Obtaining a threshold for the stewart index and its extension to ridge regression
| Autor: | Catalina Beatriz García García, Román Salmerón Gómez, Ainara Rodríguez Sánchez |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Variables media_common.quotation_subject 05 social sciences Collinearity 01 natural sciences Measure (mathematics) Regression 010104 statistics & probability Computational Mathematics Multicollinearity 0502 economics and business Ordinary least squares Linear regression Statistics 0101 mathematics Statistics Probability and Uncertainty Condition number 050205 econometrics Mathematics media_common |
| Zdroj: | Computational Statistics. 36:1011-1029 |
| ISSN: | 1613-9658 0943-4062 |
| DOI: | 10.1007/s00180-020-01047-2 |
| Popis: | The linear regression model is widely applied to measure the relationship between a dependent variable and a set of independent variables. When the independent variables are related to each other, it is said that the model presents collinearity. If the relationship is between the intercept and at least one of the independent variables, the collinearity is nonessential, while if the relationship is between the independent variables (excluding the intercept), the collinearity is essential. The Stewart index allows the detection of both types of near multicollinearity. However, to the best of our knowledge, there are no established thresholds for this measure from which to consider that the multicollinearity is worrying. This is the main goal of this paper, which presents a Monte Carlo simulation to relate this measure to the condition number. An additional goal of this paper is to extend the Stewart index for its application after the estimation by ridge regression that is widely applied to estimate model with multicollinearity as an alternative to ordinary least squares (OLS). This extension could be also applied to determine the appropriate value for the ridge factor. |
| Databáze: | OpenAIRE |
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