US EPA

4286986 

Journal Article 

Model-averaged profile likelihood intervals 

Fletcher, D; Turek, D 

2012 

Yes 

Journal of Agricultural, Biological, and Environmental Statistics
ISSN: 1085-7117
EISSN: 1537-2693 

17 

1 

38-51 

English 

10.1007/s13253-011-0064-8 

WOS:000302070300003 

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. 

Coverage rate; Information criterion; Model uncertainty; Model weight