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| title: "中介变量或者因变量是因子变量的中介分析" | ||
| date: 2024-11-04T00:47:46Z | ||
| draft: ["false"] | ||
| tags: [ | ||
| "fetched", | ||
| "R 学习践行者" | ||
| ] | ||
| categories: ["Acdemic"] | ||
| --- | ||
| 中介变量或者因变量是因子变量的中介分析 by R 学习践行者 | ||
| ------ | ||
| <div><p> 在中介变量或因变量为类别变量的中介分析中，需要使用 Logistic 回归取代通常的线性回归；此时因为a、b、c’系数存在尺度上的问题所以需要进行系数转换，使得回归系数变成具有相同的尺度。</p><p> 下面使用示例展示这种类型的中介分析过程，示例中自变量是多分类变量，中介变量是连续变量，因变量是二分类变量。</p><pre><code><span>library</span>(mediation)<br>data(jobs)</code></pre><p> 我们仍然depress1作为自变量，econ_hard作为中介变量，depress2作为因变量；同时把depress1和depress2转换成因子变量：</p><pre><code>hist(jobs$depress2)</code></pre><p><img data-imgfileid="100003138" data-ratio="0.7138888888888889" data-type="png" data-w="1080" width="672" data-src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaYHcI4CHC4ZSfOORhKpArjYnNTUTIuxLkVQbjP7T6JAibna40vEMt5uQ/640?wx_fmt=png&from=appmsg" src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaYHcI4CHC4ZSfOORhKpArjYnNTUTIuxLkVQbjP7T6JAibna40vEMt5uQ/640?wx_fmt=png&from=appmsg"></p><pre><code>jobs$depress1<-ifelse(<br> jobs$depress1<<span>1.5</span>,<span>"d1"</span>,<br> ifelse(jobs$depress1>=<span>1.5</span> & jobs$depress1<<span>2</span>,<span>"d2"</span>,<br> ifelse(jobs$depress1>=<span>2</span> & jobs$depress1<<span>2.5</span>,<br> <span>"d3"</span>,<span>"d4"</span>)))<br><br>jobs$depress1<-factor(jobs$depress1,levels = c(<span>"d1"</span>,<span>"d2"</span>,<span>"d3"</span>,<span>"d4"</span>))<br><br>jobs$depress2<-ifelse(jobs$depress2><span>2</span>,<span>1</span>,<span>0</span>)<br><br>table(jobs$depress2)</code></pre><pre><code> <br> 0 1 <br> 655 244</code></pre><pre><code><span># 转换多类别变量 X 为虚拟变量</span><br>X_dummy <- model.matrix(~ depress1 - <span>1</span>, data = jobs) <span># 创建虚拟变量矩阵</span><br>jobs<- cbind(jobs, X_dummy) <span># 合并虚拟变量至原数据集中</span></code></pre><p>1.拟合模型</p><p>第一个模型：</p><pre><code>model.0 <- glm(depress2 ~ depress1d2+depress1d3+depress1d4, <br> data=jobs,<br> family = binomial(link = <span>"logit"</span>))<br>summary(model.0)</code></pre><pre><code> <br> Call:<br> glm(formula = depress2 ~ depress1d2 + depress1d3 + depress1d4, <br> family = binomial(link = "logit"), data = jobs)<br> <br> Coefficients:<br> Estimate Std. Error z value Pr(>|z|) <br> (Intercept) -2.0534 0.1822 -11.272 < 2e-16 ***<br> depress1d2 0.7300 0.2531 2.884 0.00393 ** <br> depress1d3 1.4504 0.2258 6.424 1.32e-10 ***<br> depress1d4 2.1163 0.2416 8.760 < 2e-16 ***<br> ---<br> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<br> <br> (Dispersion parameter for binomial family taken to be 1)<br> <br> Null deviance: 1051.2 on 898 degrees of freedom<br> Residual deviance: 952.3 on 895 degrees of freedom<br> AIC: 960.3<br> <br> Number of Fisher Scoring iterations: 4</code></pre><p>第二个模型：</p><pre><code>model.1 <- lm(econ_hard~ depress1d2 + depress1d3 + depress1d4,<br> data=jobs)<br>summary(model.1)</code></pre><pre><code> <br> Call:<br> lm(formula = econ_hard ~ depress1d2 + depress1d3 + depress1d4, <br> data = jobs)<br> <br> Residuals:<br> Min 1Q Median 3Q Max <br> -2.35006 -0.66874 -0.00874 0.66126 2.38124 <br> <br> Coefficients:<br> Estimate Std. Error t value Pr(>|t|) <br> (Intercept) 2.61876 0.05410 48.410 < 2e-16 ***<br> depress1d2 0.36431 0.08610 4.231 2.56e-05 ***<br> depress1d3 0.71998 0.08052 8.942 < 2e-16 ***<br> depress1d4 0.73130 0.09181 7.965 4.99e-15 ***<br> ---<br> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<br> <br> Residual standard error: 0.9354 on 895 degrees of freedom<br> Multiple R-squared: 0.1038, Adjusted R-squared: 0.1008 <br> F-statistic: 34.55 on 3 and 895 DF, p-value: < 2.2e-16</code></pre><p>第三个模型：</p><pre><code>model.2 <- glm(depress2~ econ_hard+depress1d2 + <br> depress1d3 + depress1d4, <br> data=jobs,<br> family = binomial(link = <span>"logit"</span>))<br>summary(model.2)</code></pre><pre><code> <br> Call:<br> glm(formula = depress2 ~ econ_hard + depress1d2 + depress1d3 + <br> depress1d4, family = binomial(link = "logit"), data = jobs)<br> <br> Coefficients:<br> Estimate Std. Error z value Pr(>|z|) <br> (Intercept) -2.63074 0.29810 -8.825 < 2e-16 ***<br> econ_hard 0.21455 0.08527 2.516 0.0119 * <br> depress1d2 0.65628 0.25527 2.571 0.0101 * <br> depress1d3 1.30567 0.23268 5.612 2.01e-08 ***<br> depress1d4 1.97533 0.24750 7.981 1.45e-15 ***<br> ---<br> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<br> <br> (Dispersion parameter for binomial family taken to be 1)<br> <br> Null deviance: 1051.22 on 898 degrees of freedom<br> Residual deviance: 945.92 on 894 degrees of freedom<br> AIC: 955.92<br> <br> Number of Fisher Scoring iterations: 4</code></pre><p> 根据输出的结果我们可以绘制出一下这张图：</p><p><img data-imgfileid="100003137" data-ratio="0.8818407960199005" data-type="png" data-w="804" data-src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaZKwtC73KRYnkdjQBV2LeDTajSgg5fODYcjNp5ib7Xm9jmRicJJJO0jfQ/640?wx_fmt=png&from=appmsg" src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaZKwtC73KRYnkdjQBV2LeDTajSgg5fODYcjNp5ib7Xm9jmRicJJJO0jfQ/640?wx_fmt=png&from=appmsg"> 我们可以看到未进行系数转换，总效应与直接效应+间接效应之和差异较大。</p><p><br></p><p>2.回归系数标准</p><p><img data-imgfileid="100003140" data-ratio="0.8078902229845626" data-type="png" data-w="583" data-src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaTxoS8IIeNnTwN87pOXcMVHmNLibfm7yubr9tENf994DRWSJ1Vqg4VJA/640?wx_fmt=png&from=appmsg" src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HaTxoS8IIeNnTwN87pOXcMVHmNLibfm7yubr9tENf994DRWSJ1Vqg4VJA/640?wx_fmt=png&from=appmsg"></p><pre><code><span>#对自变量b2水平的b、c'、c系数标准化</span><br>b2_var<-var(jobs$depress1d2)<br>b2<-<span>0.73</span>^<span>2</span>*b2_var+pi^<span>2</span>/<span>3</span><br>SD1_b2<-sqrt(b2)<br><br>m_var<-var(jobs$econ_hard)<br>b2_m_cor<-cov(jobs$depress1d2,jobs$econ_hard)<br><br>b2_1<-<span>0.65628</span>^<span>2</span>*b2_var+<span>0.21455</span>^<span>2</span>*m_var+<span>2</span>*<span>0.65628</span>*<span>0.21455</span>*b2_m_cor+pi^<span>2</span>/<span>3</span><br><br>SD2_b2<-sqrt(b2_1)<br><br><span>#对b、c'、c系数标准化</span><br>b2_b<-<span>0.21455</span>/SD2_b2<br>b2_c1<-<span>0.65628</span>/SD2_b2<br>b2_c<-<span>0.73</span>/SD1_b2<br><br>b2_b;b2_c1;b2_c</code></pre><pre><code> [1] 0.116264</code></pre><pre><code> [1] 0.3556361</code></pre><pre><code> [1] 0.3970391</code></pre><pre><code><span>#对自变量b3水平的b、c'、c系数标准化</span><br>b3_var<-var(jobs$depress1d3)<br>b3<-<span>1.4504</span>^<span>2</span>*b3_var+pi^<span>2</span>/<span>3</span><br>SD1_b3<-sqrt(b3)<br><br>m_var<-var(jobs$econ_hard)<br>b3_m_cor<-cov(jobs$depress1d3,jobs$econ_hard)<br><br>b3_1<-<span>1.30567</span>^<span>2</span>*b3_var+<span>0.21455</span>^<span>2</span>*m_var+<span>2</span>*<span>1.30567</span>*<span>0.21455</span>*b3_m_cor+pi^<span>2</span>/<span>3</span><br><br>SD2_b3<-sqrt(b3_1)<br><br><span>#对b、c'、c系数标准化</span><br>b3_b<-<span>0.21455</span>/SD2_b3<br>b3_c1<-<span>1.30567</span>/SD2_b3<br>b3_c<-<span>1.4504</span>/SD1_b3<br><br>b3_b;b3_c1;b3_c</code></pre><pre><code> [1] 0.1112067</code></pre><pre><code> [1] 0.6767617</code></pre><pre><code> [1] 0.7531668</code></pre><pre><code><span>#对自变量b4水平的b、c'、c系数标准化</span><br>b4_var<-var(jobs$depress1d4)<br>b4<-<span>2.1163</span>^<span>2</span>*b4_var+pi^<span>2</span>/<span>3</span><br>SD1_b4<-sqrt(b4)<br><br>m_var<-var(jobs$econ_hard)<br>b4_m_cor<-cov(jobs$depress1d4,jobs$econ_hard)<br><br>b4_1<-<span>1.97533</span>^<span>2</span>*b4_var+<span>0.21455</span>^<span>2</span>*m_var+<span>2</span>*<span>1.97533</span>*<span>0.21455</span>*b4_m_cor+pi^<span>2</span>/<span>3</span><br><br>SD2_b4<-sqrt(b4_1)<br><br><span>#对b、c'、c系数标准化</span><br>b4_b<-<span>0.21455</span>/SD2_b4<br>b4_c1<-<span>1.97533</span>/SD2_b4<br>b4_c<-<span>2.1163</span>/SD1_b4<br><br>b4_b;b4_c1;b4_c</code></pre><pre><code> [1] 0.107921</code></pre><pre><code> [1] 0.9936122</code></pre><pre><code> [1] 1.065822</code></pre><p> 经过系数标准化后，虽然总效应不完全等于直接效应+间接效应，但是两者差异已经非常小了，如下图所示。因此我们可以采用整个流程并使用自助法计算直接效应（标准化的c’）、间接效应（a*b(标准化的)）、总效应（标准化的c）的置信区间。</p><p><img data-imgfileid="100003139" data-ratio="0.801948051948052" data-type="png" data-w="924" data-src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HayEr5PdhITEx0j7ujG19xtZgvtDAxEOTyYyRhicFgelRFy0UQfIcAu5A/640?wx_fmt=png&from=appmsg" src="https://mmbiz.qpic.cn/sz_mmbiz_png/IGjxEGEQ50neUDgPojaCEgXzJdVGF8HayEr5PdhITEx0j7ujG19xtZgvtDAxEOTyYyRhicFgelRFy0UQfIcAu5A/640?wx_fmt=png&from=appmsg"></p><p><br></p><p>3.使用RMediation包检验Za*Zb</p><p><mp-pay-preview-filter data-offset="40"></mp-pay-preview-filter></p></div> | ||
| <hr> | ||
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