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<h1>Robust Regression</h1>
<blockquote>
<p>Robust regression can be used in any situation where OLS regression can be applied. It generally gives better accuracies over OLS because it uses a weighting mechanism to weigh down the influential observations. It is particularly resourceful when there are no compelling reasons to exclude outliers in your data.</p>
</blockquote>
<p>Robust regression can be implemented using the <code>rlm()</code> function in MASS package. The outliers can be weighted down differently based on <code>psi.huber</code>, <code>psi.hampel</code> and <code>psi.bisquare</code> methods specified by the <code>psi</code> argument.</p>
<h2>How To Specify A Robust Regression Model</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(MASS)
rlm_mod <-<span class="st"> </span><span class="kw">rlm</span>(stack.loss ~<span class="st"> </span>., stackloss, <span class="dt">psi =</span> psi.bisquare) <span class="co"># robust reg model</span>
<span class="kw">summary</span>(rlm_mod)
<span class="co">#> Call: rlm(formula = stack.loss ~ ., data = stackloss)</span>
<span class="co">#> Residuals:</span>
<span class="co">#> Min 1Q Median 3Q Max </span>
<span class="co">#> -8.91753 -1.73127 0.06187 1.54306 6.50163 </span>
<span class="co">#> </span>
<span class="co">#> Coefficients:</span>
<span class="co">#> Value Std. Error t value </span>
<span class="co">#> (Intercept) -41.0265 9.8073 -4.1832</span>
<span class="co">#> Air.Flow 0.8294 0.1112 7.4597</span>
<span class="co">#> Water.Temp 0.9261 0.3034 3.0524</span>
<span class="co">#> Acid.Conc. -0.1278 0.1289 -0.9922</span>
<span class="co">#> </span>
<span class="co">#> Residual standard error: 2.441 on 17 degrees of freedom</span></code></pre></div>
<h2>Compare Performance of <code>rlm()</code> with <code>lm()</code></h2>
<p>Lets build the equivalent <code>lm()</code> model so we can compare the errors against the respective fitted values.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">lm_mod <-<span class="st"> </span><span class="kw">lm</span>(stack.loss ~<span class="st"> </span>., stackloss) <span class="co"># lm reg model</span></code></pre></div>
<h4>Calculate the Errors</h4>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Errors from lm() model</span>
DMwR::<span class="kw">regr.eval</span>(stackloss$stack.loss, lm_mod$fitted.values)
<span class="co">#> mae mse rmse mape </span>
<span class="co">#> 2.3666202 8.5157125 2.9181694 0.1458878</span>
<span class="co"># Errors from rlm() model</span>
DMwR::<span class="kw">regr.eval</span>(stackloss$stack.loss, rlm_mod$fitted.values)
<span class="co">#> mae mse rmse mape </span>
<span class="co">#> 2.1952232 9.0735283 3.0122298 0.1317191</span></code></pre></div>
<p>As expected, the errors from the robust regression model is lesser than the linear regression model.</p>
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