mokken-package: Mokken Scale Analysis
In vandenman/mokken: Conducts Mokken Scale Analysis

Description Details Author(s) References Examples

Mokken scale analysis (Mokken, 1971; Sijtsma and Molenaar, 2002; Sijtsma and Van der Ark, 2017) is a scaling procedure for both dichotomous and polytomous items. It consists of an item selection algorithm to partition a set of items into Mokken scales and several methods to check the assumptions of two nonparametric item response theory models: the monotone homogeneity model and the double monotonicity model. The output of this R-package resembles the output of the stand-alone program MSP (Molenaar and Sijtsma, 2000).

Package:	mokken
Type:	Package
Version:	2.8.11
Date:	2018-06-03
License:	GPL Version 2 or later

The package contains principal functions for Mokken scale analysis.

The package contains the following data sets

`acl`	Scores on a personality checklist.
`cavalini`	Scores on an inventory on industrial malodor
`transreas`	Scores on a transitive reasoning test
`DS14`	Scores on a Type D test (bootstrap sample)

A guide for Mokken scale analysis in R for people who do not know R (Van der Ark, 2010) is available as a vignette from https://sites.google.com/a/tilburguniversity.edu/avdrark/mokken.

Thanks are due to Michael Allerhand, Don van den Berg, Geert H. van Kollenburg, Letty Koopman, Renske E. Kuijpers, Rudy Ligtvoet, Hannah E. M. Oosterhuis, J. Hendrik Straat, and Daniel W. van der Palm for contributing R code; to Don van den Bergh, Geert H. van Kollenburg, Letty Koopman, Rudy Ligtvoet, Patrick Mair, J. Hendrik Straat, and Don van Ravenswaaij for testing the software; to Wijbrandt van Schuur for comments on the vignette; to Michael Allerhand, Stephen Cubbellotti, Michael Dewey, Jasmin Durstin, Wilco H. M. Emons, Jue Huang, Michael Kubovy, Ivo Molenaar, Jonathan Rose, Tobias Schlaffer, Klaas Sijtsma, Iris Smits, Jia Jia Syu, Stefan Vermeent, Roger Watson, and Na Yang for reporting comments or bugs; to Diederick Stoel (ProfitWise) for financial support, to Harrie C. M. Vorst, Pierre Cavalini, and Johan Denollet for permission to use their data; to Robert J. Mokken for lending his last name.

Version 0 was introduced in Van der Ark (2007). It included the functions

`coefH`	Scalability coefficients
`coefZ`	Test statistics for scalability coefficients
`check.monotonicity`	Investigate monotonicity assumptions
`check.restscore`	Investigate nonintersection assumption using Method Restscore
`check.pmatrix`	Investigate nonintersection assumption using Method Pmatrix
`search.normal`	Mokken's automated item selection algorithm

The following major modifications have been made.

`aisp`	More general automated item selection algorithm.
	Function `search` has become obsolete (Version 2.0)
`check.reliability`	Compute reliability coefficients (Version 2.0)
`check.iio`	Investigate invariant item orderings (Version 2.4)
`coefH`	Standard errors for scalability coefficients included (Version 2.6)

All updates until version 2.7 are described in Van der Ark (2012). The following modifications have been made in Version 2.7 in comparison to previous versions.

`check.errors`	Inclusion new function to compute weighted Guttman errors for each person.
`check.iio`	`plot` has been added.
`check.monotonicity`	Computation of number of active pairs for dichotomous items has been corrected.
`check.pmatrix`	Summary of the results has been corrected.
`check.restscore`	Code pertaining to IIO has been deleted. The procedure is now equivalent to MSP.
`coefH`	Option included to compare scalability coefficients across groups

The following modifications have been made in Version 2.7.1 in comparison to previous versions.

`mokken`	Some legal issues

The following modifications have been made in Version 2.7.2 in comparison to previous versions.

`check.iio`	Violations of IIO for dichotomous items are now tested using a z-test rather than a t-test.

The following modifications have been made in Version 2.7.3 in comparison to previous versions.

`plot.iio.class`	Confidence envelopes around estimated response functions
`plot.monotonicity.class`	Confidence envelopes around estimated response functions
`plot.restscore.class`	Confidence envelopes around estimated response functions

The following modifications have been made in Version 2.8.1 in comparison to previous versions.

`aisp`	Startsets have been added

The following modifications have been made in Version 2.8.2 in comparison to previous versions.

`recode`	New
`check.ca`	New
`check.norms`	New
`check.errors`	Outlier score O+ has been included

The following modifications have been made in Version 2.8.3 in comparison to previous versions.

`twoway`	New
`DS14`	New data set
`check.errors`	Outlier cutoff scores have been included

The following modifications have been made in Version 2.8.4 in comparison to previous versions.

`check.iio`	New code for computing HT for large samples

The following modifications have been made in Version 2.8.5 in comparison to previous versions.

`MLcoefH`	New code for computing two-level scalability coefficients and standard errors
`autonomySupport`	New two-level data set.

The following modifications have been made in Version 2.8.9 and 2.8.10 in comparison to previous versions.

`coefH`	Included possibility to include a fixed item-step order
`MLcoefH`	Code updated
`check.errors`	Code updated

The following modifications have been made in Version 2.8.11 in comparison to previous versions.

`plot`	The level of tranparancy of the plotted confidence intervals can be adjusted manually
`MLcoefH`	Code updated

The following modifications have been made in Version 2.8.12 in comparison to previous versions.

`check.monotonicity`	Z statistic adjusted (Molenaar & Sijtsma, 2000. p. 72 )
`check.norms`	Z Output corrected for `nice.output = FALSE`

The following modifications have been made in Version 2.9.0 in comparison to previous versions.

`coefH`	Z Solution of Koopman et al. (2017) implemented to solve the problem of equal item steps and code updated
`MLcoefH`	Z Solution of Koopman et al. (2017) implemented to solve the problem of equal item steps and code updated

L. Andries van der Ark Maintainer: L. Andries van der Ark <L.A.vanderArk@uva.nl>.

Mokken, R. J. (1971) A Theory and Procedure of Scale Analysis. Berlin, Germany: De Gruyter.

Molenaar, I.W. and Sijtsma, K. (2000) User's Manual MSP5 for Windows [Software manual]. Groningen, The Netherlands: IEC ProGAMMA.

Sijtsma, K., and Molenaar, I. W. (2002) Introduction to nonparametric item response theory. Thousand Oaks, CA: Sage.

Sijtsma, K., and Van der Ark, L. A. (2017). A tutorial on how to do a Mokken scale analysis on your test and questionnaire data. British Journal of Mathematical and Statistical Psychology, 70, 137-158. doi: 10.1111/bmsp.12078

Van der Ark, L. A. (2007). Mokken scale analysis in R. Journal of Statistical Software, 20(11), 1-19. http://www.jstatsoft.org/v20/i11

Van der Ark, L. A. (2010). Getting started with Mokken scale analysis in R. Unpublished manuscript. https://sites.google.com/a/tilburguniversity.edu/avdrark/mokken

Van der Ark, L. A. (2012). New developments in Mokken scale analysis in R. Journal of Statistical Software, 48(5), 1-27. http://www.jstatsoft.org/v48/i5

# Personality test
data(acl)               

# Select the items of the scale Communality
Communality <- acl[,1:10]

# Compute scalability coefficients
coefH(Communality)

# Investigate the assumption of monotonicity
monotonicity.list <- check.monotonicity(Communality)
summary(monotonicity.list)
plot(monotonicity.list)

# Investigate the assumption of non-intersecting ISRFs using method restscore
restscore.list <- check.restscore(Communality)
summary(restscore.list)
plot(restscore.list)

# Investigate the assumption of non-intersecting ISRFs using method pmatrix
pmatrix.list <- check.pmatrix(Communality)
summary(pmatrix.list)
plot(pmatrix.list)

# Investigate the assumption of IIO using method MIIO
iio.list <- check.iio(Communality)
summary(iio.list)
plot(iio.list)

# Compute the reliability of the scale
check.reliability(Communality)

# Partition the the scale into mokken scales
aisp(Communality)