Causes and Consequences of Multicollinearity

Being a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy, this content has taken pleasure in helping you outline the causes and consequences of multicollinearity in a wrong modelled regression.

Multicollinearity is a term used in data analytics that describes the occurrence of two exploratory variables in a linear regression model that is found to be correlated through adequate analysis and a predetermined degree of accuracy. The variables are independent and are found to be correlated in some regard.

Multicollinearity comes with many pitfalls that can affect the efficacy of a model and understanding why it can lead to stronger models and a better ability to make decisions.

Creating an Accurate Multicollinearity

Once you’ve determined that there’s an issue with multicollinearity in your model, there are several different ways that you can go about trying to fix it so that you can create an accurate regression model.

  • Obtain more data: The more data you obtain for your model, the more precise the measurements can be and the less variance there will be. This is one of the more obvious solutions to multicollinearity.
  • Removing a variable: Removing a variable can make your model less representative; however, it can sometimes be the only solution to removing and avoiding multicollinearity altogether.
  • Create a standard set of independent variables.
  • Utilize a ridge regression or partial squares regression in conjunction with your model.
  • If all else fails or you decide it’s not worth it to do any additional work on the model, do nothing: Even by not changing a model where you know multicollinearity exists, it still may not affect the efficiency of taking data from the existing model.

Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multivariate regression model with collinear predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others.

Causes and Consequences of Multicollinearity

Dissecting the causes and consequences of multicollinearity, you will be taken through the pros and cons of the subject and then taught to watch out for certain principles to avoid or embrace.

Pitfalls That Brought About the Multicollinearity

  • Poor Experiments

Data-based multicollinearity caused by poorly designed experiments, data that is 100% observational, or data collection methods that cannot be manipulated. In some cases, variables may be highly correlated (usually due to collecting data from purely observational studies) and there is no error on the researcher’s part. For this reason, you should conduct experiments whenever possible, setting the level of the predictor variables in advance.

  • Strange Predictor Variable

Structural multicollinearity caused by you, the researcher, creating new predictor variables.

  • Inadequacy of Data

In some cases, collecting more data can resolve the issue.

  • Incorrect Use of Variables

Dummy variables may be incorrectly used. For example, the researcher may fail to exclude one category, or add a dummy variable for every category (e.g. spring, summer, autumn, winter). Including a variable in the regression that is actually a combination of two other variables. For example, including “total investment income” when total investment income = income from stocks and bonds + income from savings interest.

Including two identical (or almost identical) variables. For example, weight in pounds and weight in kilos, or investment income and savings/bond income.

Effects That Multicollinearity Bring

  • Inaccuracy

One consequence of a high degree of multicollinearity is that, even if the matrix {\displaystyle X^{\mathsf {T}}X} is invertible, a computer algorithm may be unsuccessful in obtaining an approximate inverse, and if it does obtain one, the inverse may be numerically inaccurate. But even in the presence of an accurate {\displaystyle X^{\mathsf {T}}X} matrix, the other consequences may arise.

  • Precision Problem

The usual interpretation of a regression coefficient is that it estimates the effect of a one-unit change in an independent variable, {\displaystyle X_{1}}, holding the other variables constant. In the presence of multicollinearity, this tends to be less precise than if predictors were uncorrelated with one another. If {\displaystyle X_{1}} is highly correlated with another independent variable {\displaystyle X_{2}} in the given data set, then {\displaystyle X_{1}} and {\displaystyle X_{2}} have a particular linear stochastic relationship in the set. In other words, changes in {\displaystyle X_{1}} are not independent of changes in {\displaystyle X_{2}}. This correlation creates an imprecise estimate of the effect of independent changes in {\displaystyle X_{1}}.

  • Redundancy

In some sense, the collinear variables contain the same information about the dependent variable. If nominally “different” measures quantify the same phenomenon, then they are redundant. Alternatively, if the variables are accorded different names and perhaps employ different numeric measurement scales but are highly correlated with each other, then they suffer from redundancy.

A principal danger of such data redundancy is overfitting in regression analysis models. The best regression models are those in which the predictor variables each correlate highly with the dependent variable (outcome) but correlate only minimally with each other. Such a model is often called “low noise” and will be statistically robust (that is, it will predict reliably across numerous samples of variable sets drawn from the same statistical population).

  • Biased Specification

If the underlying specification is anything less than complete and correct, multicollinearity amplifies misspecification biases. Even though not often recognized in methods texts, this is a common problem in the social sciences where a complete, correct specification of an OLS regression model is rarely known and at least some relevant variables will be unobservable.

As a result, the estimated coefficients of correlated independent variables in an OLS regression will be biased by multicollinearity. As the correlation approaches one, the coefficient estimates will misleadingly tend toward infinite magnitudes in opposite directions, even if the variables’ true effects are small and of the same sign.

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