Comparison between Highly Complex Location Models and GAMLSS.

Thiago G Ramires,Carlos A B Pereira,Renan J Carvalho,Luiz R Nakamura,Ana J Righetto,Lucas A Vieira

doi:10.3390/e23040469

Abstract

This paper presents a discussion regarding regression models, especially those belonging to the location class. Our main motivation is that, with simple distributions having simple interpretations, in some cases, one gets better results than the ones obtained with overly complex distributions. For instance, with the reverse Gumbel (RG) distribution, it is possible to explain response variables by making use of the generalized additive models for location, scale, and shape (GAMLSS) framework, which allows the fitting of several parameters (characteristics) of the probabilistic distributions, like mean, mode, variance, and others. Three real data applications are used to compare several location models against the RG under the GAMLSS framework. The intention is to show that the use of a simple distribution (e.g., RG) based on a more sophisticated regression structure may be preferable than using a more complex location model.

Highlights

With the increasing use of new data analysis techniques, mainly artificial intelligence, machine learning, neural networks, and big data, regression analysis has become, perhaps, the most important tool among the various statistical methods of optimization, and of decision-making management
We shall highlight that the maximum likelihood estimates (MLEs), as well as Akaike information criterion (AIC) and Bayesian information criterion (BIC) values presented in Reference [23], seem slightly off for the log-Weibull Marshall-Olkin Weibull (LWMOW) model and the results presented in Table 1 differ from their original paper
As in the previous application, we provide the results of the parametric GAMLSS (pGAMLSS) framework based on the reverse Gumbel (RG) distribution, which regression structures are given by μi = 15.314 −

Summary

Introduction

With the increasing use of new data analysis techniques, mainly artificial intelligence, machine learning, neural networks, and big data, regression analysis has become, perhaps, the most important tool among the various statistical (learning) methods of optimization, and of decision-making management. The number of papers with increasingly complex techniques is naturally emerging because of the need to extract more accurate information from the data. This manuscript is more of a work belonging to this class of papers, we think it is less complex compared to its alternatives, which are mainly presented as (log linear) location models. The location parameters are associated to other important parameters like mean, percentiles, standard deviation, skewness, and kurtosis, in which these characteristics are implicitly modeled. For instance: the three parameter log-xgamma Weibull regression model [1], the four parameter Topp Leone generated Burr XII [2], log-odd log-logistic

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Results

Conclusion