An efficient adaptive dimension selection algorithm for multidimensional probit graded response models
2026-07-20 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of figuring out how many hidden traits (dimensions) underlie responses to ordinal questionnaires, such as those used in psychology. Instead of trying many fixed models and picking the best one afterward, they propose a Bayesian method that automatically decides the number of relevant dimensions during the model fitting process. Their approach uses a special prior that gradually shrinks unnecessary dimensions to zero, making the model simpler without losing important information. Through simulations and real data examples, the authors show their method can accurately find the true latent structure more efficiently than traditional approaches.
Multidimensional graded response modelOrdinal dataLatent dimensionsBayesian dimension selectionCumulative shrinkage processSpike-and-slab priorProbit modelAlbert–Chib augmentationGibbs samplingLatent trait models
Authors
Yu Zhou, Yincai Tang, Bin Lv, Meng Gao
Abstract
Multidimensional graded response models (MGRMs) are widely used for analyzing ordinal questionnaire data in psychological and educational assessments. A central challenge in applying these models is determining the number of latent dimensions. Conventional approaches usually fit multiple fixed-dimensional models and select among them using post-hoc criteria such as AIC, BIC, or cross-validation, which can be computationally demanding and ignore uncertainty in dimensionality during estimation. We develop an adaptive Bayesian dimension selection framework for probit MGRMs. Building on the cumulative shrinkage process, we assign a cumulative ordered spike-and-slab (COSS) prior to the column-specific variances of the item loading matrix. This prior induces increasing shrinkage across latent dimensions, allowing redundant dimensions to be shrunk toward zero while preserving flexibility for active dimensions. Albert--Chib latent response augmentation is used to handle the ordinal probit likelihood, yielding conditionally Gaussian updates for item loadings and latent traits. These updates are combined with Gibbs updates for threshold and shrinkage parameters in an efficient adaptive sampler. Simulation studies evaluate the proposed method in terms of dimension recovery, parameter estimation accuracy, and computational efficiency, with comparisons to conventional fixed-dimensional estimation and model selection procedures. The results show that the proposed approach accurately recovers the latent structure while avoiding repeated model fitting over multiple candidate dimensions. We further illustrate the method using real psychological assessment data, demonstrating its practical utility for uncovering interpretable latent structures in ordinal item responses.