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Title: Bayesian probability of agreement for comparing the similarity of response surfaces

Abstract

For a variety of linear and generalized linear models, there may be interest in evaluating whether the expected response values in two different populations are sufficiently similar to be considered practically equivalent. The probability of agreement has been introduced as a strategy for quantifying the similarity between two groups. We propose a Bayesian version of the probability of agreement to quantify the similarity between linear and generalized linear response surfaces. The proposed methodology is based on Markov chain Monte Carlo estimation and it allows for an intuitive interpretation based directly on population parameters. As demonstrated, the methodology can be flexibly applied to a variety of different models. We illustrate its use with three examples for which the response depends on predictor variables through a linear, logistic, or Poisson regression model. The computation associated with this approach has been automated with a freely available R Shiny app.

Authors:
 [1];  [2];  [3]
  1. Univ. of San Francisco, CA (United States)
  2. Saint Louis Univ., MO (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1514939
Report Number(s):
LA-UR-17-24158
Journal ID: ISSN 0022-4065
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Quality Technology
Additional Journal Information:
Journal Volume: 52; Journal Issue: 1; Journal ID: ISSN 0022-4065
Publisher:
American Society for Quality (ASQ)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; comparing subpopulations; equivalence testing; linear regression; logistic regression; Markov chain Monte Carlo; Poisson regression

Citation Formats

Stevens, Nathaniel T., Rigdon, Steven E., and Anderson-Cook, Christine M. Bayesian probability of agreement for comparing the similarity of response surfaces. United States: N. p., 2019. Web. doi:10.1080/00224065.2019.1569961.
Stevens, Nathaniel T., Rigdon, Steven E., & Anderson-Cook, Christine M. Bayesian probability of agreement for comparing the similarity of response surfaces. United States. doi:10.1080/00224065.2019.1569961.
Stevens, Nathaniel T., Rigdon, Steven E., and Anderson-Cook, Christine M. Mon . "Bayesian probability of agreement for comparing the similarity of response surfaces". United States. doi:10.1080/00224065.2019.1569961.
@article{osti_1514939,
title = {Bayesian probability of agreement for comparing the similarity of response surfaces},
author = {Stevens, Nathaniel T. and Rigdon, Steven E. and Anderson-Cook, Christine M.},
abstractNote = {For a variety of linear and generalized linear models, there may be interest in evaluating whether the expected response values in two different populations are sufficiently similar to be considered practically equivalent. The probability of agreement has been introduced as a strategy for quantifying the similarity between two groups. We propose a Bayesian version of the probability of agreement to quantify the similarity between linear and generalized linear response surfaces. The proposed methodology is based on Markov chain Monte Carlo estimation and it allows for an intuitive interpretation based directly on population parameters. As demonstrated, the methodology can be flexibly applied to a variety of different models. We illustrate its use with three examples for which the response depends on predictor variables through a linear, logistic, or Poisson regression model. The computation associated with this approach has been automated with a freely available R Shiny app.},
doi = {10.1080/00224065.2019.1569961},
journal = {Journal of Quality Technology},
number = 1,
volume = 52,
place = {United States},
year = {2019},
month = {4}
}

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Works referenced in this record:

The difference between “equivalent” and “not different”
journal, October 2015


Comparing heteroscedastic measurement systems with the probability of agreement
journal, May 2017

  • Stevens, Nathaniel T.; Steiner, Stefan H.; MacKay, R. Jock
  • Statistical Methods in Medical Research, Vol. 27, Issue 11
  • DOI: 10.1177/0962280217702540

Design and Analysis of Method Equivalence Studies
journal, December 2009

  • Borman, Phil J.; Chatfield, Marion J.; Damjanov, Ivana
  • Analytical Chemistry, Vol. 81, Issue 24
  • DOI: 10.1021/ac901945f

Equivalence and Noninferiority Tests for Quality, Manufacturing and Test Engineers
journal, October 2014


Quantifying similarity in reliability surfaces using the probability of agreement
journal, March 2017


Design and analysis of confirmation experiments
journal, April 2019


Bayesian probability of predictive agreement for comparing the outcome of two separate regressions: Bayesian probability of predictive agreement for comparing the outcome of two separate regressions
journal, April 2018

  • Stevens, Nathaniel T.; Rigdon, Steven E.; Anderson-Cook, Christine M.
  • Quality and Reliability Engineering International, Vol. 34, Issue 6
  • DOI: 10.1002/qre.2284

Comparing the Reliability of Related Populations With the Probability of Agreement
journal, July 2016


Assessing agreement between two measurement systems: An alternative to the limits of agreement approach
journal, September 2015

  • Stevens, Nathaniel T.; Steiner, Stefan H.; MacKay, R. Jock
  • Statistical Methods in Medical Research, Vol. 26, Issue 6
  • DOI: 10.1177/0962280215601133

A Method for Determining Equivalence in Industrial Applications
journal, March 2002


    Works referencing / citing this record:

    Assessing agreement between two measurement systems: An alternative to the limits of agreement approach
    journal, September 2015

    • Stevens, Nathaniel T.; Steiner, Stefan H.; MacKay, R. Jock
    • Statistical Methods in Medical Research, Vol. 26, Issue 6
    • DOI: 10.1177/0962280215601133

    Equivalence and Noninferiority Tests for Quality, Manufacturing and Test Engineers
    journal, October 2014


    Design and Analysis of Method Equivalence Studies
    journal, December 2009

    • Borman, Phil J.; Chatfield, Marion J.; Damjanov, Ivana
    • Analytical Chemistry, Vol. 81, Issue 24
    • DOI: 10.1021/ac901945f

    Comparing the Reliability of Related Populations With the Probability of Agreement
    journal, July 2016


    Comparing heteroscedastic measurement systems with the probability of agreement
    journal, May 2017

    • Stevens, Nathaniel T.; Steiner, Stefan H.; MacKay, R. Jock
    • Statistical Methods in Medical Research, Vol. 27, Issue 11
    • DOI: 10.1177/0962280217702540

    Quantifying similarity in reliability surfaces using the probability of agreement
    journal, March 2017


    Design and analysis of confirmation experiments
    journal, April 2019


    The difference between “equivalent” and “not different”
    journal, October 2015


    Bayesian probability of predictive agreement for comparing the outcome of two separate regressions: Bayesian probability of predictive agreement for comparing the outcome of two separate regressions
    journal, April 2018

    • Stevens, Nathaniel T.; Rigdon, Steven E.; Anderson-Cook, Christine M.
    • Quality and Reliability Engineering International, Vol. 34, Issue 6
    • DOI: 10.1002/qre.2284