, M. A. (2013). Standard errors and confidence intervals for scalability coefficients in Mokken scale analysis using marginal models. Sociological Methodology, 43, 42-69.

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. https://sites.google.com/a/tilburguniversity.edu/avdrark/mokken

Van der Ark, L. A., Croon, M. A., and Sijtsma (2008). Mokken scale analysis for dichotomous items using marginal models. Psychometrika, 73, 183-208.

coefZ, search.normal

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

# Compute scalability coefficients and standard errors
coefH(Communality)

# Scalability coefficients but no standard errors
coefH(Communality, se=FALSE)

# Scalability coefficients for different groups:
subgroup <- ifelse(acl[,11] < 2,1,2)
coefH(Communality, group.var = subgroup)

# Nested data:
data(autonomySupport)
scores <- autonomySupport[, -1]
classes <- autonomySupport[, 1]
coefH(scores, level.two.var = classes)