Prediction via Orthogonalized Model Mixing
Abstract
We introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors. We focus on the choice of predictors in linear models, and mix over possible subsets of candidate predictors. Our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix. Advantages are both statistical and computational. Statistically, orthogonalization often leads to a reduction in the number of competing models by eliminating correlations. Computationally, large model spaces cannot be enumerated; recent approaches are based on sampling models with high posterior probability via Markov chains. Based on orthogonalization of the space of candidate predictors, we can approximate the posterior probabilities of models by products of predictor-specific terms. This leads to an importance sampling function for sampling directly from the joint distribution over the model space, without resorting to Markov chains. Compared to the latter, orthogonalized model mixing by importance sampling is faster in sampling models and is also more efficient in finding models that contribute significantly to the prediction. Further advantages are in the speed of convergence and the availability of more reliable convergence diagnostic tools. We illustrate these in practice, using a data set on prediction of crime rates. The model space is small enough so that enumeration of all models is available for comparison and convergence checks. Als…
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Orthogonalizing can reduce the number of competing plausible models.
“One advantage to this approach is that orthogonalizing can reduce the number of competing plausible models.”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Clyde, DeSimone and Parmigiani (1996)
When orthogonalized model mixing is appropriate, it can be much more efficient than MC3.
“When orthgonalized model mixing is appropriate, it can be muchmore efficient th an MC 3 .”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Clyde, DeSimone and Parmigiani (1996)
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Carvalho, C. M. (2006) · Cited by 6 · see citing works
Paddock, S. M. (2007) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/j.1467-9876.2007.00578.x · Cited by 5 · see citing works
Orthogonalizations and Prior Distributions for Orthogonalized Model Mixing
Clyde, M. A., & Parmigiani, G. (1996) · Springer eBooks · doi:10.1007/978-1-4612-2414-3_13 · Cited by 5 · see citing works
Self-citationFinite population estimators in stochastic search variable selection
Clyde, M. A., & Ghosh, J. (2012) · Biometrika · doi:10.1093/biomet/ass040 · Cited by 5 · see citing works
Self-citationEldomiaty, T. I., & Ismail, M. A. (2006) · Advanced in quantitative analysis of finance and accounting · doi:10.1142/9789812772824_0008 · Cited by 5 · see citing works
Jointness of Determinants of Economics GrowthPreprint
Doppelhofer, G., Martín, X. S. I., & Weeks, M. (2005) · RePEc: Research Papers in Economics · Cited by 5 · see citing works
- Authors
- Clyde, M., Desimone, H., & Parmigiani, G.
- Affiliations
- Duke University (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1996-09
- Volume
- 91
- Issue
- 435
- Pages
- 1197-1208
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2033149996
- Cited by
- 145
- References
- 32
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 3 · 2023: 1 · 2022: 3 · 2021: 4 · 2020: 1 · 2019: 2 · 2018: 8 · 2017: 1 · 2016: 5 · 2015: 4 · 2014: 6 · 2013: 3 · 2012: 9
- FWCI
- 4.47
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- orthogonalization, correlated predictors, model selection, importance sampling, posterior model probabilities, linear models, model space exploration, prediction intervals, crime rate prediction, storage conditions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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