MLcoefZ {mokken}

Computation of Z-Values for two-level scalability coefficients

Description

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).

Usage

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".

Details

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.

Value

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

Author(s)

L. A. van der Ark [e-mail] L. Koopman

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) 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. doi:10.1007/978-3-030-74772-5_16

See Also

MLcoefH

Examples

data(SWMD)

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

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