Over the past decade, Mokken scale analysis (MSA) has rapidly grown in popularity among researchers from many different research areas. This tutorial provides researchers with a set of techniques and a procedure for their application, such that the construction of scales that have superior measurement properties is further optimized, taking full advantage of the properties of MSA. First, we define the conceptual context of MSA, discuss the two item response theory (IRT) models that constitute the basis of MSA, and discuss how these models differ from other IRT models. Second, we discuss dos and don'ts for MSA; the don'ts include misunderstandings we have frequently encountered with researchers in our three decades of experience with real-data MSA. Third, we discuss a methodology for MSA on real data that consist of a sample of persons who have provided scores on a set of items that, depending on the composition of the item set, constitute the basis for one or more scales, and we use the methodology to analyse an example real-data set.

Investigating an invariant item ordering for polytomously scored itemsLigtvoet, R.; van der Ark, L.A.; Te Marvelde, J.M.; Sijtsma, K. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

This article first discusses a statistical test for investigating whether or not the pattern of missing scores in a respondent-by-item data matrix is random. Since this is an asymptotic test, we investigate whether it is useful in small but realistic sample sizes. Then, we discuss two known simple imputation methods, person mean (PM) and two-way (TW) imputation, and we propose two new imputation methods, response-function (RF) and mean response-function (MRF) imputation. These methods are based on few assumptions about the data structure. An empirical data example with simulated missing item scores shows that the new method RF was superior to the methods PM, TW, and MRF in recovering from incomplete data several statistical properties of the original complete data. Methods TW and RF are useful both when item score missingness is ignorable and nonignorable.

We explain why invariant item ordering (IIO) is an important property in non-cognitive measurement and we discuss that IIO cannot be easily generalized from dichotomous data to polytomous data, as some authors seem to suggest. Methods are discussed to investigate IIO for polytomous items and an empirical example shows how these methods can be used in practice.

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