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Parametric modal regression with varying precision.

Marcelo Bourguignon1, Jeremias Leão2, Diego I Gallardo3

  • 1Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil.

Biometrical Journal. Biometrische Zeitschrift
|October 30, 2019
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Summary
This summary is machine-generated.

We introduce a new parametric modal linear regression model for gamma-distributed data. This model offers direct interpretation of regression coefficients for the positive response variable's mode.

Keywords:
gamma distributionlinear regressionmodal regressionparametric regression

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Generalized linear models (GLMs) are widely used but often lack direct interpretation of coefficients for specific distributional parameters.
  • Existing regression models for gamma-distributed data may not directly parameterize the mode, hindering intuitive analysis.

Purpose of the Study:

  • To propose a novel parametric modal linear regression model for gamma-distributed response variables.
  • To introduce a new parameterization of the gamma distribution indexed by mode and precision.
  • To facilitate straightforward interpretation of regression coefficients in terms of the response variable's mode.

Main Methods:

  • Development of a new parameterization for the gamma distribution using mode and precision.
  • Formulation of a modal linear regression model where modal and precision responses link to a linear predictor.
  • Inclusion of covariates and unknown regression parameters within the linear predictor.
  • Discussion of residuals and influence diagnostic tools.
  • Conducting a Monte Carlo simulation study to assess estimator performance.

Main Results:

  • The proposed model allows for direct interpretation of regression coefficients related to the mode of the positive response variable.
  • Parametric inference for mode regression is achievable via the likelihood paradigm.
  • Monte Carlo simulations provide insights into the finite sample performance of the estimators.

Conclusions:

  • The new modal linear regression model provides a valuable alternative for analyzing positive, gamma-distributed data, particularly when the mode is of primary interest.
  • The model's straightforward coefficient interpretation enhances its applicability in fields like biology and demography.
  • The developed diagnostic tools aid in model assessment and validation.