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Generalized Regression Penalty against Complexity
Published in Chong Ho Alex Yu, Data Mining and Exploration, 2022
Understanding multi-collinearity should go hand in hand with understanding variance inflation. Variance inflation is the consequence of multi-collinearity. We may distinguish them by saying that multi-collinearity is the symptom while variance inflation is the disease. Variance inflation factor (VIF) provides an index that measures how much the variance of an estimated regression coefficient is increased due to collinearity. The formula of VIF is: 1–(1–R2). To compute the VIF of each predictor, the predictor becomes the dependent variable, and all other variables are used to regress against it. The analyst can decide which variable to throw out by examining the size of the VIF. A general rule is that the VIF should not exceed 10 (Belsley et al. 2013). As mentioned before, when the number of predictors increases, the R2 also increases. As a remedy, the adjusted R2 is used to scale down the R2 by adjusting for the number of predictors. When the VIF of some predictors approaches 10, the multiple regression model might yield a negative adjusted R2 because the so-called model is worse than no model at all! In addition, when collinearity exists, there would be no unique solution for the regression coefficients. Rather, there would be an infinite number of solutions (O’Brien 2012).
Linear Regression
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
The most common remedial measures are now described. The interested reader is directed to other references to explore in greater detail remedial measures for dealing with multicollinearity (e.g., Neter et al., 1996; Greene, 2000; Myers, 1990). Often pairwise correlation between variables is used to detect multicollinearity. It is possible, however, to have serious multicollinearity between groups of independent variables; for example, X3 is highly correlated with a linear combination of X1 and X2. The variance inflation factor (VIF) is often used to detect serious multicollinearity.Ridge regression, a method that produces biased but efficient estimators for obtaining parameter estimates, is also used to avoid the inefficient parameter estimates obtained under multicollinearity.Often when variables have serious multicollinearity, one of the offending variables is removed from the model. This action is justified when there are theoretical grounds for removing the variable. For example, an independent variable thought to have an associative rather than causal relationship with the response might be omitted. Another justification might be that only one of the variables is collected in practice and used for future predictions. Removing a variable, however, also removes any unique effects this variable may have on the outcome variable.Doing nothing is a common response to multicollinearity. The effects of leaving correlated variables in the model and the limitations involved with interpreting the model should be recognized and documented.An ideal remedy for multicollinearity is to control levels of the suspected multicollinear variables during the study design phase. Although this solution requires the ability to understand the threats of multicollinearity prior to data collection, it is the optimal statistical solution. For example, a suspected high correlation between the variables household income and value of vehicle might be remedied by stratifying households to ensure that all stratifications of low, medium, and high household income and low, medium, and high value of vehicle are obtained.
Combination four different ensemble algorithms with the generalized linear model (GLM) for predicting forest fire susceptibility
Published in Geomatics, Natural Hazards and Risk, 2023
Saeid Janizadeh, Sayed M. Bateni, Changhyun Jun, Jungho Im, Hao-Thing Pai, Shahab S. Band, Amir Mosavi
Multicollinearity is a problem that arises when predictor variables in machine learning (ML) models are highly correlated with each other. This can result in unreliable coefficients, reduced interpretability of the model, and decreased prediction accuracy (Alin, 2010). To mitigate these issues, it is essential to assess the strength of multicollinearity among input variables in ML models. One of the most widely used metrics for assessing multicollinearity is the variance inflation factor (VIF). VIF quantifies the increase in variance of an estimated regression coefficient due to collinearity in the predictor variables (Paul, 2006). The VIF is calculated as: where is the determination coefficient of the regression of the ith predictor variable on all the other predictor variables. VIF values less than 1 imply no multicollinearity, while VIF values from 1 to 5 show mild multicollinearity. Moderate multicollinearity occurs when the VIF is between 5 and 10, and severe multicollinearity happens for the VIF of larger than 10. By conducting a VIF analysis, researchers can gain insights into the extent of multicollinearity among input variables and make informed decisions about which predictor variables to include or exclude from the model (Paul, 2006; Alin, 2010).
Effects of Seated Postural Sway on Visually Induced Motion Sickness: A Multiple Regression and RUSBoost Classification Approach
Published in International Journal of Human–Computer Interaction, 2023
The predictor values and gender explained 75.2% of the SSQdiff. variance among the samples of all participants (F = 12.359; df = 4, 11; p < 0.001; Durbin–Watson = 2.433). Multicollinearity indicates a high degree of linear intercorrelation among independent variables in a multiple regression model, and it can lead to biased results of regression analyses. The statistical values, such as tolerance and variance inflation factor (VIF) are significant criteria for determining the presence of multicollinearity. If the tolerance and VIF values are both below 0.1 and higher than 10, respectively, it could potentially lead to a significant multicollinearity issue (Daoud, 2017). We identified that the regression models used in this study had no multicollinearity problem among the independent variables (i.e., tolerance values in the range of 0.616–0.769; VIF values in the range of 1.300–1.623). The equation that estimates the SSQ score (i.e., SSQdiff.) of motion sickness from the and, gender was extracted as follows:
Eco-friendly value or others’ environmental norms? Arguing the environmental using psychology of bike-sharing for the general public
Published in Transportation Letters, 2019
To comprehend any multicollinearity effects of correlations, this research confirms any warning information produced by the AMOS results of a problem of multicollinearity. The output indicated no proof of multicollinearity; regression analysis was then used to assess multicollinearity further. For regression analysis, the variance inflation factor (VIF) is generally applied to estimate the level at which every independent variable is interpreted by other independent variables, and is an ordinary evaluation method for multicollinearity (Hair et al. 2010). Keith (2014) showed that the VIF is less than or equal to 10, and tolerance is more than 0.1 among variables with no multicollinearity. In this study, the VIFs of perceived environmental value, environmental trust, and environmental subjective norms for users (and non-users) were 1.230 (1.483), 1.423 (1.616), and 1.251 (1.185), respectively, and therefore, showed no further evidence of multicollinearity.