MLcoefZ function

Computation of Z-Values for two-level scalability coefficients

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")

Arguments

• X: 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
• lowerbound: 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.
• type.z: 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".

Returns

• Zij: matrix containing the Z-values of the item-pairs

• Zi: vector containing Z-values of the items

• Z: Z-value of the entire scale

Details

For the estimated item-pair coefficient $Hij$ with standard error $SE(Hij)$, the Z-score is computed as

if type.z = "WB", and the Z-score is computed as

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.

References

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")

Author(s)

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

L. Koopman

See Also

MLcoefH

Examples

data(SWMD)

# Compute the Z-score using lowerbound 0
MLcoefZ(SWMD)

# Using lowerbound .1
MLcoefZ(SWMD, lowerbound = .1)