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<h1>Collinearity diagnostics</h1>
<small class="dont-index">Source: <a href='https://github.com/rsquaredacademy/blorr/blob/master/R/blr-collinearity-diagnostics.R'><code>R/blr-collinearity-diagnostics.R</code></a></small>
<div class="hidden name"><code>blr_coll_diag.Rd</code></div>
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<div class="ref-description">
<p>Variance inflation factor, tolerance, eigenvalues and condition indices.</p>
</div>
<pre class="usage"><span class='fu'>blr_coll_diag</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span>
<span class='fu'>blr_vif_tol</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span>
<span class='fu'>blr_eigen_cindex</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>model</th>
<td><p>An object of class <code>glm</code>.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p><code>blr_coll_diag</code> returns an object of class <code>"blr_coll_diag"</code>.
An object of class <code>"blr_coll_diag"</code> is a list containing the
following components:</p>
<dt>vif_t</dt><dd><p>tolerance and variance inflation factors</p></dd>
<dt>eig_cindex</dt><dd><p>eigen values and condition index</p></dd>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>Collinearity implies two variables are near perfect linear combinations of
one another. Multicollinearity involves more than two variables. In the
presence of multicollinearity, regression estimates are unstable and have
high standard errors.</p>
<p><em>Tolerance</em></p>
<p>Percent of variance in the predictor that cannot be accounted for by other predictors.</p>
<p><em>Variance Inflation Factor</em></p>
<p>Variance inflation factors measure the inflation in the variances of the parameter estimates due to
collinearities that exist among the predictors. It is a measure of how much the variance of the estimated
regression coefficient \(\beta_k\) is inflated by the existence of correlation among the predictor variables
in the model. A VIF of 1 means that there is no correlation among the kth predictor and the remaining predictor
variables, and hence the variance of \(\beta_k\) is not inflated at all. The general rule of thumb is that VIFs
exceeding 4 warrant further investigation, while VIFs exceeding 10 are signs of serious multicollinearity
requiring correction.</p>
<p><em>Condition Index</em></p>
<p>Most multivariate statistical approaches involve decomposing a correlation matrix into linear
combinations of variables. The linear combinations are chosen so that the first combination has
the largest possible variance (subject to some restrictions), the second combination
has the next largest variance, subject to being uncorrelated with the first, the third has the largest
possible variance, subject to being uncorrelated with the first and second, and so forth. The variance
of each of these linear combinations is called an eigenvalue. Collinearity is spotted by finding 2 or
more variables that have large proportions of variance (.50 or more) that correspond to large condition
indices. A rule of thumb is to label as large those condition indices in the range of 30 or larger.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Belsley, D. A., Kuh, E., and Welsch, R. E. (1980). Regression Diagnostics: Identifying Influential Data and
Sources of Collinearity. New York: John Wiley & Sons.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><span class='r-in'><span class='co'># model</span></span>
<span class='r-in'><span class='va'>model</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/glm.html'>glm</a></span><span class='op'>(</span><span class='va'>honcomp</span> <span class='op'>~</span> <span class='va'>female</span> <span class='op'>+</span> <span class='va'>read</span> <span class='op'>+</span> <span class='va'>science</span>, data <span class='op'>=</span> <span class='va'>hsb2</span>,</span>
<span class='r-in'>family <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/stats/family.html'>binomial</a></span><span class='op'>(</span>link <span class='op'>=</span> <span class='st'>'logit'</span><span class='op'>)</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># vif and tolerance</span></span>
<span class='r-in'><span class='fu'>blr_vif_tol</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span></span>
<span class='r-out co'><span class='r-pr'>#></span> Variable Tolerance VIF</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 female1 0.9824347 1.017879</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 read 0.6021370 1.660752</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 science 0.5939847 1.683545</span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># eigenvalues and condition indices</span></span>
<span class='r-in'><span class='fu'>blr_eigen_cindex</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span></span>
<span class='r-out co'><span class='r-pr'>#></span> Eigenvalue Condition Index intercept female1 read</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 3.57391760 1.000000 3.500782e-06 2.232611e-05 0.0006577134</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 0.39409893 3.011408 5.155657e-06 8.559696e-04 0.0015266309</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 0.01888407 13.757025 1.632498e-03 4.397949e-05 0.1143698337</span>
<span class='r-out co'><span class='r-pr'>#></span> 4 0.01309940 16.517583 5.619292e-05 1.312420e-05 0.2758987745</span>
<span class='r-out co'><span class='r-pr'>#></span> science</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 0.0009448623</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 0.0025603607</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 0.0545537252</span>
<span class='r-out co'><span class='r-pr'>#></span> 4 0.5468553525</span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># collinearity diagnostics</span></span>
<span class='r-in'><span class='fu'>blr_coll_diag</span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span></span>
<span class='r-out co'><span class='r-pr'>#></span> Tolerance and Variance Inflation Factor</span>
<span class='r-out co'><span class='r-pr'>#></span> ---------------------------------------</span>
<span class='r-out co'><span class='r-pr'>#></span> Variable Tolerance VIF</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 female1 0.9824347 1.017879</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 read 0.6021370 1.660752</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 science 0.5939847 1.683545</span>
<span class='r-out co'><span class='r-pr'>#></span> </span>
<span class='r-out co'><span class='r-pr'>#></span> </span>
<span class='r-out co'><span class='r-pr'>#></span> Eigenvalue and Condition Index</span>
<span class='r-out co'><span class='r-pr'>#></span> ------------------------------</span>
<span class='r-out co'><span class='r-pr'>#></span> Eigenvalue Condition Index intercept female1 read</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 3.57391760 1.000000 3.500782e-06 2.232611e-05 0.0006577134</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 0.39409893 3.011408 5.155657e-06 8.559696e-04 0.0015266309</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 0.01888407 13.757025 1.632498e-03 4.397949e-05 0.1143698337</span>
<span class='r-out co'><span class='r-pr'>#></span> 4 0.01309940 16.517583 5.619292e-05 1.312420e-05 0.2758987745</span>
<span class='r-out co'><span class='r-pr'>#></span> science</span>
<span class='r-out co'><span class='r-pr'>#></span> 1 0.0009448623</span>
<span class='r-out co'><span class='r-pr'>#></span> 2 0.0025603607</span>
<span class='r-out co'><span class='r-pr'>#></span> 3 0.0545537252</span>
<span class='r-out co'><span class='r-pr'>#></span> 4 0.5468553525</span>
<span class='r-in'></span>
</pre>
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