<p><div><div><div><div data-width="100" data-show-faces="false" data-send="true" data-layout="button_count" data-height="21" data-href="http://www.r-bloggers.com/principal-components-regression-in-r-part-2/"></div></div><div><a data-url="http://www.r-bloggers.com/principal-components-regression-in-r-part-2/" data-counturl="http://www.r-bloggers.com/principal-components-regression-in-r-part-2/" data-count="horizontal" data-text="Principal Components Regression in R: Part 2" class="twitter-share-button" data-via="rbloggers" href="https://twitter.com/share"></a></div><div></div></div><div></div></div>
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(This article was first published on <strong><a href="http://blog.revolutionanalytics.com/2016/05/principal-components-regression-part-2.html"> Revolutions</a></strong>, and kindly contributed to <a rel="nofollow" href="http://www.r-bloggers.com/">R-bloggers)</a> </div>
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<p>by John Mount Ph. D.<br>Data Scientist at<a target="_blank" href="http://www.win-vector.com/site/staff/"> Win-Vector LLC</a></p>
<p>In <a target="_blank" href="http://www.win-vector.com/blog/2016/05/pcr_part2_yaware">part 2</a> of her series on Principal Components Regression Dr. Nina Zumel illustrates so-called <em>y</em>-aware techniques. These often neglected methods use the fact that for predictive modeling problems we know the dependent variable, outcome or <em>y</em>, so we can use this during data preparation <em>in addition to</em> using it during modeling. Dr. Zumel shows the incorporation of <em>y</em>-aware preparation into Principal Components Analyses can capture more of the problem structure in fewer variables. Such methods include:</p>
<ul>
<li>Effects based variable pruning</li>
<li>Significance based variable pruning</li>
<li>Effects based variable scaling.</li>
</ul>
<p>This recovers more domain structure and leads to better models. Using the foundation set in the first article Dr. Zumel quickly shows how to move from a traditional <em>x</em>-only analysis that fails to preserve a domain-specific relation of two variables to outcome to a <em>y</em>-aware analysis that preserves the relation. Or in other words how to move away from a middling result where different values of y (rendered as three colors) are hopelessly intermingled when plotted against the first two found latent variables as shown below.</p>
<p><img title="NewImage.png" alt="NewImage" src="http://i0.wp.com/www.win-vector.com/blog/wp-content/uploads/2016/05/NewImage-1.png?resize=456%2C456" border="0" data-recalc-dims="1"></p>
<p>Dr. Zumel shows how to perform a decisive analysis where <em>y</em> is somewhat sortable by the each of the first two latent variable <em>and</em> the first two latent variables capture complementary effects, making them good mutual candidates for further modeling (as shown below).</p>
<p><img title="NewImage.png" alt="NewImage" src="http://i2.wp.com/www.win-vector.com/blog/wp-content/uploads/2016/05/NewImage.png?resize=456%2C456" border="0" data-recalc-dims="1"> Click <a target="_blank" href="http://www.win-vector.com/blog/2016/05/pcr_part2_yaware">here (part 2 <em>y</em>-aware methods)</a> for the discussion, examples, and references. Part 1 (<em>x</em> only methods) can be found <a target="_blank" href="http://www.win-vector.com/blog/2016/05/pcr_part1_xonly">here</a>.</p>
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<div>To <strong>leave a comment</strong> for the author, please follow the link and comment on their blog: <strong><a href="http://blog.revolutionanalytics.com/2016/05/principal-components-regression-part-2.html"> Revolutions</a></strong>.</div>
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