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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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

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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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  1. AAEC 4302ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 13.3 Multicollinearity

  2. 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

  3. 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

  4. 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

  5. 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

  6. Symptoms of Multicollinearity • The symptoms of a multicollinearity problem • independent variable(s) considered critical in explaining the model’s dependent variable are not statistically significant according to the tests

  7. Symptoms of Multicollinearity • High R2, highly significant F-test, but few or no statistically significant t tests • Parameter estimates drastically change values and become statistically significant when excluding some independent variables from the regression

  8. 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:

  9. 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

  10. 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

  11. 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

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