Computes Zij-values of item pairs, Zi-values of items, and Z-value of the entire scale,
which are used to test whether Hij, Hi, and H, respectively (within- and between-rater versions),
are significantly greater a specified lowerbound using the delta method (Koopman et al., in press a).
The test uses either Wald-based (WB) or range-preserving (RP) asymptotic theory
(Koopman et al., in press b).
MLcoefZ(X, lowerbound = 0, type.z = "WB")
matrix containing the Z-values of the item-pairs
vector containing Z-values of the items
Z-value of the entire scale
matrix or data frame of numeric data
containing the responses of nrow(X) respondents to ncol(X) - 1 items.
The first column of X is assumed to be a subject column, see ?MLcoefH() for details.
Missing values are not allowed
Value of the null hypothesis to which the scalability are compared to compute the z-score (see details),
0 <= lowerbound < 1. The default is 0.
Indicates which type of z-score is computed: "WB": Wald-based z-score based on standard errors as approximated by the delta method (Kuijpers et al., 2013; Koopman et al., in press a); "RP": Range-preserving z-score, also based on the delta method (Koopman et al., in press b). The default is "WB".
L. A. van der Ark L.A.vanderArk@uva.nl L. Koopman
For the estimated item-pair coefficient \(Hij\) with standard error \(SE(Hij)\), the Z-score is computed as $$Zij = (Hij - lowerbound) / SE(Hij)$$
if type.z = "WB", and the Z-score is computed as $$Zij = -(log(1 - Hij) - log(1 - lowerbound)) / (SE(Hij) / (1 - Hij))$$ if type.z = "RP"
(Koopman et al., in press b). For the estimate item-scalability coefficients \(Hi\) and total-scalbility coefficients \(H\) a similar procedure
is used. Standard errors of the Z-scores are not provided.
Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (in press a). A two-step, test-guided Mokken scale analysis for nonclustered and clustered data. Quality of Life Research. (advanced online publication) tools:::Rd_expr_doi("10.1007/s11136-021-02840-2")
Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (in press b). Range-preserving confidence intervals and significance tests for scalability coefficients in Mokken scale analysis. In M. Wiberg, D. Molenaar, J. Gonzalez, & Kim, J.-S. (Eds.), Quantitative Psychology; The 1st Online Meeting of the Psychometric Society, 2020. Springer. tools:::Rd_expr_doi("10.1007/978-3-030-74772-5_16")
MLcoefH
data(SWMD)
# Compute the Z-score using lowerbound 0
MLcoefZ(SWMD)
# Using lowerbound .1
MLcoefZ(SWMD, lowerbound = .1)
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