Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

Macedo, Pedro

doi:10.1080/03610918.2015.1096378

Cited by 11 publications

(8 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4. Although the coefficient of variable OI is not significantly different from zero in any case, the not expected negative sign obtained in model in Equation 15is corrected in models Equations (17) and (18). 5.…”

Section: Raised Limmentioning

confidence: 58%

“…In the words of Tutz and Ulbricht [13] "the elastic net catches all the big fish", meaning that it selects the whole group. From a different point of view, other authors have also presented different techniques and methods well suited for dealing with the collinearity problems: continuum regression ( [14]), least angle regression ( [15]), generalized maximum entropy ( [16][17][18]), the principal component analysis (PCA) regression ( [19,20]), the principal correlation components estimator ( [21]), penalized splines ( [22]), partial least squares (PLS) regression ( [23,24]), or the surrogate estimator focused on the solution of the normal equations presented by Jensen and Ramirez [25].…”

Section: Introductionmentioning

confidence: 99%

“…Estimations of the models in Equations (15)-(18): Standard deviation is inside the parenthesis, R 2 is the coefficient of determination, F 3,11 is the experimental value of the joint significance contrast, andσ 2 is the variance estimate of the random perturbation.…”

mentioning

confidence: 99%

See 2 more Smart Citations

The VIF and MSE in Raise Regression

et al. 2020

View full text Add to dashboard Cite

The raise regression has been proposed as an alternative to ordinary least squares estimation when a model presents collinearity. In order to analyze whether the problem has been mitigated, it is necessary to develop measures to detect collinearity after the application of the raise regression. This paper extends the concept of the variance inflation factor to be applied in a raise regression. The relevance of this extension is that it can be applied to determine the raising factor which allows an optimal application of this technique. The mean square error is also calculated since the raise regression provides a biased estimator. The results are illustrated by two empirical examples where the application of the raise estimator is compared to the application of the ridge and Lasso estimators that are commonly applied to estimate models with multicollinearity as an alternative to ordinary least squares.

show abstract

Section: Raised Limmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The VIF and MSE in Raise Regression

et al. 2020

View full text Add to dashboard Cite

show abstract

“…They have found that when the sample size increases, the Prediction Sum of Squares (PRESS) value decreases as the correlation coefficient becomes large. Macedo [33] has improved the ridge-GME parameter estimator, which combines ridge regression and generalized maximum entropy to eliminate the subjectivity in the analysis of the ridge trace. Lukman et al [34] classify the estimators based on Dorugade [14] into different forms.…”

Section: Literature Reviewmentioning

confidence: 99%

A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

Sevinç

Göktaş

2019

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

One of the major problems in fitting an appropriate linear regression model is multicollinearity which occurs when regressors are highly correlated. To overcome this problem, ridge regression estimator which is an alternative method to the ordinary least squares (OLS) estimator, has been used. Heteroscedasticity, which violates the assumption of constant variances, is another major problem in regression estimation. To solve this violation problem, weighted least squares estimation is used to fit a more robust linear regression equation. However, when there is both multicollinearity and heteroscedasticity problem, weighted ridge regression estimation should be employed. Ridge regression depends on the ridge parameter which does not have an explicit form of calculation. There are various ridge parameters proposed in the literature. A simulation study was conducted to compare the performances of these ridge parameters for both multicollinear and heteroscedastic data. The following factors were varied: the number of regressors, sample sizes and degrees of multicollinearity. The performances of the parameters were compared using mean square error. The study also shows that when the data are both heteroscedastic and multicollinear, the estimation performances of the ridge parameters differs from the case for only multicollinear data.

show abstract

“…Usually, the last option is the only one applicable, and so alternative estimation methods must be applied. Macedo () proposed a list of methods with which to estimate when the degree of multicollinearity is severe, including ridge regression, principal component regression, partial least squares regression, continuum regression, lasso, elastic net, least angle regression, and generalised maximum entropy. However, in this paper, we apply orthogonal regression, a methodology that was introduced by Novales, Salmerón, García, García & López () for the regression model with three independent variables and which was later expanded by Salmerón, García, García, and García () for four variables.…”

Section: Logistic Regressionmentioning

confidence: 99%

A Bayesian asymmetric logistic model of factors underlying team success in top‐level basketball in Spain

Sánchez

Gómez

Ocaña‐Peinado

2018

Statistica Neerlandica

View full text Add to dashboard Cite

This paper analyses the factors underlying the victories and defeats of the Spanish basketball teams Real Madrid and Barcelona in the national league, ACB. The following research questions were addressed: (a) Is it possible to identify the factors underlying these results? (b) Can knowledge of these factors increase the probability of winning and thus help coaches take better decisions? We analysed 80 and 79 games played in the 2013-2014 season by Real Madrid and Barcelona, respectively. Logistic regression analysis was performed to predict the probability of the team winning. The models were estimated by standard (frequentist) and Bayesian methods, taking into account the asymmetry of the data, that is, the fact that the database contained many more wins than losses. Thus, the analysis consisted of an asymmetric logistic regression. From the Bayesian standpoint, this model was considered the most appropriate, as it highlighted relevant factors that might remain undetected by standard logistic regression. The prediction quality of the models obtained was tested by application to the results produced in the following season (2014)(2015).field. In short, asymmetric logistic regression is a valuable tool that can help coaches improve their game strategies. KEYWORDS asymmetric link, Bayesian estimation, logistic regression, model selection INTRODUCTIONIn sports clubs, as in all organisations, decisions must be taken in order to maintain and, if possible, improve performance. Quantitative methods can be used to assist in the decision-making process and thus avoid excessive subjectivity. In the context of professional sports, the emergence of the "Moneyball phenomenon" (Lewis, 2004) has produced many changes in the use of information sources. The main focus of this approach is to measure the contributions made by each player, from the data generated during a game, in order to optimise available resources and thus improve the team's performance.Sports decisions, regarding the team design, transfers, or new signings (of players or coaches), are restricted by the economic limitations facing the organisation. Clearly, wealthier clubs have greater possibilities of signing elite athletes and thus of buying better performance. Clubs with fewer resources, however, might counter this imbalanced situation by analysing quantitative information in order to sign the best human resources possible in accordance with the available budget or to detect and exploit their opponents' weaknesses. However, the "Moneyball philosophy" cannot readily be extrapolated to basketball, due to the great complexity of this sport. Innumerable factors may influence the performance of a player and his team, such as the opponent (defence tactics, types of players, pace, etc.), teammates' abilities, the team's playing style, the coach's philosophy, and the stage of the match. Certainly, it is very complicated to measure all these aspects using only the traditional box score. In response, much has been done to improve the quality and quantity of available i...

show abstract

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

Cited by 11 publications

References 35 publications

The VIF and MSE in Raise Regression

The VIF and MSE in Raise Regression

A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

A Bayesian asymmetric logistic model of factors underlying team success in top‐level basketball in Spain

Contact Info

Product

Resources

About