check.monotonicity function

Check of Monotonicity

Returns a list (of class monotonicity.class) with results from the investigation of monotonicity (Junker & Sijtsma, 2000; Mokken, 1971; Molenaar & Sijtsma, 2000; Sijtsma & Molenaar, 2002).

For two-level test data (clustered respondents) argument level.two.var exist, such that two lists are returned, containing the results for level 1 (person level) and level 2 (cluster level), respectively. Only method MIIO is implemented for two-level test data.

check.monotonicity(X, minvi = 0.03, minsize = default.minsize, level.two.var = NULL)

Arguments

• X: matrix or data frame of numeric data containing the responses of nrow(X) respondents to ncol(X) items. Missing values are not allowed
• minvi: minimum size of a violation that is reported
• minsize: minimum size of a rest score group. By default minsize = $N/10$ if $N \ge 500$; minsize = $N/5 if$ $250 \le N < 500$; and minsize = max$(N/3,50)$ if $N < 250$
• level.two.var: Add respondent-clustering variable to get results for Level 1 (person level) and Level 2 (cluster level; see Koopman et al., 2023a,b)

.

Details

The output is of class monotonicity.class, and is often numerous. Functions plot and summary can be used to summarize the output. See Van der Ark (2007) for an example.

Returns

• results: A list with as many components as there are items. Each component itself is also a list containing the results of the check of monotonicity.

• I.labels: The item labels

• Hi: The item scalability coefficients Hi

• m: The number of answer categories.

References

Junker, B.W., & Sijtsma, K. (2000). Latent and manifest monotonicity in item response models. Applied Psychological Measurement, 24, 65-81. tools:::Rd_expr_doi("10.1177/01466216000241004")

Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (2023a). Assumptions and Properties of Two-Level Nonparametric Item Response Theory Models. Manuscript submitted for publication.

Koopman, L., Zijlstra, B. J. H., & Van der Ark, L. A. (2023b). Evaluating Model Fit in Two-Level Mokken Scale Analysis. Manuscript submitted for publication.

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. tools:::Rd_expr_doi("10.18637/jss.v020.i11")

Author(s)

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

See Also

check.errors, check.iio, check.restscore, check.pmatrix, check.reliability, coefH, plot.monotonicity.class, summary.monotonicity.class

Examples

data(acl)
Communality <- acl[,1:10]
monotonicity.list <- check.monotonicity(Communality)
plot(monotonicity.list)
summary(monotonicity.list)

# Compute two-level fit statistics (Koopman et al., 2023a, 2023b)
data("autonomySupport")
dat <- autonomySupport[, -1]
groups <- autonomySupport[, 1]
autonomyMM <- check.monotonicity(dat, level.two.var = groups)
summary(autonomyMM)
plot(autonomyMM)