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Comparisons: Penalised criteria

This section contains references which compare various model selection criteria, in particular the penalised criteria, and which could thus be classified under several of Bayesian criteria, AIC and cross-validation. I have not yet moved all such articles into this section.

Sclove (1987) [333] Review of various penlized criteria and examples of their applications, particularly in multivariate analysis.

Zhang (1992) [395] Linear models with ordered candidate predictors, sigma2 known, true model a member of this set. Considers penalised criteria, and the distribution of the selected oreder and of the criterion at the selected order. Compared to `grouped' cross-validation. Suggestions on the choice of the penalty in practice. Diminishing returns from increasing penalty even when the true model is of finite order.

Wong (1994) [390] Three-way tables, especially considering whether association of two vary across leves of the third (group). Log-linear and related (e.g. unidiff and uniform association) models. Comparing L2, L2/df, R2L, BIC and AIC in a simulation. Interesting paper.

George and Foster (1997) [157] Subset selection in normal linear regression. Shows the equivalence between penalised criteria (Cp, AIC and BIC) and Bayesian posterior model probabilities with appropriate priors. Choice of the prior parameters. Suggests an empirical Bayes approach and a resulting selection criterion, which performs well in simulations.

Spigelhalter et al. (1998) [] Defines the `Deviance information criterion' (DIC) where fit is summarized by the posterior expectation of the deviance and complexity (effective number of parameters) as the expected deviance minus deviance at the the posterior expectation of the parameters, both calculated from MCMC output. Asymptotics, information-theoretic motivation and link to other criteria (especially AIC and NIC/TIC). Discussion of different selection criteria. Plenty of examples of DIC in different model types and applied examples. An interesting paper.


next up previous contents
Next: Significance Testing, Goodness-of-fit Tests Up: Model selection: general Previous: Model selection: general   Contents
Jouni Kuha 2003-07-16