Model-averaging is commonly used as a means of allowing for model uncertainty in parameter estimation. In the frequentist framework, a model-averaged estimate of a parameter is the weighted mean of the estimates from each of the candidate models, the weights typically being chosen using an information criterion. Current methods for calculating a model-averaged confidence interval assume approximate normality of the model-averaged estimate, i.e., they are Wald intervals. As in the single-model setting, we might improve the coverage performance of this interval by a one-to-one transformation of the parameter, obtaining a Wald interval, and then back-transforming the endpoints. However, a transformation that works in the single-model setting may not when model-averaging, due to the weighting and the need to estimate the weights. In the single-model setting, a natural alternative is to use a profile likelihood interval, which generally provides better coverage than a Wald interval. We propose a method for model-averaging a set of single-model profile likelihood intervals, making use of the link between profile likelihood intervals and Bayesian credible intervals. We illustrate its use in an example involving negative binomial regression, and perform two simulation studies to compare its coverage properties with the existing Wald intervals.
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Brown, L., Cai, T., and DasGupta, A. (2003), “Interval Estimation in Exponential Families,'' Statistica Sinica, 13 (1), 19–50.
Buckland, S. T., Burnham, K. P., and Augustin, N. H. (1997), “Model Selection: An Integral Part of Inference,'' Biometrics, 53 (2), 603–618.
Burnham, K., and Anderson, D. (2004), “Multimodel Inference,'' Sociological Methods & Research, 33, 261–304.
Burnham, K. P., and Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), New York: Springer.
Chatfield, C. (1995), “Model Uncertainty, Data Mining and Statistical Inference,'' Journal of the Royal Statistical Society. Series A. Statistics in Society, 158 (3), 419–466.
Claeskens, G., and Hjort, N. L. (2008), Model Selection and Model Averaging. Cambridge Series on Statistical and Probabilistic Mathematics, Vol. 27. Cambridge: Cambridge University Press, xvii, 312.
Cox, D., and Hinkley, D. (1974), Theoretical Statistics, London: Chapman and Hall.
Draper, D. (1995). “Assessment and Propagation of Model Uncertainty.'' Journal of the Royal Statistical Society. Series B. Methodological, 45–97.
Fletcher, D., MacKenzie, D., and Villouta, E. (2005), “Modelling Skewed Data With Many Zeros: A Simple Approach Combining Ordinary and Logistic Regression,'' Environmental and Ecological Statistics, 12 (1), 45–54.
Hjort, N. L., and Claeskens, G. (2003), “Frequentist Model Average Estimators,'' Journal of the American Statistical Association, 98 (464), 879–899.
Hoeting, J., Madigan, D., Raftery, A., and Volinsky, C. (1999), “Bayesian Model Averaging: A Tutorial,'' (with comments by M. Clyde, David Draper and E.I. George, and a rejoinder by the authors), Statistical Science, 14 (4), 382–417.
Hurvich, C. M., and Tsai, C. L. (1990), “The Impact of Model Selection on Inference in Linear Regression,'' The American Statistician, 44 (3), 214–217.
Link, W., and Barker, R. (2006), “Model Weights and the Foundations of Multimodel Inference,'' Ecology, 87 (10), 2626–2635.
Lukacs, P. M., Burnham, K. P., and Anderson, D. R. (2010), “Model Selection Bias and Freedman’s Paradox,'' Annals of the Institute of Statistical Mathematics, 62 (1), 117–125.
Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997), “Bayesian Model Averaging for Linear Regression Models,'' Journal of the American Statistical Association, 92 (437), 179–191.
Severini, T. (1991), “On the Relationship Between Bayesian and Non-Bayesian Interval Estimates,'' Journal of the Royal Statistical Society. Series B. Methodological, 53 (3), 611–618.
Volinsky, C. T., Madigan, D., Raftery, A. E., and Kronmal, R. A. (1997), “Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke,'' Journal of the Royal Statistical Society. Series C, Applied Statistics, 46 (4), 433–448.
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Fletcher, D., Turek, D. Model-Averaged Profile Likelihood Intervals. JABES 17, 38–51 (2012). https://doi.org/10.1007/s13253-011-0064-8