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)
and possibly confidence intervals (Koopman, Zijlstra, & Van der Ark, 2020a, 2020b).
Mokken's coefficients and standard errors can also be estimated in two-level data (Koopman, Zijlstra, & Van der Ark, 2020a).
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). The estimated variance-covariance matrix of the coefficients
is invisible but can be printed by saving the result, see examples.
coefH(X, se = TRUE, ci = FALSE, nice.output = TRUE, level.two.var = NULL,
group.var = NULL, fixed.itemstep.order = NULL, type.ci = "WB",
results = TRUE)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
The confidence level between 0 and 1 of the range-preserving confidence intervals.
If FALSE (default), no confidence intervals are printed (Koopman, Zijlstra, & Van der Ark, 2020b).
Logical: If TRUE, scalability coefficients and standard errors are combined in an a single object of class noquote
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., 2020a.
vector of length nrow(X) or matrix with number of rows equal to nrow(X) to be used as grouping variable
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.
If WB, Wald-based confidence interval are printed, if RP range-preserving confidence intervals are printed (Koopman, Zijlstra, & Van der Ark, 2020b, 2020c). Default is WB. Used only if ci has been specified.
Logical: If TRUE results are printed to the screen. Option FALSE is useful only for some internal functions
scalability coefficients of the item pairs (possibly with standard errors; see details)
vector containing scalability coefficients of the items (possibly with standard errors; see details)
scalability coefficient of the entire scale (possibly with standard error; see details)
standard errors of the scalability coefficients of the item pairs (only if nice.output = FALSE and se = TRUE; see details)
standard errors of the scalability coefficients of the items (see details)
standard error of the scalability coefficient of the entire scale (see details)
confidence intervals of the scalability coefficients of the item pairs (only if nice.output = FALSE and/or se = TRUE; see details)
confidence intervals of the scalability coefficients of the items (see details)
confidence intervals of the scalability coefficient of the entire scale (see details)
Scalability coefficients for subgroups (see 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 ci is specified and se = TRUE or nice.output = FALSE, there is one additional matrix for the ci's of the Hij 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.
Koopman, L. Zijlstra, B. J. H, & Van der Ark, L. A. (2020a). A two-step, test-guided Mokken scale analysis for nonclustered and clustered data. Manuscript submitted for publication.
Koopman, L. Zijlstra, B. J. H, & Van der Ark, L. A. (2020b). Range-preserving confidence intervals for scalability coefficients in Mokken scale analysis. Manuscript in preparation.
Kuijpers, R. E., Van der Ark, L. A., & Croon, M. A. (2013). Standard errors and confidence intervals for scalability coefficients in Mokken scale analysis using marginal models. Sociological Methodology, 43, 42-69. https://doi.org/10.1177/0081175013481958
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. De Gruyter.
Molenaar, I.W., & Sijtsma, K. (2000) User's Manual MSP5 for Windows [Software manual]. IEC ProGAMMA.
Sijtsma, K., & Molenaar, I. W. (2002) Introduction to nonparametric item response theory. Sage.
Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software, 20 (11), 1-19. https://www.jstatsoft.org/article/view/v020i11
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., & Sijtsma (2008). Mokken scale analysis for dichotomous items using marginal models. Psychometrika, 73, 183-208. https://doi.org/10.1007/s11336-007-9034-z
# NOT RUN {
data(acl)
Communality <- acl[, 1:10]
# Compute scalability coefficients and standard errors
Hs <- coefH(Communality)
# Compute scalability coefficients, standard errors, and range-preserving confidence intervals
coefH(Communality, ci = .95)
# 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)
# Extract variance-covariance matrices
attributes(Hs)
Hs$covHij
Hs$covHi
Hs$covH
# Nested data:
data(autonomySupport)
scores <- autonomySupport[, -1]
classes <- autonomySupport[, 1]
coefH(scores, level.two.var = classes, ci = .95)
# }
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