DMCEE - Artículoshttps://hdl.handle.net/10481/137572024-03-28T13:27:10Z2024-03-28T13:27:10ZThe raise estimator: estimation, inference, and propertiesSalmerón Gómez, RománGarcía García, CatalinaGarcía Pérez, JoséLópez Martín, María Del Marhttps://hdl.handle.net/10481/896762024-02-29T10:00:36ZThe raise estimator: estimation, inference, and properties
Salmerón Gómez, Román; García García, Catalina; García Pérez, José; López Martín, María Del Mar
Several methods using different approaches have been developed to remedy the consequences of collinearity. To the best of our knowledge, only the raise estimator proposed by García et al. (Citation2010) deals with this problem from a geometric perspective. This article fully develops the raise estimator for a model with two standardized explanatory variables. Inference in the raise estimator is examined, showing that it can be obtained from ordinary least squares methodology. In addition, contrary to what happens in ridge regression, the raise estimator maintains the coefficient of determination value constant. The expression of the variance inflation factor for the raise estimator is also presented. Finally, a comparative study of the raise and ridge estimators is carried out using an example.
The coefficient of determination in the ridge regressionRodríguez Sánchez, AinaraSalmerón Gómez, RománGarcía García, Catalinahttps://hdl.handle.net/10481/896742024-02-29T09:52:25ZThe coefficient of determination in the ridge regression
Rodríguez Sánchez, Ainara; Salmerón Gómez, Román; García García, Catalina
In a linear regression, the coefficient of determination, R2, is a relevant measure that represents the percentage of variation in the dependent variable that is explained by a set of independent variables. Thus, it measures the predictive ability of the estimated model. For an ordinary least squares (OLS) estimator, this coefficient is calculated from the decomposition of the sum of squares. However, when the model presents collinearity problems (a strong linear relation between the independent variables), the OLS estimation is unstable, and other estimation methodologies are proposed, with the ridge estimation being the most widely applied. This paper shows that the decomposition of the sum of squares is not verified in the ridge regression and proposes how the coefficient of determination should be calculated in this case.
Standardization of Variables and Collinearity Diagnostic in Ridge RegressionGarcía Pérez, JoséSalmerón Gómez, RománGarcía García, CatalinaLópez Martín, María Del Marhttps://hdl.handle.net/10481/896732024-02-29T09:40:12ZStandardization of Variables and Collinearity Diagnostic in Ridge Regression
García Pérez, José; Salmerón Gómez, Román; García García, Catalina; López Martín, María Del Mar
Ridge estimation (RE) is an alternative method to ordinary least squares when there exists a collinearity problem in a linear regression model. The variance inflator factor (VIF) is applied to test if the problem exists in the original model and is also necessary after applying the ridge estimate to check if the chosen value for parameter k has mitigated the collinearity problem. This paper shows that the application of the original data when working with the ridge estimate leads to non-monotone VIF values. García et al. (2014) showed some problems with the traditional VIF used in RE. We propose an augmented VIF, VIFR(j,k), associated with RE, which is obtained by standardizing the data before augmenting the model. The VIFR(j,k) will coincide with the VIF associated with the ordinary least squares estimator when k = 0. The augmented VIF has the very desirable properties of being continuous, monotone in the ridge parameter and higher than one.
This paper has been partially supported by the project ‘Valoración de proyectos gubernamentales a largo plazo: obtención de la tasa social de descuento’, reference: P09-SEJ-05404, Proyectos de Excelencia de la Junta de Andalucía and Fondos FEDER.
Residualization: justification, properties and applicationGarcía García, CatalinaSalmerón Gómez, RománGarcía García, ClaudiaGarcía Pérez, Joséhttps://hdl.handle.net/10481/896712024-02-29T09:27:30ZResidualization: justification, properties and application
García García, Catalina; Salmerón Gómez, Román; García García, Claudia; García Pérez, José
Although it is usual to find collinearity in econometric models, it is commonly disregarded. An extended solution is to eliminate the variable causing the problem but, in some cases, this decision can affect the goal of the research. Alternatively, residualization not only allows mitigation of collinearity, but it also provides an alternative interpretation of the coefficients isolating the effect of the residualized variable. This paper fully develops the residualization procedure and justifies its application not only for dealing with multicollinearity but also for separating the individual effects of the regressor variables. This contribution is illustrated by two econometric models with financial and ecological data, although it can also be extended to many different fields.
Collinearity diagnostic applied in ridge estimation through the variance inflation factorSalmerón Gómez, RománGarcía Pérez, JoséLópez Martín, María Del MarGarcía García, Catalinahttps://hdl.handle.net/10481/896692024-02-29T09:16:43ZCollinearity diagnostic applied in ridge estimation through the variance inflation factor
Salmerón Gómez, Román; García Pérez, José; López Martín, María Del Mar; García García, Catalina
The variance inflation factor (VIF) is used to detect the presence of linear relationships between two or more independent variables (i.e. collinearity) in the multiple linear regression model. However, the traditionally used VIF definitions encounter some problems when extended to the case of the ridge estimation (RE). This paper presents an extension of the VIF in RE by providing two alternative VIF expressions that overcome these problems in the general case. Some characteristics of these expressions are also presented and compared with the traditional expression. The results are illustrated with an economic example in the case of three independent variables and with a Monte Carlo simulation for the general case.