Multicollinearity
What Is Multicollinearity?
Multicollinearity is the occurrence of high intercorrelations among two or more independent variables in a multiple regression model. Multicollinearity can lead to skewed or misleading results when a researcher or analyst attempts to determine how well each independent variable can be used most effectively to predict or understand the dependent variable in a statistical model.
In general, multicollinearity can lead to wider confidence intervals that produce less reliable probabilities in terms of the effect of independent variables in a model.
Understanding Multicollinearity
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 referred to as the outcome, target, or criterion variable.
An example is a multivariate regression model that attempts to anticipate stock returns based on items, for example, price-to-earnings ratios (P/E ratios), market capitalization, past performance, or other data. The stock return is the dependent variable and the different pieces of financial data are the independent variables.
Multicollinearity in a multiple regression model indicates that collinear independent variables are related in some fashion, albeit the relationship could conceivably be easygoing. For example, past performance may be related to market capitalization, as stocks that have performed well in the past will have increasing market values.
In other words, multicollinearity can exist when two independent variables are highly correlated. It can likewise happen on the off chance that an independent variable is computed from other variables in the data set or on the other hand assuming two independent variables provide comparative and repetitive results.
Special Considerations
One of the most common approaches to eliminating the problem of multicollinearity is to initially identify collinear independent variables and afterward remove everything except one.
Wiping out multicollinearity by consolidating two or more collinear variables into a single variable is likewise possible. Statistical analysis can then be conducted to study the relationship between the specified dependent variable and just a single independent variable.
The statistical inferences from a model that contains multicollinearity may not be dependable.
Examples of Multicollinearity
In Investing
For investing, multicollinearity is a common consideration when performing technical analysis to predict probable future price movements of a security, for example, a stock or a commodity future.
Market analysts need to try not to use technical indicators that are collinear in that they are based on very comparable or related inputs; they tend to reveal comparative predictions regarding the dependent variable of price movement. Instead, the market analysis must be based on markedly different independent variables to ensure that they analyze the market from different independent insightful viewpoints.
An example of a potential multicollinearity problem is performing technical analysis just utilizing several comparable indicators.
Noted technical analyst John Bollinger, creator of the Bollinger Bands indicator, notes that "a foundational guideline for the successful use of technical analysis requires staying away from multicollinearity in the midst of indicators." To solve the problem, analysts try not to use two or more technical indicators of the same type. Instead, they analyze a security utilizing one type of indicator, like a momentum indicator, and afterward do a separate analysis utilizing a different type of indicator, like a trend indicator.
For example, stochastics, the relative strength index (RSI), and Williams %R are all momentum indicators that rely on comparable inputs and are likely to produce comparative results. In this case, it is better to remove everything except one of the indicators or figure out how to merge several of them into just one indicator, while likewise adding a trend indicator that isn't likely to be highly correlated with the momentum indicator.
In Biology
Multicollinearity is likewise observed in numerous other contexts. One such context is human science. For example, a singular's circulatory strain isn't collinear with age, yet additionally weight, stress, and pulse.
Highlights
- Multicollinearity is a statistical concept where several independent variables in a model are correlated.
- Multicollinearity among independent variables will result in less reliable statistical inferences.
- It is better to use independent variables that are not correlated or repetitive when building multiple regression models that use two or more variables.
- Two variables are considered to be perfectly collinear on the off chance that their correlation coefficient is +/ - 1.0.
- The existence of multicollinearity in a data set can lead to less reliable results due to larger standard errors.
FAQ
Why Is Multicollinearity a Problem?
Multicollinearity is a problem because it produces regression model results that are less reliable. This is due to wider confidence intervals (larger standard errors) that can lower the statistical significance of regression coefficients.
How Might One Deal With Multicollinearity?
To reduce the amount of multicollinearity found in a model, one can remove the specific variables that are identified as the most collinear. You can likewise try to combine or transform the offending variables to lower their correlation. In the event that that does not work or is unattainable, there are modified regression models that better deal with multicollinearity, like the ridge regression, principal component regression, or partial least squares regression.
How Do You Detect Multicollinearity?
A statistical technique called the variance inflation factor (VIF) is used to detect and measure the amount of collinearity in a multiple regression model.
What Is Perfect Collinearity?
Perfect collinearity exists when there is an exact 1:1 correspondence between two independent variables in a model. This can be either a correlation of +1.0 or - 1.0.
