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| |
| <p>SQL functions for multinomial logistic regression. |
| <a href="#details">More...</a></p> |
| <table class="memberdecls"> |
| <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a> |
| Functions</h2></td></tr> |
| <tr class="memitem:aef43e4a6363495901045daf339d5c6d7"><td class="memItemLeft" align="right" valign="top">float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#aef43e4a6363495901045daf339d5c6d7">__mlogregr_irls_step_transition</a> (float8[] state, integer y, integer num_categories, integer ref_category, float8[] x, float8[] prev_state)</td></tr> |
| <tr class="separator:aef43e4a6363495901045daf339d5c6d7"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a7cae4ea602fc9c159fa2cc8c1a7653a6"><td class="memItemLeft" align="right" valign="top">float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a7cae4ea602fc9c159fa2cc8c1a7653a6">__mlogregr_irls_step_merge_states</a> (float8[] state1, float8[] state2)</td></tr> |
| <tr class="separator:a7cae4ea602fc9c159fa2cc8c1a7653a6"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a690a74b753dceec66c4e0ad22f50c51e"><td class="memItemLeft" align="right" valign="top">float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a690a74b753dceec66c4e0ad22f50c51e">__mlogregr_irls_step_final</a> (float8[] state)</td></tr> |
| <tr class="separator:a690a74b753dceec66c4e0ad22f50c51e"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a695395e04b6d95afafc7c8ac9e01b7b2"><td class="memItemLeft" align="right" valign="top">aggregate float8[] </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a695395e04b6d95afafc7c8ac9e01b7b2">__mlogregr_irls_step</a> (integer y, integer numcategories, integer ref_category, float8[] x, float8[] previous_state)</td></tr> |
| <tr class="separator:a695395e04b6d95afafc7c8ac9e01b7b2"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:aad300d3120db2ecaabf4809cf6be81e7"><td class="memItemLeft" align="right" valign="top">float8 </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#aad300d3120db2ecaabf4809cf6be81e7">__internal_mlogregr_irls_step_distance</a> (float8[] state1, float8[] state2)</td></tr> |
| <tr class="separator:aad300d3120db2ecaabf4809cf6be81e7"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:ae890704e55f57bd9105b63021e0f86ae"><td class="memItemLeft" align="right" valign="top">mlogregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#ae890704e55f57bd9105b63021e0f86ae">__internal_mlogregr_irls_result</a> (float8[] state)</td></tr> |
| <tr class="separator:ae890704e55f57bd9105b63021e0f86ae"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:aacd9957b00816c3c02f6f7a1aa26393a"><td class="memItemLeft" align="right" valign="top">integer </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#aacd9957b00816c3c02f6f7a1aa26393a">__compute_mlogregr</a> (varchar source, varchar depvar, varchar indepvar, integer num_categories, integer max_num_iterations, varchar <a class="el" href="robust_8sql__in.html#a7f6d9ad99f83891c797f66843bd9500d">optimizer</a>, float8 precision, integer ref_category)</td></tr> |
| <tr class="separator:aacd9957b00816c3c02f6f7a1aa26393a"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a7be20ccb465d47808e18149140fc666f"><td class="memItemLeft" align="right" valign="top">mlogregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a7be20ccb465d47808e18149140fc666f">mlogregr</a> (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations=20, varchar <a class="el" href="robust_8sql__in.html#a7f6d9ad99f83891c797f66843bd9500d">optimizer</a>="irls", float8 precision=0.0001, integer ref_category)</td></tr> |
| <tr class="memdesc:a7be20ccb465d47808e18149140fc666f"><td class="mdescLeft"> </td><td class="mdescRight">Compute logistic-regression coefficients and diagnostic statistics. <a href="#a7be20ccb465d47808e18149140fc666f">More...</a><br/></td></tr> |
| <tr class="separator:a7be20ccb465d47808e18149140fc666f"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a116c95de21b112dedf99035a9b243fd7"><td class="memItemLeft" align="right" valign="top">mlogregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a116c95de21b112dedf99035a9b243fd7">mlogregr</a> (varchar source, varchar depvar, varchar indepvar)</td></tr> |
| <tr class="separator:a116c95de21b112dedf99035a9b243fd7"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:a1ab68f7396f53ae3e32362240d077cbf"><td class="memItemLeft" align="right" valign="top">mlogregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#a1ab68f7396f53ae3e32362240d077cbf">mlogregr</a> (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations)</td></tr> |
| <tr class="separator:a1ab68f7396f53ae3e32362240d077cbf"><td class="memSeparator" colspan="2"> </td></tr> |
| <tr class="memitem:ae1b5954340a0c98a6ed06eb5f3bb43b8"><td class="memItemLeft" align="right" valign="top">mlogregr_result </td><td class="memItemRight" valign="bottom"><a class="el" href="multilogistic_8sql__in.html#ae1b5954340a0c98a6ed06eb5f3bb43b8">mlogregr</a> (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations, varchar <a class="el" href="robust_8sql__in.html#a7f6d9ad99f83891c797f66843bd9500d">optimizer</a>)</td></tr> |
| <tr class="separator:ae1b5954340a0c98a6ed06eb5f3bb43b8"><td class="memSeparator" colspan="2"> </td></tr> |
| </table> |
| <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2> |
| <div class="textblock"><dl class="section date"><dt>Date</dt><dd>July 2012</dd></dl> |
| <dl class="section see"><dt>See Also</dt><dd>For a brief introduction to multinomial <a class="el" href="logistic_8sql__in.html#a4ded9be5c8b111dbb3109efaad83d69e" title="Evaluate the usual logistic function in an under-/overflow-safe way. ">logistic</a> regression, see the module description <a class="el" href="group__grp__mlogreg.html">Multinomial Logistic Regression</a>. </dd></dl> |
| </div><h2 class="groupheader">Function Documentation</h2> |
| <a class="anchor" id="aacd9957b00816c3c02f6f7a1aa26393a"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">integer __compute_mlogregr </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>depvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>indepvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>num_categories</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>optimizer</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>precision</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>ref_category</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ae890704e55f57bd9105b63021e0f86ae"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">mlogregr_result __internal_mlogregr_irls_result </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state</em>)</td><td></td> |
| <td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aad300d3120db2ecaabf4809cf6be81e7"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 __internal_mlogregr_irls_step_distance </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a695395e04b6d95afafc7c8ac9e01b7b2"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">aggregate float8 [] __mlogregr_irls_step </td> |
| <td>(</td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>y</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>numcategories</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>ref_category</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>previous_state</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a690a74b753dceec66c4e0ad22f50c51e"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [] __mlogregr_irls_step_final </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state</em>)</td><td></td> |
| <td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a7cae4ea602fc9c159fa2cc8c1a7653a6"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [] __mlogregr_irls_step_merge_states </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state1</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state2</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="aef43e4a6363495901045daf339d5c6d7"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">float8 [] __mlogregr_irls_step_transition </td> |
| <td>(</td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>state</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>y</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>num_categories</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>ref_category</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>x</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8[] </td> |
| <td class="paramname"><em>prev_state</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a7be20ccb465d47808e18149140fc666f"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">mlogregr_result mlogregr </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>depvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>indepvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> = <code>20</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>optimizer</em> = <code>"irls"</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">float8 </td> |
| <td class="paramname"><em>precision</em> = <code>0.0001</code>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>ref_category</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| <p>To include an intercept in the model, set one coordinate in the <code>independentVariables</code> array to 1.</p> |
| <dl class="params"><dt>Parameters</dt><dd> |
| <table class="params"> |
| <tr><td class="paramname">source</td><td>Name of the source relation containing the training data </td></tr> |
| <tr><td class="paramname">depvar</td><td>Name of the dependent column (of type INTEGER < numcategories) </td></tr> |
| <tr><td class="paramname">indepvar</td><td>Name of the independent column (of type DOUBLE PRECISION[]) </td></tr> |
| <tr><td class="paramname">max_num_iterations</td><td>The maximum number of iterations </td></tr> |
| <tr><td class="paramname">optimizer</td><td>The optimizer to use ( <code>'irls'</code>/<code>'newton'</code> for iteratively reweighted least squares) </td></tr> |
| <tr><td class="paramname">precision</td><td>The difference between log-likelihood values in successive iterations that should indicate convergence. Note that a non-positive value here disables the convergence criterion, and execution will only stop after \ max_num_iterations iterations. </td></tr> |
| <tr><td class="paramname">ref_category</td><td>The reference category specified by the user</td></tr> |
| </table> |
| </dd> |
| </dl> |
| <dl class="section return"><dt>Returns</dt><dd>A composite value:<ul> |
| <li><code>ref_category INTEGER</code> - Reference category</li> |
| <li><code>coef FLOAT8[]</code> - Array of coefficients, \( \boldsymbol c \)</li> |
| <li><code>log_likelihood FLOAT8</code> - Log-likelihood \( l(\boldsymbol c) \)</li> |
| <li><code>std_err FLOAT8[]</code> - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)</li> |
| <li><code>z_stats FLOAT8[]</code> - Array of Wald z-statistics, \( \boldsymbol z \)</li> |
| <li><code>p_values FLOAT8[]</code> - Array of Wald p-values, \( \boldsymbol p \)</li> |
| <li><code>odds_ratios FLOAT8[]</code>: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)</li> |
| <li><code>condition_no FLOAT8</code> - The condition number of matrix \( X^T A X \) during the iteration immediately <em>preceding</em> convergence (i.e., \( A \) is computed using the coefficients of the previous iteration)</li> |
| <li><code>num_iterations INTEGER</code> - The number of iterations before the algorithm terminated</li> |
| </ul> |
| </dd></dl> |
| <dl class="section user"><dt>Usage</dt><dd><ul> |
| <li>Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:<br/> |
| <pre>SELECT * FROM mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>', |
| '<em>numCategories</em>', '<em>independentVariables</em>');</pre></li> |
| <li>Get vector of coefficients \( \boldsymbol c \):<br/> |
| <pre>SELECT (mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>', |
| '<em>numCategories</em>', '<em>independentVariables</em>')).coef;</pre></li> |
| <li>Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): <pre>SELECT coef, log_likelihood, p_values |
| FROM mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>', |
| '<em>numCategories</em>', '<em>independentVariables</em>');</pre></li> |
| </ul> |
| </dd></dl> |
| <dl class="section note"><dt>Note</dt><dd>This function starts an iterative algorithm. It is not an aggregate function. Source and column names have to be passed as strings (due to limitations of the SQL syntax). </dd></dl> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a116c95de21b112dedf99035a9b243fd7"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">mlogregr_result mlogregr </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>depvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>indepvar</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="a1ab68f7396f53ae3e32362240d077cbf"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">mlogregr_result mlogregr </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>depvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>indepvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
| |
| </div> |
| </div> |
| <a class="anchor" id="ae1b5954340a0c98a6ed06eb5f3bb43b8"></a> |
| <div class="memitem"> |
| <div class="memproto"> |
| <table class="memname"> |
| <tr> |
| <td class="memname">mlogregr_result mlogregr </td> |
| <td>(</td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>source</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>depvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>indepvar</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">integer </td> |
| <td class="paramname"><em>max_num_iterations</em>, </td> |
| </tr> |
| <tr> |
| <td class="paramkey"></td> |
| <td></td> |
| <td class="paramtype">varchar </td> |
| <td class="paramname"><em>optimizer</em> </td> |
| </tr> |
| <tr> |
| <td></td> |
| <td>)</td> |
| <td></td><td></td> |
| </tr> |
| </table> |
| </div><div class="memdoc"> |
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