Selection of optimal regression models via cross-validation

This paper illustrates cut-and-try techniques that point to appropriate transformations of variables and to the selection of sets of variables for an equation that may improve understanding of a social process. The substance of the research reported — the relation of mental test results to state population, cultural, and school resource indexes (Walberg and Rasher, 1974) — illustrates typical problems of behavioral data: multi-colinearity, outliers, abnormal distributions, and the lack of a consensually-validated, explicit theoretical model. Despite these problems, data originally collected for purposes other than the investigator’s may yield tentative confirmations or cautions about prior findings and provisional indications for theory or policy; such inferences may be at least partially checked by cross-validation on independent or semi-independent sets of data. After discussing the sequence of analyses and the results, we conclude by mentioning a number of uncertainties and reservations about drawing substantive or policy implications.

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WEIGHTED CROSS VALIDATION IN THE SELECTION OF ROBUST REGRESSION MODEL WITH CHANGE-POINT FOR TELEVISION RATING FORECAST

Revista Mundi Engenharia Tecnologia e Gestão (ISSN 2525-4782) ◽

10.21575/25254782rmetg2020vol5n21179 ◽

2020 ◽

Vol 5 (2) ◽

Author(s):

Carlos Alberto Huaira Contreras ◽

Carlos Cristiano Hasenclever Borges ◽

Camila Borelli Zeller ◽

Amanda Romanelli

Keyword(s):

Regression Model ◽

Change Point ◽

Regression Models ◽

Cross Validation ◽

Robust Regression ◽

Model Parameters ◽

Random Errors ◽

Type Algorithm ◽

T Distribution ◽

Selection Of

The paper proposes a weighted cross-validation (WCV) algorithm to select a linear regression model with change-point under a scale mixtures of normal (SMN) distribution that yields the best prediction results. SMN distributions are used to construct robust regression models to the influence of outliers on the parameter estimation process. Thus, we relaxed the usual assumption of normality of the regression models and considered that the random errors follow a SMN distribution, specifically the Student-t distribution. In addition, we consider the fact that the parameters of the regression model can change from a specific and unknown point, called change-point. In this context, the estimations of the model parameters, which include the change-point, are obtained via the EM-type algorithm (Expectation-Maximization). The WCV method is used in the selection of the model that presents greater robustness and that offers a smaller prediction error, considering that the weighting values come from step E of the EM-type algorithm. Finally, numerical examples considering simulated and real data (data from television audiences) are presented to illustrate the proposed methodology.

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Optimization of integrated fuzzy decision tree and regression models for selection of oil spill response method in the Arctic

Knowledge-Based Systems ◽

10.1016/j.knosys.2020.106676 ◽

2021 ◽

Vol 213 ◽

pp. 106676

Author(s):

Saeed Mohammadiun ◽

Guangji Hu ◽

Abdorreza Alavi Gharahbagh ◽

Reza Mirshahi ◽

Jianbing Li ◽

...

Keyword(s):

Decision Tree ◽

Oil Spill ◽

Regression Models ◽

The Arctic ◽

Fuzzy Decision ◽

Fuzzy Decision Tree ◽

Oil Spill Response ◽

Response Method ◽

Selection Of

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Robust order selection of mixtures of regression models with random effects

Computational Statistics ◽

10.1007/s00180-021-01177-1 ◽

2021 ◽

Author(s):

Luísa Novais ◽

Susana Faria

Keyword(s):

Random Effects ◽

Regression Models ◽

Order Selection ◽

Selection Of

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Modelling of a Stochastic Spatiotemporal Variable in Transport Domain

International Journal of Traffic and Transportation Management ◽

10.5383/jttm.03.01.004 ◽

2021 ◽

Vol 03 (01) ◽

pp. 25-31

Author(s):

Peter Krammer ◽

Marcel Kvassay ◽

Ladislav Hluchý

Keyword(s):

Regression Models ◽

Cross Validation ◽

Distribution Characteristics ◽

Spatiotemporal Modelling ◽

Bike Sharing ◽

Day Of The Week ◽

Irregular Variation ◽

Fold Cross Validation ◽

Transport Domain ◽

Cumulative Sums

In this article, building on our previous work, we engage in spatiotemporal modelling of transport demand in the Montreal metropolitan area over the period of six years. We employ classical machine learning and regression models, which predict bike-sharing demand in the form of daily cumulative sums of bike trips for each considered docking station. Hourly estimates of demand are then determined by considering the statistical distribution of demand across individual hours of an average day. In order to capture seasonal and other regular variation of demand, longer-term distribution characteristics of bike trips, such as their average number falling on each day of the week, month of the year, etc., were also used as input attributes. We initially conjectured that weather would be an important source of irregular variation in bike-sharing demand, and subsequently included several available meteorological variables in our models. We validated our models by Hold-Out and 10-Fold Cross-Validation, with encouraging results.

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Genotypic parameters for egg production in pure breed hens by using random regression model

Ciência Rural ◽

10.1590/0103-8478cr20141631 ◽

2017 ◽

Vol 47 (5) ◽

Author(s):

Priscila Becker Ferreira ◽

Paulo Roberto Nogara Rorato ◽

Fernanda Cristina Breda ◽

Vanessa Tomazetti Michelotti ◽

Alexandre Pires Rosa ◽

...

Keyword(s):

Regression Model ◽

Regression Models ◽

Egg Production ◽

Random Regression ◽

Broad Sense Heritability ◽

Residual Matrix ◽

Random Regression Model ◽

Residual Covariance ◽

Genotypic Correlations ◽

Selection Of

ABSTRACT: This study aimed to test different genotypic and residual covariance matrix structures in random regression models to model the egg production of Barred Plymouth Rock and White Plymouth Rock hens aged between 5 and 12 months. In addition, we estimated broad-sense heritability, and environmental and genotypic correlations. Six random regression models were evaluated, and for each model, 12 genotypic and residual matrix structures were tested. The random regression model with linear intercept and unstructured covariance (UN) for a matrix of random effects and unstructured correlation (UNR) for residual matrix adequately model the egg production curve of hens of the two study breeds. Genotypic correlations ranged from 0.15 (between age of 5 and 12 months) to 0.99 (between age of 10 and 11 months) and increased based on the time elapsed. Egg production heritability between 5- and 12-month-old hens increased with age, varying from 0.15 to 0.51. From the age of 9 months onward, heritability was moderate with estimates of genotypic correlations higher than 90% at the age of 10, 11, and 12 months. Results suggested that selection of hens to improve egg production should commence at the ninth month of age.

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Selection of Variables in Regression Models Based on Inflated Distributions

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v7i2-sp.300 ◽

2011 ◽

Vol 7 (2-Sp) ◽

Author(s):

Aruna Rao ◽

Sumathi K

Keyword(s):

Regression Models ◽

Selection Of Variables ◽

Selection Of

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Bayesian Model Assessment and Comparison Using Cross-Validation Predictive Densities

Neural Computation ◽

10.1162/08997660260293292 ◽

2002 ◽

Vol 14 (10) ◽

pp. 2439-2468 ◽

Cited By ~ 83

Author(s):

Aki Vehtari ◽

Jouko Lampinen

Keyword(s):

Expected Utility ◽

Cross Validation ◽

Monte Carlo Sampling ◽

Point Estimate ◽

Model Assessment ◽

Predictive Densities ◽

Fold Cross Validation ◽

Selection Of ◽

Natural Way ◽

Real World Problems

In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate because it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected utility than some other model. We propose an approach using cross-validation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions. We also discuss the probabilistic assumptions made and properties of two practical cross-validation methods, importance sampling and k-fold cross-validation. As illustrative examples, we use multilayer perceptron neural networks and gaussian processes with Markov chain Monte Carlo sampling in one toy problem and two challenging real-world problems.

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