AAEC 4302

ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

Chapter 13.3

Multicollinearity

Multicollinearity

• Multicollinearity occurs when two or more independent variables in a regression model are highly correlated to each other

• Standard error of the OLS parameter estimate will be higher if the corresponding independent variable is more highly correlated to the other independent variables in the model

Multicollinearity

• Independent variables show no statistical significance when conducting the basic significance test

• It is not a mistake in the model specification, but due to the nature of the data at hand

Perfect Multicollinearity

• Perfect multicollinearity occurs when there is a perfect linear correlation between two or more independent variables

• When independent variable takes a constant value in all observations

Severe Multicollinearity

• The OLS method cannot produce parameter estimates

• A certain degree of correlation (multicollinearity) between the independent variables is normal and expected in most cases

• Severe multicollinearity

Symptoms of Multicollinearity

• The symptoms of a multicollinearity problem

1. independent variable(s) considered critical in explaining the model’s dependent variable are not statistically significant according to the tests

Symptoms of Multicollinearity

2. High R2, highly significant F-test, but few or no statistically significant t tests

3. Parameter estimates drastically change values and become statistically significant when excluding some independent variables from the regression

Detecting Multicollinearity

• A simple test for multicollinearity is to conduct “artificial” regressions between each independent variable (as the “dependent” variable) and the remaining independent variables

• Variance Inflation Factors (VIFj) are calculated as:

•

2j

jR1

1VIF

Detecting Multicollinearity

• VIFj = 2, for example, means that variance is twice what it would be if Xj, was not affected by multicollinearity

• A VIFj>10 is clear evidence that the estimation of Bj is being affected by multicollinearity

Addressing Multicollinearity

• Although it is useful to be aware of the presence of multicollinearity, it is not easy to remedy severe (non-perfect) multicollinearity

• If possible, adding observations or taking a new sample might help lessen multicollinearity

Addressing Multicollinearity

• Exclude the independent variables that appear to be causing the problem

• Modifying the model specification sometimes help, for example:

using real instead of nominal economic data

using a reciprocal instead of a polynomial specification on a given independent variable