British Journal of Mathematical and Statistical Psychology

DeCarlo, Lawrence T.

doi: 10.1111/bmsp.70056pmid: 42249762

A model for multiple‐choice (MC) items based on signal detection theory (SDT), the MC‐SDT model (DeCarlo, 2021a), follows from assumptions about perceptual and decision processes involved when examinees choose alternatives for MC items. The model can be expressed as a hierarchical model with an ‘item‐level’, Level 1, and an ‘examinee‐level’, Level 2. Here it is shown that cognitive diagnosis models (CDMs) can also be viewed as consisting of two levels, with the MC‐SDT model serving as the first‐level model, whereas the second‐level model determines the type of CDM. Thus, the theory about how examinees make choices for MC items is unified across different CDMs. The resulting MC‐SDT‐CDM models are shown to be parsimonious sub‐models of MC‐CDMs. The models have straightforward interpretations (MC‐SDT at Level 1), avoid estimation problems, and are useful for small sample sizes. The models are illustrated with an application to MC items from the TIMSS 2007 4th grade exam.

Olvera Astivia, Oscar L.; Cheng, Yijun; Zumbo, Bruno D.

doi: 10.1111/bmsp.70055pmid: 42281395

Categorical structural equation models (cat‐SEM) typically rely on tetrachoric/polychoric correlations under a latent multivariate normality assumption. This can be generalized to an elliptical latent trait, whose radial symmetry justifies treating a single correlation parameter as the target of estimation. This article makes two contributions. First, it introduces an elliptical sieve estimator that profiles the latent correlation over a non‐parametric radial scale mixture. Simulations under a variety of latent elliptical densities show reduced pseudo‐likelihood bias and stable performance across realistic threshold schemes (including skewed floor/ceiling patterns), category numbers (3–5) and sample sizes typical of cat‐SEM. Second, an ordinal tail asymmetry test is proposed that uses checkerboard‐copula tail contrasts and a randomization reference distribution to diagnose violations of latent radial symmetry. For items with 4–5 categories and symmetric thresholds, or thresholds skewed in the same direction, the test maintains near‐nominal Type I error under elliptical densities, and achieves high power against non‐elliptical copulas. However, with binary items and with three‐category items whose thresholds are strongly asymmetric and oriented in opposite directions, Type I error inflates even under ellipticity. In such coarse, highly unbalanced designs, fully parametric latent‐copula models remain preferable to semiparametric ordinal diagnostics.

Cotugno, Lorenza; Rooij, Mark; Siciliano, Roberta

doi: 10.1111/bmsp.70057pmid: 42272067

In this paper, we introduce the Generalized Mixed Regularized Reduced Rank Regression model (GMR4), an extension of the GMR3 model designed to improve performance in high‐dimensional settings. GMR3 is a regression method for a mix of numeric, binary and ordinal response variables, while also allowing for mixed‐type predictors through optimal scaling. GMR4 extends this approach by incorporating regularization techniques, such as Ridge, Lasso, Group Lasso, or any combination thereof, making the model suitable for datasets with a large number of predictors or collinearity among them. In addition, we propose a cross‐validation procedure that enables the estimation of the rank S$$ S $$ and the penalty parameter λ$$ \lambda $$. Through a simulation study, we evaluate the performance of the model under different scenarios, varying the sample size, the number of non‐informative predictors and response dimension. The results of the simulation study guide the choice of the penalty parameter λ$$ \lambda $$ in the empirical application ISSP: Health and Healthcare I–II (2023), which includes mixed‐type predictors and ordinal responses. In this application, the model results in a sparse and interpretable solution, with a limited set of influential predictors that provide insights into public attitudes towards health care.