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| <div class="title">multilogistic.sql_in</div> </div> |
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| <a href="multilogistic_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file multilogistic.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for multinomial logistic regression</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * @date July 2012</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * @sa For a brief introduction to multinomial logistic regression, see the</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * module description \ref grp_mlogreg.</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> </div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">@addtogroup grp_mlogreg</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">Multinomial logistic regression is a widely used regression analysis tool that models the outcomes of categorical dependent</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">random variables (denoted \f$ Y \in \{ 0,1,2 \ldots k \} \f$). The models assumes that the conditional mean of the</span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">dependant categorical variables is the logistic function of an affine combination of independent</span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">variables (usually denoted \f$ \boldsymbol x \f$). That is,</span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> E[Y \mid \boldsymbol x] = \sigma(\boldsymbol c^T \boldsymbol x)</span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">for some unknown vector of coefficients \f$ \boldsymbol c \f$ and where</span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">\f$ \sigma(x) = \frac{1}{1 + \exp(-x)} \f$ is the logistic function. Multinomial Logistic</span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">regression finds the vector of coefficients \f$ \boldsymbol c \f$ that maximizes</span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">the likelihood of the observations.</span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">Let</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">- \f$ \boldsymbol y \in \{ 0,1 \}^{n \times k} \f$ denote the vector of observed dependent</span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> variables, with \f$ n \f$ rows and \f$ k \f$ columns, containing the observed values of the</span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> dependent variable,</span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">- \f$ X \in \mathbf R^{n \times k} \f$ denote the design matrix with \f$ k \f$</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> columns and \f$ n \f$ rows, containing all observed vectors of independent</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> variables \f$ \boldsymbol x_i \f$ as rows.</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">By definition,</span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> P[Y = y_i | \boldsymbol x_i]</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> = \sigma((-1)^{y_i} \cdot \boldsymbol c^T \boldsymbol x_i)</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">Maximizing the likelihood</span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">\f$ \prod_{i=1}^n \Pr(Y = y_i \mid \boldsymbol x_i) \f$</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">is equivalent to maximizing the log-likelihood</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">\f$ \sum_{i=1}^n \log \Pr(Y = y_i \mid \boldsymbol x_i) \f$, which simplifies to</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> l(\boldsymbol c) =</span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment"> -\sum_{i=1}^n \log(1 + \exp((-1)^{y_i}</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> \cdot \boldsymbol c^T \boldsymbol x_i))</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">The Hessian of this objective is \f$ H = -X^T A X \f$ where</span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">\f$ A = \text{diag}(a_1, \dots, a_n) \f$ is the diagonal matrix with</span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> a_i = \sigma(\boldsymbol c^T \boldsymbol x)</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> \cdot</span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> \sigma(-\boldsymbol c^T \boldsymbol x)</span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">\f$</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">Since \f$ H \f$ is non-positive definite, \f$ l(\boldsymbol c) \f$ is convex.</span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">There are many techniques for solving convex optimization problems. Currently,</span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">logistic regression in MADlib can use:</span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">- Iteratively Reweighted Least Squares</span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">We estimate the standard error for coefficient \f$ i \f$ as</span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> \mathit{se}(c_i) = \left( (X^T A X)^{-1} \right)_{ii}</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">The Wald z-statistic is</span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> z_i = \frac{c_i}{\mathit{se}(c_i)}</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> \,.</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">The Wald \f$ p \f$-value for coefficient \f$ i \f$ gives the probability (under</span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">the assumptions inherent in the Wald test) of seeing a value at least as extreme</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">as the one observed, provided that the null hypothesis (\f$ c_i = 0 \f$) is</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">true. Letting \f$ F \f$ denote the cumulative density function of a standard</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">normal distribution, the Wald \f$ p \f$-value for coefficient \f$ i \f$ is</span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">therefore</span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> p_i = \Pr(|Z| \geq |z_i|) = 2 \cdot (1 - F( |z_i| ))</span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">where \f$ Z \f$ is a standard normally distributed random variable.</span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">The odds ratio for coefficient \f$ i \f$ is estimated as \f$ \exp(c_i) \f$.</span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">The condition number is computed as \f$ \kappa(X^T A X) \f$ during the iteration</span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">immediately <em>preceding</em> convergence (i.e., \f$ A \f$ is computed using</span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">the coefficients of the previous iteration). A large condition number (say, more</span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">than 1000) indicates the presence of significant multicollinearity.</span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">The multinomial logistic regression uses a default reference category of zero,</span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">and the regression coefficients in the output are in the order described below.</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">For a problem with</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">\f$ K \f$ dependent variables \f$ (1, ..., K) \f$ and \f$ J \f$ categories \f$ (0, ..., J-1)</span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">\f$, let \f$ {m_{k,j}} \f$ denote the coefficient for dependent variable \f$ k</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">\f$ and category \f$ j \f$. The output is \f$ {m_{k_1, j_0}, m_{k_1, j_1}</span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">\ldots m_{k_1, j_{J-1}}, m_{k_2, j_0}, m_{k_2, j_1}, \ldots m_{k_2, j_{J-1}} \ldots m_{k_K, j_{J-1}}} \f$.</span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">The order is NOT CONSISTENT with the multinomial regression marginal effect</span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment">calculation with function <em>marginal_mlogregr</em>. This is deliberate</span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment">because the interfaces of all multinomial regressions (robust, clustered, ...)</span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">will be moved to match that used in marginal.</span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">@input</span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">The training data is expected to be of the following form:\n</span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"><pre>{TABLE|VIEW} <em>sourceName</em> (</span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"> <em>dependentVariable</em> INTEGER,</span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> <em>independentVariables</em> FLOAT8[],</span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">)</pre></span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">@usage</span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">- The number of independent variables cannot exceed 65535.</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment">- The reference category ranges from [0, numCategories-1]. The default reference</span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">category is zero.</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">- Get vector of coefficients \f$ \boldsymbol c \f$ and all diagnostic</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment"> statistics:\n</span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"> <pre>SELECT * FROM \ref mlogregr(</span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"> '<em>sourceName</em>',</span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> '<em>dependentVariable</em>',</span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"> '<em>independentVariables</em>' [,</span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> <em>numberOfIterations</em> [,</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> '<em>optimizer</em>' [,</span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> <em>precision</em>, [,</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> <em>ref_category</em>]]]]</span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment">);</pre></span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> Output:</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"><pre></span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">ref_category | coef | log_likelihood | std_err | z_stats | p_values | odds_ratios | condition_no | num_iterations\n ----+------+----------------+---------+---------+----------+-------------+--------------+---------------</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"></pre></span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">- Get vector of coefficients \f$ \boldsymbol c \f$:\n</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> <pre>SELECT (\ref mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>', '<em>independentVariables</em>')).coef;</pre></span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">- Get a subset of the output columns, e.g., only the array of coefficients</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> \f$ \boldsymbol c \f$, the log-likelihood of determination</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> \f$ l(\boldsymbol c) \f$, and the array of p-values \f$ \boldsymbol p \f$:</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> <pre>SELECT coef, log_likelihood, p_values</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment">FROM \ref mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>', '<em>independentVariables</em>');</pre></span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">Note that the categories are encoded as integers with values from {0, 1, 2,..., numCategories-1}</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment">@examp</span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment">-# Create the sample data set:</span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">sql> SELECT * FROM data;</span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> r1 | val</span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">---------------------------------------------+-----</span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> {1,3.01789340097457,0.454183579888195} | 1</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment"> {1,-2.59380532894284,0.602678326424211} | 0</span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"> {1,-1.30643094424158,0.151587064377964} | 1</span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> {1,3.60722299199551,0.963550757616758} | 1</span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> {1,-1.52197745628655,0.0782248834148049} | 1</span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> {1,-4.8746574902907,0.345104880165309} | 0</span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">...</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">-# Run the multi-logistic regression function:</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">@verbatim</span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment">sql> \x on</span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment">Expanded display is off.</span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">sql> SELECT * FROM mlogregr('data', 'val', '2', 'r1', 100, 'irls', 0.001);</span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">-[ RECORD 1 ]--+--------------------------------------------------------------</span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">coef | {5.59049410898112,2.11077546770772,-0.237276684606453}</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">log_likelihood | -467.214718489873</span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">std_err | {0.318943457652178,0.101518723785383,0.294509929481773}</span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment">z_stats | {17.5281667482197,20.7919819024719,-0.805666162169712}</span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">p_values | {8.73403463417837e-69,5.11539430631541e-96,0.420435365338518}</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">odds_ratios | {267.867942976278,8.2546400100702,0.788773016471171}</span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">condition_no | 179.186118573205</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">num_iterations | 9</span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">@literature</span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment">A collection of nice write-ups, with valuable pointers into</span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment">further literature:</span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">[1] Annette J . Dobson: An Introduction to Generalized Linear Models, Second Edition. Nov 2001</span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment">[2] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 18 November</span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"> 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf</span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">[3] Srikrishna Sridhar, Mark Wellons, Caleb Welton: Multilogistic Regression:</span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> Notes and References, Jul 12 2012, http://www.cs.wisc.edu/~srikris/mlogit.pdf</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">[4] Scott A. Czepiel: Maximum Likelihood Estimation</span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"> of Logistic Regression Models: Theory and Implementation,</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> Retrieved Jul 12 2012, http://czep.net/stat/mlelr.pdf</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment">@sa File multilogistic.sql_in (documenting the SQL functions)</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">@internal</span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">@sa Namespace multilogistic (documenting the driver/outer loop implemented in</span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> Python), Namespace</span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> \ref madlib::modules::regress documenting the implementation in C++</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">@endinternal</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> </div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> </div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> DROP TYPE IF EXISTS MADLIB_SCHEMA.mlogregr_result;</div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> CREATE TYPE MADLIB_SCHEMA.mlogregr_result AS</div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> (</div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  ref_category INTEGER,</div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  coef DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  log_likelihood DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  std_err DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  z_stats DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  p_values DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  odds_ratios DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  condition_no DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  num_iterations INTEGER</div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> );</div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> </div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__mlogregr_irls_step_transition</div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> (</div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  state DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  y INTEGER,</div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  num_categories INTEGER,</div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  ref_category INTEGER,</div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  x DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  prev_state DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> )</div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> RETURNS DOUBLE PRECISION[]</div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="stringliteral">LANGUAGE C IMMUTABLE;</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__mlogregr_irls_step_merge_states</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="stringliteral">(</span></div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="stringliteral"> state1 DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="stringliteral"> state2 DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="stringliteral">RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__mlogregr_irls_step_final</span></div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="stringliteral">(</span></div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="stringliteral"> state DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="stringliteral">RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="comment"> * @internal</span></div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment"> * @brief Perform one iteration of the iteratively-reweighted-least-squares</span></div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="comment"> * method for computing linear regression</span></div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> CREATE AGGREGATE MADLIB_SCHEMA.__mlogregr_irls_step(</div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  /*+ y */ INTEGER,</div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  /*+ numCategories */ INTEGER,</div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  /*+ ref_category */ INTEGER,</div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  /*+ x */ DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  /*+ previous_state */ DOUBLE PRECISION[]) (</div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  STYPE=DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  SFUNC=MADLIB_SCHEMA.__mlogregr_irls_step_transition,</div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  m4_ifdef(`__GREENPLUM__',`prefunc=MADLIB_SCHEMA.__mlogregr_irls_step_merge_states,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.__mlogregr_irls_step_final,</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="stringliteral"> INITCOND='</span>{0,0,0,0,0}<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__internal_mlogregr_irls_step_distance(</span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="stringliteral"> /*+ state1 */ DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="stringliteral"> /*+ state2 */ DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="stringliteral">RETURNS DOUBLE PRECISION AS</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="stringliteral">'</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="stringliteral">LANGUAGE c IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.__internal_mlogregr_irls_result(</span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="stringliteral"> /*+ state */ DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.mlogregr_result AS</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="stringliteral">'</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="stringliteral">LANGUAGE c IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="stringliteral">-- We only need to document the last one (unfortunately, in Greenplum we have to</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="stringliteral">-- use function overloading instead of default arguments).</span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.__compute_mlogregr</span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="stringliteral">(</span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="stringliteral"> source VARCHAR,</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="stringliteral"> depvar VARCHAR,</span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="stringliteral"> indepvar VARCHAR,</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="stringliteral"> numcategories INTEGER,</span></div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="stringliteral"> maxnumiterations INTEGER,</span></div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="stringliteral"> optimizer VARCHAR,</span></div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="stringliteral"> "precision" DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="stringliteral"> ref_category INTEGER</span></div> |
| <div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="stringliteral">RETURNS INTEGER</span></div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="stringliteral">AS $$</span></div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="stringliteral"> PythonFunction(regress, multilogistic, compute_mlogregr)</span></div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="stringliteral">$$ LANGUAGE plpythonu VOLATILE STRICT;</span></div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"> * @brief Compute logistic-regression coefficients and diagnostic statistics</span></div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment"> * To include an intercept in the model, set one coordinate in the</span></div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="comment"> * <tt>independentVariables</tt> array to 1.</span></div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment"> * @param source Name of the source relation containing the training data</span></div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment"> * @param depvar Name of the dependent column (of type INTEGER < numcategories)</span></div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment"> * @param indepvar Name of the independent column (of type DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="comment"> * @param maxnumiterations The maximum number of iterations</span></div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span> <span class="comment"> * @param optimizer The optimizer to use (</span></div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="comment"> * <tt>'irls'</tt>/<tt>'newton'</tt> for iteratively reweighted least</span></div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="comment"> * squares)</span></div> |
| <div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="comment"> * @param precision The difference between log-likelihood values in successive</span></div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="comment"> * iterations that should indicate convergence. Note that a non-positive</span></div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> <span class="comment"> * value here disables the convergence criterion, and execution will only</span></div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="comment"> * stop after \ maxNumIterations iterations.</span></div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="comment"> * @param ref_category The reference category specified by the user</span></div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="comment"> * @return A composite value:</span></div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="comment"> * - <tt>ref_category INTEGER</tt> - Reference category</span></div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment"> * - <tt>coef FLOAT8[]</tt> - Array of coefficients, \f$ \boldsymbol c \f$</span></div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="comment"> * - <tt>log_likelihood FLOAT8</tt> - Log-likelihood \f$ l(\boldsymbol c) \f$</span></div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="comment"> * - <tt>std_err FLOAT8[]</tt> - Array of standard errors,</span></div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="comment"> * \f$ \mathit{se}(c_1), \dots, \mathit{se}(c_k) \f$</span></div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment"> * - <tt>z_stats FLOAT8[]</tt> - Array of Wald z-statistics, \f$ \boldsymbol z \f$</span></div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment"> * - <tt>p_values FLOAT8[]</tt> - Array of Wald p-values, \f$ \boldsymbol p \f$</span></div> |
| <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment"> * - <tt>odds_ratios FLOAT8[]</tt>: Array of odds ratios,</span></div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="comment"> * \f$ \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \f$</span></div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="comment"> * - <tt>condition_no FLOAT8</tt> - The condition number of matrix</span></div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="comment"> * \f$ X^T A X \f$ during the iteration immediately <em>preceding</em></span></div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="comment"> * convergence (i.e., \f$ A \f$ is computed using the coefficients of the</span></div> |
| <div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment"> * previous iteration)</span></div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment"> * - <tt>num_iterations INTEGER</tt> - The number of iterations before the</span></div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"> * algorithm terminated</span></div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment"> * - Get vector of coefficients \f$ \boldsymbol c \f$ and all diagnostic</span></div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment"> * statistics:\n</span></div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment"> * <pre>SELECT * FROM mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>',</span></div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment"> * '<em>numCategories</em>', '<em>independentVariables</em>');</pre></span></div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment"> * - Get vector of coefficients \f$ \boldsymbol c \f$:\n</span></div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="comment"> * <pre>SELECT (mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>',</span></div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="comment"> * '<em>numCategories</em>', '<em>independentVariables</em>')).coef;</pre></span></div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="comment"> * - Get a subset of the output columns, e.g., only the array of coefficients</span></div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="comment"> * \f$ \boldsymbol c \f$, the log-likelihood of determination</span></div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="comment"> * \f$ l(\boldsymbol c) \f$, and the array of p-values \f$ \boldsymbol p \f$:</span></div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span> <span class="comment"> * <pre>SELECT coef, log_likelihood, p_values</span></div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment"> * FROM mlogregr('<em>sourceName</em>', '<em>dependentVariable</em>',</span></div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment"> * '<em>numCategories</em>', '<em>independentVariables</em>');</pre></span></div> |
| <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"> * @note This function starts an iterative algorithm. It is not an aggregate</span></div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment"> * function. Source and column names have to be passed as strings (due to</span></div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment"> * limitations of the SQL syntax).</span></div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment"> * @internal</span></div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment"> * @sa This function is a wrapper for multilogistic::__compute_mlogregr(), which</span></div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="comment"> * sets the default values.</span></div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span> CREATE FUNCTION MADLIB_SCHEMA.mlogregr</div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span> (</div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  source VARCHAR,</div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  depvar VARCHAR,</div> |
| <div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  indepvar VARCHAR,</div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  maxnumiterations INTEGER /*+ DEFAULT 20 */,</div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  optimizer VARCHAR /*+ DEFAULT 'irls<span class="stringliteral">' */,</span></div> |
| <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="stringliteral"> "precision" DOUBLE PRECISION /*+ DEFAULT 0.0001 */,</span></div> |
| <div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="stringliteral"> ref_category INTEGER</span></div> |
| <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.mlogregr_result AS $$</span></div> |
| <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="stringliteral">DECLARE</span></div> |
| <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="stringliteral"> observed_count INTEGER;</span></div> |
| <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="stringliteral"> theIteration INTEGER;</span></div> |
| <div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="stringliteral"> fnName VARCHAR;</span></div> |
| <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="stringliteral"> theResult MADLIB_SCHEMA.mlogregr_result;</span></div> |
| <div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="stringliteral"> numcategories INTEGER;</span></div> |
| <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="stringliteral"> min_category INTEGER;</span></div> |
| <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="stringliteral"> max_category INTEGER;</span></div> |
| <div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="stringliteral">BEGIN</span></div> |
| <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="stringliteral"> IF (source IS NULL OR trim(source) = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid source table given<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00393"></a><span class="lineno"><a class="code" href="multilogistic_8sql__in.html#af1456a7d62a2a79047c9cf8f75e2ab74"> 393</a></span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="stringliteral"> IF (depvar IS NULL OR trim(depvar) = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid depvar given<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="stringliteral"> IF (indepvar IS NULL OR trim(indepvar) = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid indepvar given<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="stringliteral"> IF (maxnumiterations IS NULL OR maxnumiterations < 1) THEN</span></div> |
| <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Number of max iterations must be positive<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="stringliteral"> IF (optimizer IS NULL OR trim(optimizer) = '</span><span class="stringliteral">') THEN</span></div> |
| <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid optimizer given<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="stringliteral"> IF (precision IS NULL) THEN</span></div> |
| <div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid precision given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="stringliteral"> IF (ref_category IS NULL OR ref_category < 0) THEN</span></div> |
| <div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Invalid ref_category given.<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="stringliteral"> IF (SELECT atttypid::regtype <> '</span>INTEGER<span class="stringliteral">'::regtype</span></div> |
| <div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="stringliteral"> FROM pg_attribute</span></div> |
| <div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="stringliteral"> WHERE attrelid = source::regclass AND attname = depvar) THEN</span></div> |
| <div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="stringliteral"> RAISE EXCEPTION '</span>The dependent variable column should be of type INTEGER<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="stringliteral"> EXECUTE $sql$ SELECT count(DISTINCT $sql$ || depvar || $sql$ )</span></div> |
| <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="stringliteral"> FROM $sql$ || textin(regclassout(source))</span></div> |
| <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="stringliteral"> INTO observed_count;</span></div> |
| <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="stringliteral"> numcategories := observed_count;</span></div> |
| <div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="stringliteral"> EXECUTE $sql$ SELECT max($sql$ || depvar || $sql$ )</span></div> |
| <div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="stringliteral"> FROM $sql$ || textin(regclassout(source))</span></div> |
| <div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="stringliteral"> INTO max_category;</span></div> |
| <div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="stringliteral"> EXECUTE $sql$ SELECT min($sql$ || depvar || $sql$ )</span></div> |
| <div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="stringliteral"> FROM $sql$ || textin(regclassout(source))</span></div> |
| <div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="stringliteral"> INTO min_category;</span></div> |
| <div class="line"><a name="l00431"></a><span class="lineno"> 431</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="stringliteral"> IF max_category != numcategories - 1 OR min_category != 0 THEN</span></div> |
| <div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="stringliteral"> RAISE EXCEPTION '</span>The value of the dependent variable should be in the</div> |
| <div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  range of [0, %)<span class="stringliteral">', numcategories;</span></div> |
| <div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="stringliteral"> IF ref_category > numcategories -1 OR ref_category < 0 THEN</span></div> |
| <div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="stringliteral"> RAISE EXCEPTION '</span>The value of the reference category should be in the</div> |
| <div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  range of [0, <span class="stringliteral">"%"</span>)<span class="stringliteral">', numcategories;</span></div> |
| <div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="stringliteral"> IF optimizer = '</span>irls<span class="stringliteral">' OR optimizer = '</span>newton<span class="stringliteral">' THEN</span></div> |
| <div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="stringliteral"> fnName := '</span>__internal_mlogregr_irls_result<span class="stringliteral">';</span></div> |
| <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="stringliteral"> ELSE</span></div> |
| <div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="stringliteral"> RAISE EXCEPTION '</span>Unknown optimizer (<span class="stringliteral">''</span>%<span class="stringliteral">''</span>). Must be <span class="stringliteral">"newton"</span> or <span class="stringliteral">"irls"</span><span class="stringliteral">', optimizer;</span></div> |
| <div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="stringliteral"> theIteration := (</span></div> |
| <div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.__compute_mlogregr(</span></div> |
| <div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="stringliteral"> $1, $2, $3, numcategories, $4, $5, $6, $7)</span></div> |
| <div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="stringliteral"> );</span></div> |
| <div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="stringliteral"> -- Because of Greenplum bug MPP-10050, we have to use dynamic SQL (using</span></div> |
| <div class="line"><a name="l00454"></a><span class="lineno"> 454</span> <span class="stringliteral"> -- EXECUTE) in the following</span></div> |
| <div class="line"><a name="l00455"></a><span class="lineno"> 455</span> <span class="stringliteral"> -- Because of Greenplum bug MPP-6731, we have to hide the tuple-returning</span></div> |
| <div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="stringliteral"> -- function in a subquery</span></div> |
| <div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="stringliteral"> EXECUTE</span></div> |
| <div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="stringliteral"> $sql$</span></div> |
| <div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="stringliteral"> SELECT (result).*</span></div> |
| <div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="stringliteral"> FROM (</span></div> |
| <div class="line"><a name="l00461"></a><span class="lineno"> 461</span> <span class="stringliteral"> SELECT</span></div> |
| <div class="line"><a name="l00462"></a><span class="lineno"> 462</span> <span class="stringliteral"> MADLIB_SCHEMA.$sql$ || fnName || $sql$(_madlib_state) AS result</span></div> |
| <div class="line"><a name="l00463"></a><span class="lineno"> 463</span> <span class="stringliteral"> FROM _madlib_iterative_alg</span></div> |
| <div class="line"><a name="l00464"></a><span class="lineno"> 464</span> <span class="stringliteral"> WHERE _madlib_iteration = $sql$ || theIteration || $sql$</span></div> |
| <div class="line"><a name="l00465"></a><span class="lineno"> 465</span> <span class="stringliteral"> ) subq</span></div> |
| <div class="line"><a name="l00466"></a><span class="lineno"> 466</span> <span class="stringliteral"> $sql$</span></div> |
| <div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="stringliteral"> INTO theResult;</span></div> |
| <div class="line"><a name="l00468"></a><span class="lineno"> 468</span> <span class="stringliteral"> -- The number of iterations are not updated in the C++ code. We do it here.</span></div> |
| <div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="stringliteral"> IF NOT (theResult IS NULL) THEN</span></div> |
| <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="stringliteral"> theResult.num_iterations = theIteration;</span></div> |
| <div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="stringliteral"> END IF;</span></div> |
| <div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="stringliteral"> RETURN theResult;</span></div> |
| <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.mlogregr</span></div> |
| <div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="stringliteral">(</span></div> |
| <div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="stringliteral"> source VARCHAR,</span></div> |
| <div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="stringliteral"> depvar VARCHAR,</span></div> |
| <div class="line"><a name="l00481"></a><span class="lineno"> 481</span> <span class="stringliteral"> indepvar VARCHAR</span></div> |
| <div class="line"><a name="l00482"></a><span class="lineno"> 482</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00483"></a><span class="lineno"> 483</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.mlogregr_result AS</span></div> |
| <div class="line"><a name="l00484"></a><span class="lineno"> 484</span> <span class="stringliteral">$$</span></div> |
| <div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.mlogregr($1, $2, $3, 20, '</span>irls<span class="stringliteral">', 0.0001, 0);</span></div> |
| <div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="stringliteral">$$ LANGUAGE sql VOLATILE;</span></div> |
| <div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00488"></a><span class="lineno"> 488</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.mlogregr(</span></div> |
| <div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="stringliteral"> source VARCHAR,</span></div> |
| <div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="stringliteral"> depvar VARCHAR,</span></div> |
| <div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="stringliteral"> indepvar VARCHAR,</span></div> |
| <div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="stringliteral"> maxnumiterations INTEGER</span></div> |
| <div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.mlogregr_result AS</span></div> |
| <div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="stringliteral">$$</span></div> |
| <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.mlogregr($1, $2, $3, $4, '</span>irls<span class="stringliteral">', 0.0001, 0);</span></div> |
| <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="stringliteral">$$ LANGUAGE sql VOLATILE;</span></div> |
| <div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="stringliteral">CREATE FUNCTION MADLIB_SCHEMA.mlogregr(</span></div> |
| <div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="stringliteral"> source VARCHAR,</span></div> |
| <div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="stringliteral"> depvar VARCHAR,</span></div> |
| <div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="stringliteral"> indepvar VARCHAR,</span></div> |
| <div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="stringliteral"> maxbumiterations INTEGER,</span></div> |
| <div class="line"><a name="l00504"></a><span class="lineno"> 504</span> <span class="stringliteral"> optimizer VARCHAR</span></div> |
| <div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="stringliteral">)</span></div> |
| <div class="line"><a name="l00506"></a><span class="lineno"> 506</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.mlogregr_result AS</span></div> |
| <div class="line"><a name="l00507"></a><span class="lineno"> 507</span> <span class="stringliteral">$$</span></div> |
| <div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="stringliteral"> SELECT MADLIB_SCHEMA.mlogregr($1, $2, $3, $4, $5, 0.0001, 0);</span></div> |
| <div class="line"><a name="l00509"></a><span class="lineno"> 509</span> <span class="stringliteral">$$ LANGUAGE sql VOLATILE;</span></div> |
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