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Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models

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Abstract

We consider the standard linear multiple regression model in which the parameter of interest is the ratio of two regression coefficients. Our setup includes a broad range of applications. We show that the 1− α confidence interval for the interest parameter based on the profile, conditional profile, modified profile or adjusted profile likelihood can potentially become the entire real line, while appropriately chosen integrated likelihoods do not suffer from this drawback. We further explore the asymptotic length of confidence intervals in order to compare integrated likelihood-based proposals. The analysis is facilitated by an orthogonal parameterization.

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Authors and Affiliations

  1. Department of Statistics, University of Florida, Gainesville, FL, 32611, USA

    Malay Ghosh

  2. Department of Statistics, University of Georgia, Athens, GA, 30602, USA

    Gauri Sankar Datta

  3. Department of Statistics, Kyungpook National University, Taegu, South Korea

    Dalho Kim

  4. Department of Statistical Science, University College London, WC1E 6BT, London, UK

    Trevor J. Sweeting

Authors
  1. Malay Ghosh
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  2. Gauri Sankar Datta
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  3. Dalho Kim
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  4. Trevor J. Sweeting
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Correspondence to Gauri Sankar Datta.

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Ghosh, M., Datta, G.S., Kim, D. et al. Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models. Ann Inst Stat Math 58, 457–473 (2006). https://doi.org/10.1007/s10463-005-0027-3

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  • DOI: https://doi.org/10.1007/s10463-005-0027-3

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