The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
Conditional Akaike information for mixed-effects models
Abstract
This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, cAIC. The penalty term in cAIC is related to the effective degrees of freedom ρ for a linear mixed model proposed by Hodges & Sargent (2001); ρ reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The cAIC is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data application is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional AIC in model selection.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Model selection and multimodel inference: a practical information-theoretic approach.
Guthery, F. S., Burnham, K. P., & Anderson, D. R. (2003) · The Journal of Wildlife Management · doi:10.2307/3802723 · Cited by 41,495
Information Theory and an Extension of the Maximum Likelihood Principle
Akaike, H. (1998) · Springer Series in Statistics · doi:10.1007/978-1-4612-1694-0_15 · Cited by 17,781
Mixed-Effects Models in S and S-PLUS
(2001) · Technometrics · doi:10.1198/tech.2001.s574 · Cited by 9,278
Random-Effects Models for Longitudinal Data
Laird, N. M., & Ware, J. H. (1982) · Biometrics · doi:10.2307/2529876 · Cited by 8,923
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Brown, R. A., Hastie, T. J., & Tibshirani, R. J. (1991) · Biometrics · doi:10.2307/2532174 · Cited by 8,176
Regression and time series model selection in small samples
HURVICH, C. M., & TSAI, C.-L. (1989) · Biometrika · doi:10.1093/biomet/76.2.297 · Cited by 6,586
Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author)
Breiman, L. (2001) · Statistical Science · doi:10.1214/ss/1009213726 · Cited by 4,340
Flexible smoothing with B-splines and penalties
Eilers, P. H. C., & Marx, B. D. (1996) · Statistical Science · doi:10.1214/ss/1038425655 · Cited by 3,666
TESTING FOR SERIAL CORRELATION IN LEAST SQUARES REGRESSION. II
DURBIN, J., & WATSON, G. S. (1951) · Biometrika · doi:10.1093/biomet/38.1-2.159 · Cited by 3,619
Cited by
Fitting Linear Mixed-Effects Models Using lme4
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015) · Journal of Statistical Software · doi:10.18637/jss.v067.i01 · Cited by 86,835
Generalized linear mixed models: a practical guide for ecology and evolution
Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., & White, J.-S. S. (2009) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2008.10.008 · Cited by 8,910
A brief introduction to mixed effects modelling and multi-model inference in ecology
Harrison, X. A., Donaldson, L., Correa-Cano, M. E., Evans, J., Fisher, D. N., Goodwin, C. E. D., Robinson, B. S., Hodgson, D. J., & Inger, R. (2018) · PeerJ · doi:10.7717/peerj.4794 · Cited by 2,094
Dynamic Structural Equation Models
Asparouhov, T., Hamaker, E. L., & Muthén, B. (2018) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705511.2017.1406803 · Cited by 985
(2013) · Bayesian Data Analysis · doi:10.1201/b16018-21 · Cited by 631
Metadata
- Authors
- Vaida, F., & Blanchard, S.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 2005-06-01
- Volume
- 92
- Issue
- 2
- Pages
- 351-370
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2100128674
- Cited by
- 585
- References
- 23
- FWCI
- 13.11
- Type
- journal article
- Language
- en
- Open access
- closed
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.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Conditional Akaike information for mixed-effects models. https://app.cochat.ai/papers/10.1093/biomet/92.2.351
- The paper
- Vaida, F., & Blanchard, S. (2005). Conditional Akaike information for mixed-effects models. Biometrika. https://doi.org/10.1093/biomet/92.2.351
Data sources
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.
