A Discussion on Quadrature for Latent Variable Models with Categorical Responses

• Activity Number: 72
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xiangxiang Meng*+ and Xinming An
• Companies: SAS Institute and SAS Institute
• Keywords: Gauss-Hermite quadrature ; adaptive quadrature ; generalized linear mixed model ; item response theory ; numerical integration

Abstract

The estimation in latent variable models with categorical responses, such as generalized linear mixed models (GLMM) and item response models (IRT), often involves integration that cannot be solved analytically. Numerous approaches have been proposed to tackle this problem, among which numerical integration, for example Gauss-Hermite quadrature, has proven to generate more accurate estimations as compared with other methods. G-H quadrature with 20 points per dimension is widely considered to be able to produce quality estimations. However, several researches have reported unstable or biased estimations even with more than 20 quadrature points per dimension under some special conditions, for example when the variances of latent variables are large. The objective of this research is to investigate when and why standard G-H quadrature will be inadequate even with a large number of quadrature