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<!DOCTYPE html>
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<title>Robust Linear Models — statsmodels 0.15.1 (+11)</title>
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<section id="robust-linear-models">
<span id="rlm"></span><h1>Robust Linear Models<a class="headerlink" href="#robust-linear-models" title="Link to this heading">#</a></h1>
<p>Robust linear models with support for the M-estimators listed under <a class="reference internal" href="#norms">Norms</a>.</p>
<p>See <a class="reference internal" href="#module-reference">Module Reference</a> for commands and arguments.</p>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading">#</a></h2>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="go"># Load modules and data</span>
<span class="gp">In [1]: </span><span class="kn">import</span><span class="w"> </span><span class="nn">statsmodels.api</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">sm</span>
<span class="gp">In [2]: </span><span class="n">data</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">stackloss</span><span class="o">.</span><span class="n">load</span><span class="p">()</span>
<span class="gp">In [3]: </span><span class="n">data</span><span class="o">.</span><span class="n">exog</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">exog</span><span class="p">)</span>
<span class="go"># Fit model and print summary</span>
<span class="gp">In [4]: </span><span class="n">rlm_model</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">RLM</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">data</span><span class="o">.</span><span class="n">exog</span><span class="p">,</span> <span class="n">M</span><span class="o">=</span><span class="n">sm</span><span class="o">.</span><span class="n">robust</span><span class="o">.</span><span class="n">norms</span><span class="o">.</span><span class="n">HuberT</span><span class="p">())</span>
<span class="gp">In [5]: </span><span class="n">rlm_results</span> <span class="o">=</span> <span class="n">rlm_model</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
<span class="gp">In [6]: </span><span class="nb">print</span><span class="p">(</span><span class="n">rlm_results</span><span class="o">.</span><span class="n">params</span><span class="p">)</span>
<span class="go">const -41.026498</span>
<span class="go">AIRFLOW 0.829384</span>
<span class="go">WATERTEMP 0.926066</span>
<span class="go">ACIDCONC -0.127847</span>
<span class="go">dtype: float64</span>
</pre></div>
</div>
<p>Detailed examples can be found here:</p>
<ul class="simple">
<li><p><a class="reference internal" href="examples/notebooks/generated/robust_models_0.html"><span class="doc">Robust Models 1</span></a></p></li>
<li><p><a class="reference internal" href="examples/notebooks/generated/robust_models_1.html"><span class="doc">Robust Models 2</span></a></p></li>
</ul>
</section>
<section id="technical-documentation">
<h2>Technical Documentation<a class="headerlink" href="#technical-documentation" title="Link to this heading">#</a></h2>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="rlm_techn1.html">Weight Functions</a></li>
</ul>
</div>
<section id="references">
<h3>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h3>
<ul class="simple">
<li><p>PJ Huber. ‘Robust Statistics’ John Wiley and Sons, Inc., New York. 1981.</p></li>
<li><p>PJ Huber. 1973, ‘The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.’ The Annals of Statistics, 1.5, 799-821.</p></li>
<li><p>R Venables, B Ripley. ‘Modern Applied Statistics in S’ Springer, New York,</p></li>
<li><p>C Croux, PJ Rousseeuw, ‘Time-efficient algorithms for two highly robust estimators of scale’ Computational statistics. Physica, Heidelberg, 1992.</p></li>
</ul>
</section>
</section>
<section id="module-statsmodels.robust">
<span id="module-reference"></span><h2>Module Reference<a class="headerlink" href="#module-statsmodels.robust" title="Link to this heading">#</a></h2>
<section id="module-statsmodels.robust.robust_linear_model">
<span id="model-classes"></span><h3>Model Classes<a class="headerlink" href="#module-statsmodels.robust.robust_linear_model" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.robust_linear_model.RLM.html#statsmodels.robust.robust_linear_model.RLM" title="statsmodels.robust.robust_linear_model.RLM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RLM</span></code></a>(endog, exog[, M, missing])</p></td>
<td><p>Robust Linear Model</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="model-results">
<h3>Model Results<a class="headerlink" href="#model-results" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.robust_linear_model.RLMResults.html#statsmodels.robust.robust_linear_model.RLMResults" title="statsmodels.robust.robust_linear_model.RLMResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RLMResults</span></code></a>(model, params, ...[, cov])</p></td>
<td><p>Class to contain RLM results</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="norms">
<span id="id1"></span><h3>Norms<a class="headerlink" href="#norms" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.AndrewWave.html#statsmodels.robust.norms.AndrewWave" title="statsmodels.robust.norms.AndrewWave"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AndrewWave</span></code></a>([a])</p></td>
<td><p>Andrew's wave for M estimation</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.Hampel.html#statsmodels.robust.norms.Hampel" title="statsmodels.robust.norms.Hampel"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Hampel</span></code></a>([a, b, c])</p></td>
<td><p>Hampel function for M-estimation</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.HuberT.html#statsmodels.robust.norms.HuberT" title="statsmodels.robust.norms.HuberT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">HuberT</span></code></a>([t])</p></td>
<td><p>Huber's T for M estimation</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.LeastSquares.html#statsmodels.robust.norms.LeastSquares" title="statsmodels.robust.norms.LeastSquares"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LeastSquares</span></code></a>()</p></td>
<td><p>Least squares rho for M-estimation and its derived functions</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.MQuantileNorm.html#statsmodels.robust.norms.MQuantileNorm" title="statsmodels.robust.norms.MQuantileNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MQuantileNorm</span></code></a>(q, base_norm)</p></td>
<td><p>M-quantiles objective function based on a base norm</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.RamsayE.html#statsmodels.robust.norms.RamsayE" title="statsmodels.robust.norms.RamsayE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RamsayE</span></code></a>([a])</p></td>
<td><p>Ramsay's Ea for M estimation</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.RobustNorm.html#statsmodels.robust.norms.RobustNorm" title="statsmodels.robust.norms.RobustNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RobustNorm</span></code></a>()</p></td>
<td><p>The parent class for the norms used for robust regression</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.StudentT.html#statsmodels.robust.norms.StudentT" title="statsmodels.robust.norms.StudentT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">StudentT</span></code></a>([c, df])</p></td>
<td><p>Robust norm based on t distribution</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.TrimmedMean.html#statsmodels.robust.norms.TrimmedMean" title="statsmodels.robust.norms.TrimmedMean"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TrimmedMean</span></code></a>([c])</p></td>
<td><p>Trimmed mean function for M-estimation</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.TukeyBiweight.html#statsmodels.robust.norms.TukeyBiweight" title="statsmodels.robust.norms.TukeyBiweight"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TukeyBiweight</span></code></a>([c])</p></td>
<td><p>Tukey's biweight function for M-estimation</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.TukeyQuartic.html#statsmodels.robust.norms.TukeyQuartic" title="statsmodels.robust.norms.TukeyQuartic"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TukeyQuartic</span></code></a>([c, k])</p></td>
<td><p>Variant of Tukey's biweight function with power 4 for M-estimation</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.norms.estimate_location.html#statsmodels.robust.norms.estimate_location" title="statsmodels.robust.norms.estimate_location"><code class="xref py py-obj docutils literal notranslate"><span class="pre">estimate_location</span></code></a>(a, scale[, norm, axis, ...])</p></td>
<td><p>Estimate a robust location parameter using an M-estimator.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="module-statsmodels.robust.scale">
<span id="scale"></span><h3>Scale<a class="headerlink" href="#module-statsmodels.robust.scale" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.Huber.html#statsmodels.robust.scale.Huber" title="statsmodels.robust.scale.Huber"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Huber</span></code></a>([c, tol, maxiter, norm])</p></td>
<td><p>Huber's proposal 2 for estimating location and scale jointly</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.HuberScale.html#statsmodels.robust.scale.HuberScale" title="statsmodels.robust.scale.HuberScale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">HuberScale</span></code></a>([d, tol, maxiter])</p></td>
<td><p>Huber's scaling for fitting robust linear models</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.MScale.html#statsmodels.robust.scale.MScale" title="statsmodels.robust.scale.MScale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MScale</span></code></a>(chi_func, scale_bias)</p></td>
<td><p>M-scale estimation</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.mad.html#statsmodels.robust.scale.mad" title="statsmodels.robust.scale.mad"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mad</span></code></a>(a[, c, axis, center])</p></td>
<td><p>The Median Absolute Deviation along given axis of an array</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.hubers_scale.html#statsmodels.robust.scale.hubers_scale" title="statsmodels.robust.scale.hubers_scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">hubers_scale</span></code></a></p></td>
<td><p>Huber's scaling for fitting robust linear models</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.iqr.html#statsmodels.robust.scale.iqr" title="statsmodels.robust.scale.iqr"><code class="xref py py-obj docutils literal notranslate"><span class="pre">iqr</span></code></a>(a[, c, axis])</p></td>
<td><p>The normalized interquartile range along given axis of an array</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.qn_scale.html#statsmodels.robust.scale.qn_scale" title="statsmodels.robust.scale.qn_scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">qn_scale</span></code></a>(a[, c, axis])</p></td>
<td><p>Computes the Qn robust estimator of scale</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.scale_tau.html#statsmodels.robust.scale.scale_tau" title="statsmodels.robust.scale.scale_tau"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scale_tau</span></code></a>(data[, cm, cs, weight_mean, ...])</p></td>
<td><p>Tau estimator of univariate scale</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.scale.scale_trimmed.html#statsmodels.robust.scale.scale_trimmed" title="statsmodels.robust.scale.scale_trimmed"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scale_trimmed</span></code></a>(data, alpha[, center, axis, ...])</p></td>
<td><p>Scale estimate based on symmetrically trimmed sample</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="deterministic-start-robust-covariance-estimation">
<h3>Deterministic-Start Robust Covariance Estimation<a class="headerlink" href="#deterministic-start-robust-covariance-estimation" title="Link to this heading">#</a></h3>
<p>Robust estimators of multivariate location and scatter, including the
minimum covariance determinant (MCD) and S-estimators with deterministic
(non-random) starting values.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.covariance.CovM.html#statsmodels.robust.covariance.CovM" title="statsmodels.robust.covariance.CovM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CovM</span></code></a>(data[, norm_mean, norm_scatter, ...])</p></td>
<td><p>M-estimator for multivariate Mean and Scatter</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.covariance.CovDetMCD.html#statsmodels.robust.covariance.CovDetMCD" title="statsmodels.robust.covariance.CovDetMCD"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CovDetMCD</span></code></a>(data)</p></td>
<td><p>Minimum covariance determinant estimator with deterministic starts</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.covariance.CovDetS.html#statsmodels.robust.covariance.CovDetS" title="statsmodels.robust.covariance.CovDetS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CovDetS</span></code></a>(data[, norm, breakdown_point])</p></td>
<td><p>S-estimator for mean and covariance with deterministic starts</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.covariance.CovDetMM.html#statsmodels.robust.covariance.CovDetMM" title="statsmodels.robust.covariance.CovDetMM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CovDetMM</span></code></a>(data[, norm, breakdown_point, ...])</p></td>
<td><p>MM estimator using DetS as first stage estimator</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="resistant-deterministic-start-regression">
<h3>Resistant (Deterministic-Start) Regression<a class="headerlink" href="#resistant-deterministic-start-regression" title="Link to this heading">#</a></h3>
<p>Regression M- and MM-estimators using S-estimator starting values computed
deterministically, rather than through random resampling.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.robust.resistant_linear_model.RLMDetS.html#statsmodels.robust.resistant_linear_model.RLMDetS" title="statsmodels.robust.resistant_linear_model.RLMDetS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RLMDetS</span></code></a>(endog, exog[, norm, ...])</p></td>
<td><p>S-estimator for linear model with deterministic starts.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.robust.resistant_linear_model.RLMDetSMM.html#statsmodels.robust.resistant_linear_model.RLMDetSMM" title="statsmodels.robust.resistant_linear_model.RLMDetSMM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RLMDetSMM</span></code></a>(endog, exog[, norm, efficiency, ...])</p></td>
<td><p>MM-estimator with S-estimator starting values.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
</section>
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