Validation of Stepwise-Based Procedure in GAMLSS

Ramires, Thiago G.; Nakamura, Luiz Ricardo; Righetto, Ana Julia; Pescim, Rodrigo R.; Mazucheli, Josmar; Rigby, Robert A.; Stasinopoulos, Dimitrios

doi:10.6339/21-jds1003

Cited by 10 publications

(7 citation statements)

References 27 publications

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“…As the explanatory variables can be included in any of the regression structures of all parameters, there are some procedures to select the additive terms. In this paper, we are using the so-called Strategy A [11,17], a stepwise-based method applied to select the terms for each model parameters based on the Akaike information criterion (AIC) [18]. This approach can be achieved using the stepGAICAll.A() function in the gamlss package.…”

Section: Estimation and Model Selectionmentioning

confidence: 99%

“…Based on the Strategy A variable selection method [11,17], the final fitted GAMLSS model, to represent Y is given by…”

Section: Application 1: Voltage Datamentioning

confidence: 99%

“…Through the Strategy A variable selection method [11,17], the final fitted GAMLSS model based on the RG distribution is given by µ i = 14.966 + s(temperature i ) and log σ i = −4.276 + 0.011 temperature i , where the fitted smoothing parameter λ for µ is 17.47. Note that, although temperature was considered to model both regression structures, the smoothing function was only necessary to model the mode µ.…”

Section: Application 2: Class-hmentioning

confidence: 99%

“…We may also note that the dispersion is influenced by X 1 and X 2 , indicating that they are probably good predictors to fit the scale parameter σ. Using the Strategy A variable selection method [11,17], the final fitted GAMLSS model based on the RG distribution is given by…”

Section: Application 3: Heartmentioning

confidence: 99%

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Comparison between Highly Complex Location Models and GAMLSS

Ramires

Nakamura

Righetto³

et al. 2021

Entropy

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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.

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Section: Estimation and Model Selectionmentioning

confidence: 99%

“…Based on the Strategy A variable selection method [11,17], the final fitted GAMLSS model, to represent Y is given by…”

Section: Application 1: Voltage Datamentioning

confidence: 99%

Section: Application 2: Class-hmentioning

confidence: 99%

Section: Application 3: Heartmentioning

confidence: 99%

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Comparison between Highly Complex Location Models and GAMLSS

Ramires

Nakamura

Righetto³

et al. 2021

Entropy

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“…Step 2: Select subsets of authentic and latent variables for each of the parameters of the response-variable distribution, using any of the applied strategies for GAMLSS models [23]. The most common procedure is a stepwise procedure called "Strategy A" [23,26,27]).…”

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confidence: 99%

Incorporating Clustering Techniques into GAMLSS

Ramires

Nakamura

Righetto³

et al. 2021

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A method for statistical analysis of multimodal and/or highly distorted data is presented. The new methodology combines different clustering methods with the GAMLSS (generalized additive models for location, scale, and shape) framework, and is therefore called c-GAMLSS, for “clustering GAMLSS. ” In this new extended structure, a latent variable (cluster) is created to explain the response-variable (target). Any and all parameters of the distribution for the response variable can also be modeled by functions of the new covariate added to other available resources (features). The method of selecting resources to be used is carried out in stages, a step-based method. A simulation study considering multiple scenarios is presented to compare the c-GAMLSS method with existing Gaussian mixture models. We show by means of four different data applications that in cases where other authentic explanatory variables are or are not available, the c-GAMLSS structure outperforms mixture models, some recently developed complex distributions, cluster-weighted models, and a mixture-of-experts model. Even though we use simple distributions in our examples, other more sophisticated distributions can be used to explain the response variable.

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