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    <p>Just to add to what Dirk said about the Condition Number method, a rule of thumb is that values of <code>CN &gt; 30 indicate severe collinearity</code>. Other methods, apart from condition number, include:</p> <p>1) the determinant of the covariance matrix which ranges from 0 (Perfect Collinearity) to 1 (No Collinearity)</p> <pre><code># using Dirk's example &gt; det(cov(mm12[,-1])) [1] 0.8856818 &gt; det(cov(mm123[,-1])) [1] 8.916092e-09 </code></pre> <p>2) Using the fact that the determinant of a diagonal matrix is the product of the eigenvalues => The presence of one or more small eigenvalues indicates collinearity</p> <pre><code>&gt; eigen(cov(mm12[,-1]))$values [1] 1.0876357 0.8143184 &gt; eigen(cov(mm123[,-1]))$values [1] 5.388022e+00 9.862794e-01 1.677819e-09 </code></pre> <p>3) The value of the Variance Inflation Factor (VIF). The VIF for predictor i is 1/(1-R_i^2), where R_i^2 is the R^2 from a regression of predictor i against the remaining predictors. Collinearity is present when VIF for at least one independent variable is large. Rule of Thumb: <code>VIF &gt; 10 is of concern</code>. For an implementation in R see <a href="http://finzi.psych.upenn.edu/R/library/HH/html/vif.html" rel="noreferrer">here</a>. I would also like to comment that the use of R^2 for determining collinearity should go hand in hand with visual examination of the scatterplots because a single outlier can "cause" collinearity where it doesn't exist, or can HIDE collinearity where it exists. </p>
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