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Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications
Author(s) -
Ventura Marcelo,
Saulo Helton,
Leiva Victor,
Monsueto Sandro
Publication year - 2019
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2433
Subject(s) - akaike information criterion , bayesian information criterion , mathematics , statistics , regression analysis , log log plot , econometrics , regression , binary logarithm , combinatorics
This work deals with log‐symmetric regression models, which are particularly useful when the response variable is continuous, strictly positive, and following an asymmetric distribution, with the possibility of modeling atypical observations by means of robust estimation. In these regression models, the distribution of the random errors is a member of the log‐symmetric family, which is composed by the log‐contaminated‐normal, log‐hyperbolic, log‐normal, log‐power‐exponential, log‐slash and log‐Student‐ t distributions, among others. One way to select the best family member in log‐symmetric regression models is using information criteria. In this paper, we formulate log‐symmetric regression models and conduct a Monte Carlo simulation study to investigate the accuracy of popular information criteria, as Akaike, Bayesian, and Hannan‐Quinn, and their respective corrected versions to choose adequate log‐symmetric regressions models. As a business application, a movie data set assembled by authors is analyzed to compare and obtain the best possible log‐symmetric regression model for box offices. The results provide relevant information for model selection criteria in log‐symmetric regressions and for the movie industry. Economic implications of our study are discussed after the numerical illustrations.