Journal article
Reconceptualizing the p-value from a likelihood ratio test: a probabilistic pairwise comparison of models based on Kullback-Leibler discrepancy measures
Journal of applied statistics, Vol.47(13-15), pp.2582-2609
11/17/2020
DOI: 10.1080/02664763.2020.1754360
PMCID: PMC9042097
PMID: 35707423
Abstract
Discrepancy measures are often employed in problems involving the selection and assessment of statistical models. A discrepancy gauges the separation between a fitted candidate model and the underlying generating model. In this work, we consider pairwise comparisons of fitted models based on a probabilistic evaluation of the ordering of the constituent discrepancies. An estimator of the probability is derived using the bootstrap. In the framework of hypothesis testing, nested models are often compared on the basis of the p-value. Specifically, the simpler null model is favored unless the p-value is sufficiently small, in which case the null model is rejected and the more general alternative model is retained. Using suitably defined discrepancy measures, we mathematically show that, in general settings, the likelihood ratio test p-value is approximated by the bootstrapped discrepancy comparison probability (BDCP). We argue that the connection between the p-value and the BDCP leads to potentially new insights regarding the utility and limitations of the p-value. The BDCP framework also facilitates discrepancy-based inferences in settings beyond the limited confines of nested model hypothesis testing.
Details
- Title: Subtitle
- Reconceptualizing the p-value from a likelihood ratio test: a probabilistic pairwise comparison of models based on Kullback-Leibler discrepancy measures
- Creators
- Benjamin Riedle - Eli Lilly and CompanyAndrew A Neath - Department of Mathematics and Statistics, Southern Illinois UniversityJoseph E Cavanaugh - Department of Biostatistics, University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of applied statistics, Vol.47(13-15), pp.2582-2609
- DOI
- 10.1080/02664763.2020.1754360
- PMID
- 35707423
- PMCID
- PMC9042097
- NLM abbreviation
- J Appl Stat
- ISSN
- 0266-4763
- eISSN
- 1360-0532
- Publisher
- Taylor & Francis
- Language
- English
- Date published
- 11/17/2020
- Academic Unit
- Statistics and Actuarial Science; Biostatistics; Injury Prevention Research Center
- Record Identifier
- 9984214706302771
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