Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 24, Issue 1, Pages 183-204Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2014.889023
Keywords
Ordinal variable; Probit model; Lasso
Categories
Funding
- NSF [DMS-0805798, DMS-1106772, DMS-1159005, DMS-0748389]
- NIH [1RC1CA145444-0110, R01GM096194]
- Direct For Mathematical & Physical Scien [1106772, 1228164, 1159005] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1407698, 1545277] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1106772, 1228164, 1159005] Funding Source: National Science Foundation
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This article considers a graphical model for ordinal variables, where it is assumed that the data are generated by discretizing the marginal distributions of a latent multivariate Gaussian distribution. The relationships between these ordinal variables are then described by the underlying Gaussian graphical model and can be inferred by estimating the corresponding concentration matrix. Direct estimation of the model is computationally expensive, but an approximate EM-like algorithm is developed to provide an accurate estimate of the parameters at a fraction of the computational cost. Numerical evidence based on simulation studies shows the strong performance of the algorithm, which is also illustrated on datasets on movie ratings and an educational survey.
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