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<p>SQL functions for robust variance linear and logistic regression.  
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<table class="memberdecls">
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Functions</h2></td></tr>
<tr class="memitem:a3f978229f9a2e229276278985d76c438"><td class="memItemLeft" align="right" valign="top">bytea8&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="robust_8sql__in.html#a3f978229f9a2e229276278985d76c438">robust_linregr_transition</a> (bytea8 state, float8 y, float8[] x, float8[] coef)</td></tr>
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<tr class="memitem:a458741a15dc6c2ca627f0d1c1d19b7f8"><td class="memItemLeft" align="right" valign="top">robust_linregr_result&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="robust_8sql__in.html#a458741a15dc6c2ca627f0d1c1d19b7f8">robust_linregr_final</a> (bytea8 state)</td></tr>
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<tr class="memitem:a840ddaa14013c4445b7a0d55e9489d8d"><td class="memItemLeft" align="right" valign="top">float8[]&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="robust_8sql__in.html#a840ddaa14013c4445b7a0d55e9489d8d">robust_logregr_step_transition</a> (float8[] state, boolean y, float8[] x, float8[] coef)</td></tr>
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<tr class="memdesc:a815cadfeb54447993db9ce2bd2aa709e"><td class="mdescLeft">&#160;</td><td class="mdescRight">The robust logistic regression function.  <a href="#a815cadfeb54447993db9ce2bd2aa709e">More...</a><br/></td></tr>
<tr class="separator:a815cadfeb54447993db9ce2bd2aa709e"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:a3928ec1e3935e8dc4dbcb9e705805660"><td class="memItemLeft" align="right" valign="top">float8[]&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="robust_8sql__in.html#a3928ec1e3935e8dc4dbcb9e705805660">mlogregr_robust_step_transition</a> (float8[] state, integer y, integer numcategories, integer ref_category, float8[] x, float8[] coef)</td></tr>
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<tr class="memdesc:a8ee938491f0cd0eda60c9fd320740566"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute robust regression diagnostic statistics for multinomial logistic regression.  <a href="#a8ee938491f0cd0eda60c9fd320740566">More...</a><br/></td></tr>
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<tr class="memitem:a4ebbb7afe6193dfa77116a5c3ae9b7dc"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="robust_8sql__in.html#a4ebbb7afe6193dfa77116a5c3ae9b7dc">robust_variance_mlogregr</a> (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer max_iter)</td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><dl class="section date"><dt>Date</dt><dd>2012</dd></dl>
<dl class="section see"><dt>See Also</dt><dd>For a brief introduction to robust variance, see <a class="el" href="group__grp__robust.html">Robust Variance</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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          <td class="memname">robust_mlogregr_result mlogregr_robust_step_final </td>
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          <td class="memname">float8 [] mlogregr_robust_step_merge_states </td>
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        <tr>
          <td class="paramkey"></td>
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          <td class="memname">float8 [] mlogregr_robust_step_transition </td>
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          <td class="paramtype">integer&#160;</td>
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          <td class="paramtype">float8[]&#160;</td>
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          <td class="paramtype">float8[]&#160;</td>
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          <td>(</td>
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          <td class="paramname"><em>state1</em>, </td>
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          <td class="paramkey"></td>
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          <td>(</td>
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          <td class="paramname"><em>state</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramkey"></td>
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          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
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          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
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          <td>(</td>
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          <td class="paramkey"></td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>&#160;</td>
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          <td class="paramkey"></td>
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          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>&#160;</td>
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          <td></td>
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          <td></td><td></td>
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          <td>(</td>
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          <td class="paramname"><em>source_table</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">float8&#160;</td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">boolean&#160;</td>
          <td class="paramname"><em>verbose_mode</em>&#160;</td>
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        <tr>
          <td></td>
          <td>)</td>
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<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">source_table</td><td>String identifying the input table </td></tr>
    <tr><td class="paramname">out_table</td><td>String identifying the output table to be created </td></tr>
    <tr><td class="paramname">dependent_varname</td><td>Column containing the dependent variable </td></tr>
    <tr><td class="paramname">independent_varname</td><td>Column containing the array of independent variables </td></tr>
    <tr><td class="paramname">grouping_cols</td><td>Columns to group by. </td></tr>
    <tr><td class="paramname">max_iter</td><td>Integer identifying the maximum iterations used by the logistic regression solver. Default is 20. </td></tr>
    <tr><td class="paramname">optimizer</td><td>String identifying the optimizer used in the logistic regression. See the documentation in the logistic regression for the available options. Default is irls. </td></tr>
    <tr><td class="paramname">tolerance</td><td>Float identifying the tolerance of the logistic regression optimizer. Default is 1e-4. </td></tr>
    <tr><td class="paramname">verbose_mode</td><td>Boolean specifying if the regression fit should print any warning messages. Default is false. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section user"><dt></dt><dd>To include an intercept in the model, set one coordinate in the <code>independent_varname</code> array to 1.</dd></dl>
<dl class="section return"><dt>Returns</dt><dd>A composite value:<ul>
<li><code>std_err FLOAT8[]</code> - Array of huber-white standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li>
<li><code>t_stats FLOAT8[]</code> - Array of t-statistics, \( \boldsymbol t \)</li>
<li><code>p_values FLOAT8[]</code> - Array of p-values, \( \boldsymbol p \)</li>
</ul>
</dd></dl>
<dl class="section user"><dt>Usage</dt><dd>For function summary information. Run sql&gt; select robust_variance_logregr('help'); OR sql&gt; select <a class="el" href="robust_8sql__in.html#abc20ec2c5e74f268e7727c33a4bb9054">robust_variance_logregr()</a>; OR sql&gt; select robust_variance_logregr('?'); For function usage information. Run sql&gt; select robust_variance_logregr('usage');<ul>
<li>Compute the coefficients, and the get the robust diagnostic statistics: <pre>
   select robust_variance_logregr(source_table, out_table, regression_type, dependentVariable, independentVariables, NULL );
  </pre></li>
<li>If the coefficients are already known, they can be provided directly <pre>select robust_variance_logregr(source_table, out_table, regression_type, dependentVariable, independentVariables, coef );
</pre> </li>
</ul>
</dd></dl>

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          <td class="memname">void robust_variance_logregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
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          <td class="paramkey"></td>
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          <td class="paramkey"></td>
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          <td class="paramname"><em>dependent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">float8&#160;</td>
          <td class="paramname"><em>tolerance</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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          <td class="memname">void robust_variance_logregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
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        </tr>
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          <td class="memname">void robust_variance_logregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
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          <td class="memname">void robust_variance_logregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_logregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_variable</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_variable</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">varchar robust_variance_mlogregr </td>
          <td>(</td>
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          <td></td>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer_params</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">boolean&#160;</td>
          <td class="paramname"><em>verbose_mode</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<p>&ndash; NOTICE ---------------------------------------------------------&mdash;&mdash; &ndash; All functions calling other modeling functions should be in the format: &ndash; accept a model table created by the underlying modeling function &ndash; and extract all parameters from the model table and summary table CREATE OR REPLACE FUNCTION MADlib.robust_variance_mlogregr( model_table VARCHAR &ndash; name of the mlogregr model table , out_table VARCHAR &ndash; name of output table ) RETURNS VOID AS $$ PythonFunction(regress, robust_mlogistic, robust_variance_mlogregr_new) $$ LANGUAGE plpythonu; &ndash; END OF NOTICE ---------------------------------------------------------&mdash;&mdash; </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">source_table</td><td>name of input table, VARCHAR </td></tr>
    <tr><td class="paramname">out_table</td><td>name of output table, VARCHAR </td></tr>
    <tr><td class="paramname">dependent_varname</td><td>dependent variable, VARCHAR </td></tr>
    <tr><td class="paramname">independent_varname</td><td>independent variables, VARCHAR </td></tr>
    <tr><td class="paramname">ref_category</td><td>Integer specifying the reference category. Default is 0. </td></tr>
    <tr><td class="paramname">grouping_cols</td><td>grouping variables, VARCHAR. Default is NULL. Currently a placeholder. </td></tr>
    <tr><td class="paramname">max_iter</td><td>Integer identifying the maximum iterations used by the logistic regression solver. Default is 20. </td></tr>
    <tr><td class="paramname">optimizer</td><td>String identifying the optimizer used in the multinomial logistic regression. See the documentation in the multinomial logistic regression for the available options. Default is 'irls'. </td></tr>
    <tr><td class="paramname">tolerance</td><td>Float identifying the tolerance of the multinomial logistic regression optimizer. Default is 1e-4. </td></tr>
    <tr><td class="paramname">verbose_mode</td><td>Boolean specifying if the multinomial logistic regression solver should print any warnings. Currently a placeholder.</td></tr>
  </table>
  </dd>
</dl>
<dl class="section user"><dt></dt><dd>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</dd></dl>
<dl class="section user"><dt>Usage</dt><dd><pre>
SELECT  madlib.robust_variance_mlogregr(
    <em>'source_table'</em>,        -- name of input table, VARCHAR
    <em>'out_table'</em>,           -- name of output table, VARCHAR
    <em>'dependent_varname'</em>,   -- dependent variable, VARCHAR
    <em>'independent_varname'</em>, -- independent variables, VARCHAR
    <em>ref_category</em>,        -- [OPTIONAL] Integer specifying the reference category. Default is 0.
    <em>'grouping_cols'</em>,        -- [OPTIONAL] grouping variables, VARCHAR. Default is NULL.
    <em>max_iter</em>,           -- [OPTIONAL] Integer identifying the maximum iterations used by the logistic regression solver.  Default is 20.
    <em>'optimizer'</em>,            -- [OPTIONAL] String identifying the optimizer used in the multinomial logistic regression.  See the documentation in the multinomial logistic regression for the available options.  Default is irls.
 <em>tolerance</em>,         -- [OPTIONAL] Float identifying the tolerance of the multinomial logistic regression optimizer. Default is 1e-4.
 <em>verbose_mode</em>        -- [OPTIONAL] Boolean specifying if the regression fit should print any warning messages.  Default is false.
);
</pre></dd></dl>
<dl class="section return"><dt>Returns</dt><dd>A composite value:<ul>
<li><code>ref_category INTEGER</code> - The reference category</li>
<li><code>coef FLOAT8[] </code> - The coefficients for the regression</li>
<li><code>std_err FLOAT8[]</code> - Array of huber-white standard errors,</li>
<li><code>z_stats FLOAT8[]</code> - Array of Wald z-statistics,</li>
<li><code>p_values FLOAT8[]</code> - Array of p-values, </li>
</ul>
</dd></dl>

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          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer_params</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">float8&#160;</td>
          <td class="paramname"><em>tolerance</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">boolean&#160;</td>
          <td class="paramname"><em>verbose_mode</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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        <tr>
          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">float8&#160;</td>
          <td class="paramname"><em>tolerance</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>optimizer</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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          <td class="memname">void robust_variance_mlogregr </td>
          <td>(</td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>source_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>out_table</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>dependent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>independent_varname</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>ref_category</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">varchar&#160;</td>
          <td class="paramname"><em>grouping_cols</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">integer&#160;</td>
          <td class="paramname"><em>max_iter</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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