Combining EQ-5D-5L items into a level summary score: demonstrating feasibility using non-parametric item response theory using an international dataset

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.

A Mokken Scale Analysis of the Last Series of the Standard Progressive Matrices (SPM-LS)

Raven’s Standard Progressive Matrices (Raven 1941) is a widely used 60-item long measure of general mental ability. It was recently suggested that, for situations where taking this test is too time consuming, a shorter version, comprised of only the last series of the Standard Progressive Matrices (Myszkowski and Storme 2018) could be used, while preserving satisfactory psychometric properties (Garcia-Garzon et al. 2019; Myszkowski and Storme 2018). In this study, I argue, however, that some psychometric properties have been left aside by previous investigations. As part of this special issue on the reinvestigation of Myszkowski and Storme’s dataset, I propose to use the non-parametric Item Response Theory framework of Mokken Scale Analysis (Mokken 1971, 1997) and its current developments (Sijtsma and van der Ark 2017) to shed new light on the SPM-LS. Extending previous findings, this investigation indicated that the SPM-LS had satisfactory scalability ( H = 0.469 ), local independence and reliability ( M S = 0.841 , L C R C = 0.874 ). Further, all item response functions were monotonically increasing, and there was overall evidence for invariant item ordering ( H T = 0.475 ), supporting the Double Monotonicity Model (Mokken 1997). Item 1, however, appeared problematic in most analyses. I discuss the implications of these results, notably regarding whether to discard item 1, whether the SPM-LS sum scores can confidently be used to order persons, and whether the invariant item ordering of the SPM-LS allows to use a stopping rule to further shorten test administration.

Do Items Order? The Psychology in IRT Models

Invariant item ordering refers to the statement that if one item is harder than another for one person, then it is harder for all people. Whether item ordering holds is a psychological statement because it describes how people may qualitatively vary. Yet, modern item response theory (IRT) makes an a priori commitment to item ordering. The Rasch model, for example, posits that items must order. Conversely, the 2PL model posits that items never order. Needed is an IRT model where item ordering or its violation is a function of the data rather than an *a priori* commitment. We develop two-parameter shift-scale models for this purpose, and find that the two-parameter uniform offers many advantages. We show how item ordering may be assessed using Bayes factor model comparison, and discuss computational issues with shift-scale IRT models.