# Tips for Handling Multicollinearity in Regression Models

Multicollinearity is a common challenge faced by data analysts and researchers when building regression models. It occurs when independent variables in a regression model are highly correlated with each other. This causes the estimates of the regression coefficients to be unstable as the individual effect of each predictor on the dependent variable is masked by the predictor variable correlations. Multicollinearity can obscure the true relationships in data, leading to misleading conclusions if not corrected.

## 1. Detect Multicollinearity by Checking Your Correlation Matrix and Variance Inflation Factors

The first step in handling multicollinearity in regression models is identifying it. The two most widely used methods are the correlation matrix and variance inflation factors. Both techniques provide valuable insights into the relationships between independent variables and help identify problematic correlations.

A correlation matrix shows the correlations between sets of variables. Each correlation coefficient ranges from -1 to 1 where 0 indicates no correlation and -1 or 1 indicate perfect a negative or positive correlation. To assess multicollinearity, a correlation matrix of all the predictor variables can be constructed. Typically, a correlation greater than 0.80 or less than -0.80 is considered strong and indicates the presence of multicollinearity.

Alternatively, the variance inflation factor (VIF) is calculated for each predictor as part of the regression modeling process and quantify how much of the variance in a coefficient is inflated due to collinearity with other predictors. A VIF of 1 indicates no correlation and a value above 10 is generally used as an indicator of multicollinearity.

## 2. Reduce the Number of Variables

Once multicollinearity has been identified, the first solution is to eliminate variables that are correlated with other predictors. When two predictors are highly correlated, the more relevant predictor can be kept if applying domain knowledge. This is particularly useful if two variables measure very similar or overlapping factors, such as customer age and years since first purchase. Manually selecting relevant variables can be preferred to purely relying on a data driven model as it can result in a more interpretable and meaningful model.

There do exist data-driven methods for reducing collinearity. Feature selection methods such as stepwise regression or backward elimination independently evaluate each variable’s contribution to the model and remove those with little or no impact on the dependent variable. Principle Component Analysis (PCA) can also transform the original variables into a smaller set of uncorrelated components that are linear combinations of the original variables. This technique is useful when dealing with a large number of predictor variables, but does result in a less interpretable model as individual variables are no longer present.

## 3. Combine Highly Correlated Variables

Another effective strategy in dealing with multicollinearity is combining highly correlated variables. This reduced redundancy and simplifies the model while preserving the information content. A simple way to do this is by creating a composite score by averaging or summing variables into a new single variable. For example, in a customer satisfaction survey, questions about service quality, product quality, and overall satisfaction may be highly correlated. You can combine these into a single composite score representing overall customer satisfaction.

Many fields, such as psychology, health, or economics, have pre-existing index scores that formulaically combine variables and might include weights or different formulas for categorical groups. For example, an employee engagement index may use different questions or weightings for various age groups to calculate a composite score. Using a standardized index from the literature or developing one that matches the data available can be a way to combine multiple correlated variables into one easily interpreted, meaningful variable.

## 4. Utilize Regularization Techniques

Regularization techniques are powerful tools for addressing multicollinearity in regression models. These methods introduce a penalty term to the regression equation, which keeps the values of the independent variables from getting to large and resulting in a model that is more generalizable. The two most common regularization a Ridge and Lasso regression. Both shrink very large coefficients, therefore preventing any single variable from having an excessively large influence on the model and reducing the effect that impactful variables with multicollinearity would have. Lasso regressions go one step further by performing variable selection and removing the least impactful variables, resulting in a more interpretable final model.

## 5. Interpret in Context

While multicollinearity can pose challenges in regression modeling, it is important to keep in mind that it might not always be problematic. In some cases, and with proper justification, multicollinearity can be left in the final model. If the primary goal of the regression model is to make accurate predictions rather than understand the unique effect of each predictor, multicollinearity may not be a concern if the model still performs well. For example, in a marketing context different forms of expenditure may be highly correlated. However, if the priority is the ability of the model to capture overall trends rather than isolating the impact of each expenditure channel, all the variables can still be left in.

When multicollinearity is present, it is crucial to communicate its implications clearly. Stakeholders should be made aware that while the model’s predictions are reliable, the interpretation of individual predictor effects should be approached with caution. Transparency about the presence of multicollinearity and its potential impact on coefficient estimates helps maintain trust in the analysis.

## Conclusion

Understanding and handling multicollinearity is a critical aspect of building a robust and reliable regression model. Knowing why it appears and having reliable techniques to address it can lead to the development of models that have strong predictive power while also having individual coefficients that speak to the distinct relationships between the independent and dependent variables in the data.

## 2 Replies to “Tips for Handling Multicollinearity in Regression Models”

1. Leslie Glasser says:

Principal Component Analysis, not “Principle”

Otherwise very clear.

1. James Carmichael says:

Thank you Leslie!