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<h1 class="post-title" itemprop="name headline">学员通过率的逻辑回归（Logistic Regression）模型</h1>
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<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/hint.css/2.4.1/hint.min.css"><h2 id="引言"><a href="#引言" class="headerlink" title="引言"></a>引言</h2><p>目前APP端已经有学员的知识点得分，知识点得分反映了学生对知识点的掌握情况，但据此来推测学生最终的通过率还略有不足，仍然有许多因素影响学员的成绩。举个例子，有的学员是属于大赛型的选手，平常表现一般，但考试的时候就比较好，相反的，有的学员平时不错，但到真正考试的时候就发挥的不太好。据此，我重新收集数据，建立学员通过率模型。<br><a id="more"></a></p>
<h2 id="Logistic-Regression"><a href="#Logistic-Regression" class="headerlink" title="Logistic Regression"></a>Logistic Regression</h2><p>学员通过与否是一个二分变量，故选择逻辑回归（Logistic Regression）模型。逻辑回归虽然名字里有回归，但不是一个回归模型，是一个分类模型。</p>
<p>逻辑回归（英语：Logistic regression 或logit regression），即逻辑模型（英语：Logit model，也译作“评定模型”、“分类评定模型”）是离散选择法模型之一，属于多重变量分析范畴，是社会学、生物统计学、临床、数量心理学、计量经济学、市场营销等统计实证分析的常用方法。（摘自维基百科）</p>
<p>逻辑回归实际上是用sigmoid函数将线性回归进行了归一化，把输出值压缩到0-1之间，这个值代表的是发生的概率。这里不过多说明模型的原理。</p>
<h2 id="数据处理"><a href="#数据处理" class="headerlink" title="数据处理"></a>数据处理</h2><p>由于现有数据的限制，我选取了<strong>思想道德修养与法律基础</strong>这门科目的1804考期的数据，共18437个样本。</p>
<p>选取字段：学员ID，分数，直播出勤时长，重播出勤时长，出勤次数，观看重播次数，学生总时长，随堂考配置题数，随堂考完成题数，随堂考正确题数，作业配置题数，作业完成题数，作业正确题数，刷题完成题数，刷题正确题数，考试次数，通过次数，试卷总分，总得分。</p>
<p>其中，分数是指学员1804的考试成绩，百分制。删除其中的缺失值，共有9191个样本。</p>
<p>增加衍生变量</p>
<ul>
<li>随堂考完成率 = 随堂考完成题数/随堂考配置题数</li>
<li>随堂考正确率 = 随堂考正确题数/随堂考完成题数</li>
<li>作业完成率 = 作业完成题数/作业配置题数</li>
<li>作业正确率 = 作业正确题数/作业完成题数</li>
<li>刷题正确率 = 刷题正确题数/刷题完成题数</li>
</ul>
<p>增加分类变量</p>
<ul>
<li>最终通过：将百分制的分数变量，按分数小于60为0，大于等于60为1，变换成二分变量</li>
<li>模考通过：按试卷总分和总得分转换成百分制的模考成绩，按相同逻辑，转换成二分变量。</li>
</ul>
<p>处理时间单位</p>
<ul>
<li>直播时长h=直播出勤时长/60</li>
<li>重播时长h=重播出勤时长/60</li>
</ul>
<p>最后再次删除缺失值，共有8851个样本。</p>
<h2 id="数据变量选取"><a href="#数据变量选取" class="headerlink" title="数据变量选取"></a>数据变量选取</h2><p>经过数据处理，变量增多，如何选取变量是个问题。筛选特征变量方法很多，我选择了递归特征消除(Recursive Feature Elimination, RFE)方法。</p>
<p>递归特征消除 (RFE)通过递归减少考察的特征集规模来选择特征。 首先，预测模型在原始特征上训练，每项特征指定一个权重。之后，那些拥有最小绝对值权重的特征被踢出特征集。如此往复递归，直至剩余的特征数量达到所需的特征数量。</p>
<p>利用调用<code>sklearn</code>中的<code>RFE</code>方法，并结合经验，最后共选取了8个变量。变量如下：直播时长h，重播时长h，随堂考完成率，随堂考正确率，作业完成率，作业正确率，刷题正确率，模考通过。</p>
<h2 id="模型结果与评估"><a href="#模型结果与评估" class="headerlink" title="模型结果与评估"></a>模型结果与评估</h2><p>选取70%作为训练集，30%作为测试集。利用<code>GridSearchCV()</code>选取模型合适的超参。</p>
<p>模型的变量系数如下：</p>
<table>
<thead>
<tr>
<th>intercept</th>
<th>直播时长h</th>
<th>重播时长h</th>
<th>随堂考完成率</th>
<th>随堂考正确率</th>
</tr>
</thead>
<tbody>
<tr>
<td>-5.68592042</td>
<td>0.01512291</td>
<td>0.01101413</td>
<td>-0.48080453</td>
<td>2.03324583</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th>作业完成率</th>
<th>作业正确率</th>
<th>刷题正确率</th>
<th>模考通过</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.86103971</td>
<td>3.58450959</td>
<td>3.0435501</td>
<td>0.13064</td>
</tr>
</tbody>
</table>
<p>模型在训练集上的评价指标如下:</p>
<table>
<thead>
<tr>
<th>准确率score</th>
<th>精确率precision</th>
<th>召回率recall</th>
<th>综合评价指标f1-score</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.8447</td>
<td>0.8538</td>
<td>0.9835</td>
<td>0.9140</td>
</tr>
</tbody>
</table>
<p>以0.5为阀值，模型在测试集上的混淆矩阵如下：</p>
<table>
<thead>
<tr>
<th></th>
<th></th>
<th>真实情况</th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>模型预测</td>
<td></td>
<td>0</td>
<td>1</td>
</tr>
<tr>
<td></td>
<td>0</td>
<td>41</td>
<td>393</td>
</tr>
<tr>
<td></td>
<td>1</td>
<td>33</td>
<td>2189</td>
</tr>
</tbody>
</table>
<p>测试集上的评价指标为：</p>
<table>
<thead>
<tr>
<th></th>
<th>precision</th>
<th>recall</th>
<th>f1-score</th>
<th>support</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td>0.55</td>
<td>0.09</td>
<td>0.16</td>
<td>434</td>
</tr>
<tr>
<td>1</td>
<td>0.85</td>
<td>0.99</td>
<td>0.91</td>
<td>2222</td>
</tr>
<tr>
<td>avg</td>
<td>0.80</td>
<td>0.84</td>
<td>0.79</td>
<td>2656</td>
</tr>
</tbody>
</table>
<p>模型在测试集上的准确度为(41+2189)/2656=0.8396。模型的准确率还是非常高的（混淆矩阵对角线代表预测正确的数量），接近84%。可是单看混淆矩阵还不够，因为当数据不平衡时，计算的准确率也同样会高，并不代表模型就会好，所以我们进一步的借助于ROC曲线下的面积来衡量模型时候合理。</p>
<p><img src="/images/logistic-auc.svg" alt="image" title="ROC Curve"></p>
<p>AUC值为0.76，说明模型预测效果不错。</p>
<h2 id="后续改进"><a href="#后续改进" class="headerlink" title="后续改进"></a>后续改进</h2><p>虽然模型的准确性达到84%，但是仍然有不少改进空间。</p>
<ol>
<li>数据完善：本次收集数据中，仍有不少缺失值和缺失字段，有不少字段没能收集到，例如学生知识点得分情况，性别，基础学历，是否拥有密训和模考五套卷等等。</li>
<li>模型改进：后续得到现实数据再次验证，进行模型参数的修改，或者寻找其他更为适合的模型进行替代。</li>
</ol>
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<div style="text-align:center;color: #ccc;font-size:14px;">-------------本文结束<i class="fa fa-paw"></i>感谢您的阅读-------------</div>
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