A Guide to Multicollinearity & VIF in Regression

At its core, multicollinearity affects the precision and reliability of regression analysis, making it a significant barrier to predicting outcomes based on multiple variables. One method for detecting whether multicollinearity is a problem is to compute the variance inflation factor, or VIF. This is a measure of how much the standard error of the estimate of the coefficient is inflated due to multicollinearity. From the last column, we can see that the VIF values for height and shoe size are both greater than 5.

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To illustrate, let’s consider a hypothetical regression analysis aiming to predict real estate prices based on factors like square footage, age of the property, and proximity to the city center. When multicollinearity is present, the precision of the estimated coefficients is reduced, which in turn clouds the interpretative clarity of the model. This section explores the adverse effects of multicollinearity on coefficient estimates and outlines why addressing this issue is essential in data analysis. Of course, this polynomial equation aims to measure and map the correlation between Y and Xn. In an ideal predictive model, none of the independent variables (Xn) are themselves correlated.

Detecting multicollinearity with the variance inflation factor (VIF)

Multicollinearity prevents predictive models from producing accurate predictions by increasing model complexity and overfitting. To reduce the amount of multicollinearity found in a statistical model, one can remove the specific variables identified as the most collinear. You can also try to combine or transform the offending variables to lower their correlation. If that does not work or is unattainable, there are modified regression models that better deal with multicollinearity, such as ridge regression, principal component regression, or partial least squares regression. Statistical analysts use multiple regression models to predict the value of a specified dependent variable based on the values of two or more independent variables. The dependent variable is sometimes called the outcome, target, or criterion variable.

• This issue can lead to erroneous decisions in policy-making, business strategy, and other areas reliant on accurate data interpretation.
• Data will have high multicollinearity when the variable inflation factor is more than five.
• A poorly designed experiment or data collection process, such as using observational data, generally results in data-based multicollinearity, where data is correlated due to the nature of the way it was collected.
• Several regularization techniques also help correct the problem of multicollinearity.
• It is reasonable to exclude unimportant predictors if they are known ahead of time to have little or no effect on the outcome; for example, local cheese production should not be used to predict the height of skyscrapers.
• One of the most direct impacts of multicollinearity is the reduction in the precision of the estimated coefficients.

Identifying the root causes of multicollinearity is crucial for effectively managing its impact in regression analysis. This section discusses the primary factors that contribute to multicollinearity, providing insight into how it can arise in both statistical modeling and practical market research scenarios. This determines if the inversion of the matrix is numerically unstable with finite-precision numbers, indicating the potential sensitivity of the computed inverse to small changes in the original matrix.

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Understanding the nuances between perfect, high, structural, and data-based multicollinearity is essential for effectively diagnosing and remedying this condition. Linearly combine the predictor variables in some way, such as adding or subtracting them from one way. By doing so, you can create one new variables that encompasses the information from both variables and you no longer have an issue of multicollinearity. Multicollinearity only affects the predictor variables that are correlated with one another. If you are interested in a predictor variable in the model that doesn’t suffer from multicollinearity, then multicollinearity isn’t a concern.

Perfect multicollinearity

In linear regression analysis, no two variables or predictors can share an exact relationship in any manner. Thus, when multicollinearity occurs, it negatively affects the regression analysis model, and the researchers obtain unreliable results. Therefore, detecting such a phenomenon beforehand saves researchers time and effort. Data-based multicollinearity arises purely from the dataset used, rather than from inherent relationships in the model. It often appears when data collection methods inadvertently create correlations between independent variables.

• The significance of multicollinearity extends beyond theoretical concerns—it has practical implications in the real world.
• For example, momentum and trend indicators share the same data, but they will not be perfectly multicollinear or even demonstrate high multicollinearity.
• When using technical analysis, multicollinearity becomes a problem because there are many indicators that present the data in the same way.
• These FAQs are designed to clarify common misconceptions and offer practical insights into the implications of multicollinearity in regression analysis.
• For example, if in a financial model, ‘total assets’ is always the sum of ‘current assets’ and ‘fixed assets,’ then using all three variables in a regression will lead to perfect multicollinearity.
• This confounding becomes substantially worse when researchers attempt to ignore or suppress it by excluding these variables from the regression (see #Misuse).

Data will have high multicollinearity when the variable inflation factor is more than five. If the VIF is between one and five, variables are moderately correlated, and if equal to one, they are not correlated. For instance, if you collected data and then used it to perform other calculations and ran a regression on the results, the outcomes will be correlated because they are derived from each other. The concept is significant in the stock market, where market analysts use technical analysis tools to determine the expected fluctuation in asset prices. This is because the analysts aim at figuring out the influence of each factor on the market in different ways from different aspects. In longitudinal studies, where data points are collected over time, multicollinearity can occur due to changes in technology, society, or the economy that influence the variables similarly.

Multicollinearity in regression analysis occurs when two or more predictor variables are highly correlated to each other, such that they do not provide unique or independent information in the regression model. Multicollinearity exists whenever an independent variable is highly correlated with one or more of the other independent variables in a multiple regression equation. Multicollinearity is a problem because it will make the statistical inferences less reliable. However, the Variance Inflation Factor (VIF) can provide information about which variable or variables are redundant, and thus the variables that have a high VIF can be removed. High multicollinearity demonstrates a correlation between multiple independent variables, but it multicollinearity meaning is not as tight as in perfect multicollinearity. Not all data points fall on the regression line, but it still signifies data is too tightly correlated to be used.

Remedies to perfect multicollinearity

In just a few minutes, you can create powerful surveys with our easy-to-use interface. Since computers perform finite-precision arithmetic, they introduce round-off errors in the computation of products and additions such as those in the matrix product . Here we provide an intuitive introduction to the concept of condition number, but see Brandimarte (2007) for a formal but easy-to-understand introduction. The condition number is the statistic most commonly used to check whether the inversion of may cause numerical problems. In such a case the design matrix is full-rank, but it is not very far from being rank-deficient. Roughly speaking, trying to invert a rank deficient matrix is like trying to compute the reciprocal of zero.

Effects on coefficient estimates

When using a scatter plot, one plots independent variable values for each data point against one another. If the scatter plot reveals a linear correlation between the chosen variables, then some degree of multicollinearity may be present. This figure illustrates multicollinear data in a scatter plot using the Montgomery et al. delivery dataset example. In some cases, one may use the squared or lagged values of independent variables as new model predictors. Of course, these new predictors will share a high correlation with the independent variables from whence they were derived.10 This is structural multicollinearity.

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If the degree of correlation is high enough between variables, it can cause problems when fitting and interpreting the regression model. Most investors won’t worry about the data and techniques behind the indicator calculations—it’s enough to understand what multicollinearity is and how it can affect an analysis. If users include the same variables named differently or a variable that combines two other variables in the model, it is an incorrect variable usage. For example, when total investment income includes two variables – income generated via stocks and bonds and savings interest income – presenting the total income investment as a variable might disturb the entire model. Therefore, researchers must remain careful about the exclusion or inclusion of the variables involved to avoid collinearity instances.