逻辑斯蒂回归

# 逻辑斯蒂回归
## 社会调查方法——第11讲
### 李代
### 中国政法大学社会学院
### 2022-05-11

---

# 逻辑斯蒂回归

## 逻辑斯蒂回归原理

## 逻辑斯蒂回归的模型构建

## 逻辑斯蒂回归实例

---
# 社会调查方法期末作业

截止时间：2022-06-06 23:59

[点击我进入提交地址](https://workspace.jianguoyun.com/inbox/collect/f8caa51b6b634a47921da5c864a14c8a/submit)

[点击我进入模板下载地址](image/qimo.doc)

要求：

1. 态度端正 + 50

1. 能体现出所学知识 + 10

---
# 逻辑斯蒂回归原理

## 线性回归不适用怎么办？

如果因变量不是连续变量，应该怎么办？

例如：

二分类变量：性别、好恶、中外……

多分类变量：爱好、品牌、国籍……

定序变量：教育程度、满意程度……

---

# 逻辑斯蒂回归原理

## 比数比

发生比、比数：odds

What are the **odds**?

[国足仍有世界杯夺冠赔率 1赔3501倒数第二压泰国](https://www.163.com/sports/article/BJG7MT7700051C8M.html)

用1元钱赌中国队夺冠，中国队如果真的夺冠了，拿回来3502元钱。

odds: 1:3501

---

# 逻辑斯蒂回归原理

## 升学率

假设有n个学生考大学，考上大学的人数是x。

升学率，是一个百分比，proportion。 `$Proportion = \frac{x}{n}$`.

概率，probability。概率不可观测，但可以通过统计推断推算。 `$p = \frac{x}{n}$`.

比数，也就是事件发生的概率比事件不发生的概率： `$odds = \frac{p}{1-p}$`.

---

# 逻辑斯蒂回归原理

## 升学率

---

# 逻辑斯蒂回归原理

## 谁更占优势？

假设有m个男学生考大学，考上大学的男生人数是x。
假设有n个女学生考大学，考上大学的女生人数是y。

假如男生的升学率比女生大，是否说明男生更占优势？

$$ p_1 - p_2 = \frac{x}{m} - \frac{y}{n} $$

$$ \frac{p_1}{p_2} = \frac{\frac{x}{m}}{\frac{y}{n}} $$

---

# 逻辑斯蒂回归原理

## 谁更占优势？

![](survey-12_files/figure-html/unnamed-chunk-4-1.png)

---

# 逻辑斯蒂回归原理

## 比数比

odds ratio

男生升学的发生比是： `$\frac{p_m}{1 - p_m}$`

女生升学的发生比是： `$\frac{p_f}{1 - p_f}$`

比数比是： `$\frac{\frac{p_m}{1 - p_m}}{\frac{p_f}{1 - p_f}}$`

---

# 逻辑斯蒂回归原理

## 比数比

![](survey-12_files/figure-html/unnamed-chunk-5-1.png)

---

# 逻辑斯蒂回归原理

## 比数比的对数(log odds ratio)

![](survey-12_files/figure-html/unnamed-chunk-6-1.png)

---

# 逻辑斯蒂回归的模型构建

---

# 逻辑斯蒂回归的模型构建

## 泰坦尼克号

![](image/titanic-hundiendose.jpg)

---

# 逻辑斯蒂回归的模型构建

## 泰坦尼克号

![](survey-12_files/figure-html/unnamed-chunk-7-1.png)

---

# 逻辑斯蒂回归的模型构建

## 泰坦尼克号

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因为 `$OR > 1$` 或者 `$log or > 0$`，乘客跟船员比都更容易幸存，一等舱最容易幸存，其次是二等舱，再次是三等舱。

---

# 逻辑斯蒂回归的模型构建

## 泰坦尼克号

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<table class="gt_table">
 
 <thead class="gt_col_headings">
 <tr>
 <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Characteristic</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1">log(OR)1,2</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1">SE2</th>
 </tr>
 </thead>
 <tbody class="gt_table_body">
 <tr><td class="gt_row gt_left">(Intercept)</td>
<td class="gt_row gt_center">-1.2***</td>
<td class="gt_row gt_center">0.079</td></tr>
 <tr><td class="gt_row gt_left">Class</td>
<td class="gt_row gt_center"></td>
<td class="gt_row gt_center"></td></tr>
 <tr><td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">Crew</td>
<td class="gt_row gt_center">—</td>
<td class="gt_row gt_center">—</td></tr>
 <tr><td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">1st</td>
<td class="gt_row gt_center">1.7***</td>
<td class="gt_row gt_center">0.139</td></tr>
 <tr><td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">2nd</td>
<td class="gt_row gt_center">0.81***</td>
<td class="gt_row gt_center">0.144</td></tr>
 <tr><td class="gt_row gt_left" style="text-align: left; text-indent: 10px;">3rd</td>
<td class="gt_row gt_center">0.07</td>
<td class="gt_row gt_center">0.117</td></tr>
 <tr><td class="gt_row gt_left" style="border-top-width: 2px; border-top-style: solid; border-top-color: #D3D3D3;">AIC</td>
<td class="gt_row gt_center" style="border-top-width: 2px; border-top-style: solid; border-top-color: #D3D3D3;">2,597</td>
<td class="gt_row gt_center" style="border-top-width: 2px; border-top-style: solid; border-top-color: #D3D3D3;"></td></tr>
 <tr><td class="gt_row gt_left">No. Obs.</td>
<td class="gt_row gt_center">2,201</td>
<td class="gt_row gt_center"></td></tr>
 </tbody>
 
 <tfoot>
 <tr class="gt_footnotes">
 <td colspan="3">
 
 
 1
 
 
 *p<0.05; **p<0.01; ***p<0.001
 
 
 
 
 2
 
 
 OR = Odds Ratio, SE = Standard Error
 
 
 </td>
 </tr>
 </tfoot>
</table>
</div>