check.monotonicity {mokken}

Check of Monotonicity

Description

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.

Usage

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.

Value

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.

Author(s)

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

References

Junker, B.W., & Sijtsma, K. (2000). Latent and manifest monotonicity in item response models. Applied Psychological Measurement, 24, 65-81. 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. doi:10.18637/jss.v020.i11

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)