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Parametric modal regression with varying precision
Author(s) -
Bourguig Marcelo,
Leão Jeremias,
Gallardo Diego I.
Publication year - 2020
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201900132
Subject(s) - parametric statistics , covariate , linear regression , estimator , proper linear model , mathematics , context (archaeology) , regression analysis , generalized linear model , statistics , monte carlo method , semiparametric regression , regression diagnostic , linear model , polynomial regression , paleontology , biology
In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.