The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Smoothing Parameter and Model Selection for General Smooth Models
Open accessAbstract
This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.
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Cites
Regression Models and Life-Tables
Cox, D. R. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00899.x · Cited by 39,793
Random-Effects Models for Longitudinal Data
Laird, N. M., & Ware, J. H. (1982) · Biometrics · doi:10.2307/2529876 · Cited by 8,923
Kass, R. E., & Steffey, D. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478825 · Cited by 474 · cited 6×
“or for other inferential tasks. In reality smoothing parameters must be estimated, and the uncertainty associated with this has generally been ignored except in fully Bayesian simulation approaches. Kass and Steffey (1989) proposed a simple first order correct ion for this sort of uncertainty in the context of i.i.d. G…”
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Metadata
- Authors
- Wood, S. N., Pya, N., & Säfken, B.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2016-10-01
- Volume
- 111
- Issue
- 516
- Pages
- 1548-1563
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2593643174
- Cited by
- 1,312
- References
- 3
- FWCI
- 49.02
- Type
- journal article
- Language
- en
- Open access
- hybrid
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
