mokken (version 3.0.4)

MLcoefZ: 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, Zijlstra, & Van der Ark, 2020a). The test uses either Wald-based (WB) or range-preserving (RP) asymptotic theory (Koopman, Zijlstra, & Van der Ark, 2020b).

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, Van der Ark, Kroon, 2013; Koopman, Zijlstra, Van der Ark, 2020a); "RP": Range-preserving z-score, also based on the delta method (Koopman, Zijlstra, Van der Ark, 2020b). The default is "WB".

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

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, Zijlstra, Van der Ark, 2020b). 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. (2020a). A two-step procedure for scaling multilevel data using Mokken's scalability coefficients. 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 submitted for publication.

See Also

MLcoefH

Examples

# NOT RUN {
data(SWMD)

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

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