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Purpose Mokken scale analysis (MSA) is an attractive scaling procedure for ordinal data. MSA is frequently used in health-related quality of life research. Two of MSA's prime features are the scalability coefficients and the automated item selection procedure (AISP). The AISP partitions a (large) set of items into scales based on the observed item scores; the resulting scales can be used as measurement instruments. There exist two issues in MSA: First, point estimates, standard errors, and test statistics for scalability coefficients are inappropriate for clustered item scores, which are omnipresent in quality of life research data. Second, the AISP insufficiently takes sampling fluctuation of Mokken’s scalability coefficients into account. Methods We solved both issues by providing point estimates and standard errors for the scalability coefficients for clustered data and by implementing a Wald-based significance test in the AISP algorithm, resulting in a test-guided AISP (T-AISP), that is available for both nonclustered and clustered test scores. Results We integrated the T-AISP into a two-step, test-guided MSA for scale construction, to guide the analysis for nonclustered and clustered data. The first step is performing a T-AISP and select the final scale( s ). For clustered data, within-group dependency is investigated on the final scale(s). In the second step, the strength of the scale(s) is determined and further analyses are performed. The procedure was demonstrated on clustered item scores obtained from administering a questionnaire on quality of life in schools to 639 students nested in 30 classrooms. Conclusions We developed a two-step, test-guided MSA for scale construction that takes into account sample fluctuation of all scalability coefficients and that can be applied to item scores obtained by a nonclustered or clustered sampling design.

Purpose In Mokken scaling, the Crit index was proposed and is sometimes used as evidence (or lack thereof) of violations of some common model assumptions. The main goal of our study was twofold: To make the formulation of the Crit index explicit and accessible, and to investigate its distribution under various measurement conditions. Methods We conducted two simulation studies in the context of dichotomously scored item responses. We manipulated the type of assumption violation, the proportion of violating items, sample size, and quality. False positive rates and power to detect assumption violations were our main outcome variables. Furthermore, we used the Crit coefficient in a Mokken scale analysis to a set of responses to the General Health Questionnaire (GHQ-12), a self-administered questionnaire for assessing current mental health. Results We found that the false positive rates of Crit were close to the nominal rate in most conditions, and that power to detect misfit depended on the sample size, type of violation, and number of assumption-violating items. Overall, in small samples Crit lacked the power to detect misfit, and in larger samples power differed considerably depending on the type of violation and proportion of misfitting items. Furthermore, we also found in our empirical example that even in large samples the Crit index may fail to detect assumption violations. Discussion Even in large samples, the Crit coefficient showed limited usefulness for detecting moderate and severe violations of monotonicity. Our findings are relevant to researchers and practitioners who use Mokken scaling for scale and questionnaire construction and revision.

Background The EQ-5D-5L is a well-established health questionnaire that estimates health utilities by applying preference-based weights. Limited work has been done to examine alternative scoring approaches when utility weights are unavailable or inapplicable. We examined whether the Mokken scaling approach can elucidate 1) if the level summary score is appropriate for the EQ-5D-5L and 2) an interpretation of such a score. Methods The R package “mokken” was used to assess monotonicity (scaling coefficients H, automated item selection procedure) and manifest invariant item ordering (MIIO: paired item response functions [IRF], HT). We used a rich dataset (the Multiple Instrument Comparison, MIC) which includes EQ-5D-5L data from six Western countries. Results While all EQ-5D-5L items demonstrated monotonicity, the anxiety/depression (AD) item had weak scalability (Hi = 0.377). Without AD, scalability improved from Hs = 0.559 to Hs = 0.714. MIIO revealed that the 5 items can be ordered, and the ordering is moderately accurate in the MIC data (HT = 0.463). Excluding AD, HT improves to 0.743. Results were largely consistent across disease and country subgroups. Discussion The 5 items of the EQ-5D-5L form a moderate to strong Mokken scale, enabling persons to be ordered using the level summary score. Item ordering suggests that the lower range of the score represents mainly problems with pain and anxiety/depression, the mid-range indicates additional problems with mobility and usual activities, and middle to higher range of scores reveals additional limitations with self-care. Scalability and item ordering are even stronger when the anxiety/depression item is not included in the scale.

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering.