Comment: Are Marginal Models Needed?

It is a pleasure to comment on three papers, where each provides substantial new work and each mentions marginal models in the title. The paper by Kuijpers, Van der Ark, and Croon (this volume, p. 42–69) presents developments in the construction of scales for categorical variables. A sequence of papers has been published in recent years in the psychometric literature on properties of this type of nonparametric scale construction for binary and polytomous items. The items here are the observed variables, each having the same number of categories or levels. A first program version for analyses was integrated several years ago into the computing environment R and updated recently by Van der Ark (2012). As a result, a well-written, thoughtful use of this type of analysis is, for instance, now available for health researchers, as discussed in Stochl, Jones, and Croudace (2012). The earliest discussions of these scales appear to be by Loevinger (1947) and the new result in the current paper is the derivation of standard errors for functions of simple correlation coefficients among the items. For these, Mokken (1971) had formulated several rules of thumb as guidelines to judge the quality of a scale. The assumptions for a Loevinger-Mokken scale build on many years of research in the area and may be summarized as

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