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.

Sexual Sadism Among Sex Offenders in Switzerland

The Sexual Sadism Scale (SeSaS) was developed to assist in the diagnosis of sexual sadism, and it revealed adequate psychometric properties in prior research. This study cross validated the SeSaS in Switzerland using a sample of 179 male sex offenders. Specifically, the SeSaS conformed to a Mokken model of double monotonicity (scalability coefficient [ H] = .46, coefficient of reproducibility [CR] = .89), indicating that it measures a unidimensional construct of sexual sadism with hierarchically ordered items. The reliability of the scale was acceptable to high (ρ = .80, λ2 = .75, κ = .88). In addition, the SeSaS was strongly associated with sexual sadism diagnoses based on mental health manuals ( rpb = .60, odds ratio [OR] = 13.02, area under the curve [AUC] = 1) but not with recidivism. The results suggest that the use of the SeSaS may improve the validity and reliability of sexual sadism diagnoses, therefore playing a role in the assessment and management of sex offenders.

Application of the Double Monotonicity Model to Polytomous Items

This paper investigates the item scalability of the Beck Depression Inventory (BDI) in 252 subjects; 126 with and 126 without eating disorders. To do so, an order was established regarding the BDI items according to the clinical characteristics of the subjects with eating disorders. The nonparametric Item Response Theory (NIRT) model was applied to evaluate Monotone Homogeneity and Double Monotonicity of items, as well as the reliability of the scale in both groups. The results show that the order of the items is satisfied in the group with eating disorders, but not in the control group. Therefore, the results obtained allow the ordering of depression scores of subjects with eating disorders according to their clinical characteristics. This order is not valid for the depression scores of subjects who did not have eating disorders. It should be noted that the application of the Double Monotonicity model to polytomous items provides new and relevant information when compared to the data provided by the Classical Test Model. In addition, it is very useful for other items and subjects having certain characteristics.