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Model-averaged confidence intervals for factorial experiments

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  • Fletcher, David
  • Dillingham, Peter W.

Abstract

We consider the coverage rate of model-averaged confidence intervals for the treatment means in a factorial experiment, when we use a normal linear model in the analysis. Model-averaging provides a useful compromise between using the full model (containing all main effects and interactions) and a "best model" obtained by some model-selection process. Use of the full model guarantees perfect coverage, whereas use of a best model is known to lead to narrow intervals with poor coverage. Model-averaging allows us to achieve good coverage using intervals that are also narrower than those from the full model. We compare four information criteria that might be used for model-averaging in this setting: AIC, AICc, and BIC. In this setting, if the full model is "truth", all the criteria will have perfect coverage rates asymptotically. We use simulation to assess the coverage rates and interval widths likely to be achieved by a confidence interval with a nominal coverage of 95%. Our results suggest that AIC performs best in terms of coverage rate; across a wide range of scenarios and replication levels, it consistently provides coverage rates within 1.5% points of the nominal level, while also leading to reductions in interval-width of up to 30%, compared to the full model. AICc performed worst overall, with a coverage rate that was up to 5.2% points too low. We recommend that model-averaging become standard practise when summarising the results of a factorial experiment in terms of the treatment means, and that AIC be used to perform the model-averaging.

Suggested Citation

  • Fletcher, David & Dillingham, Peter W., 2011. "Model-averaged confidence intervals for factorial experiments," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3041-3048, November.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:11:p:3041-3048
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    References listed on IDEAS

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    1. Paul Lukacs & Kenneth Burnham & David Anderson, 2010. "Model selection bias and Freedman’s paradox," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 117-125, February.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
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    4. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
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    Cited by:

    1. Paul Kabaila & A. H. Welsh & Waruni Abeysekera, 2016. "Model-Averaged Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 35-48, March.
    2. Shaobo Jin & Sebastian Ankargren, 2019. "Frequentist Model Averaging in Structural Equation Modelling," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 84-104, March.
    3. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
    4. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.
    5. Turek, Daniel & Fletcher, David, 2012. "Model-averaged Wald confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2809-2815.
    6. Jiaxu Zeng & David Fletcher & Peter W Dillingham & Christopher E Cornwall, 2019. "Studentized bootstrap model-averaged tail area intervals," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-16, March.
    7. Shaobo Jin, 2022. "Frequentist Model Averaging in Structure Equation Model With Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1130-1145, September.

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