使用Stata的probit回归中交互变量的边际效应

Question

我是运行概率回归，其中一个连续变量和一个虚拟变量之间存在交互作用。系数显示在回归输出中，但当我查看边际效应时，交互作用缺失。

如何得到交互变量的边际效应？

probit move_right c.real_income_change_percent##i.gender

Iteration 0:   log likelihood = -345.57292  
Iteration 1:   log likelihood = -339.10962  
Iteration 2:   log likelihood = -339.10565  
Iteration 3:   log likelihood = -339.10565  

Probit regression                                 Number of obs   =        958
                                                  LR chi2(3)      =      12.93
                                                  Prob > chi2     =     0.0048
Log likelihood = -339.10565                       Pseudo R2       =     0.0187

-----------------------------------------------------------------------------------------------------
                         move_right |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------------+----------------------------------------------------------------
         real_income_change_percent |   .0034604   .0010125     3.42   0.001      .001476    .0054448
                                    |
                             gender |
                            Female  |   .0695646   .1139538     0.61   0.542    -.1537807    .2929099
                                    |
gender#c.real_income_change_percent |
                            Female  |  -.0039908   .0015254    -2.62   0.009    -.0069805   -.0010011
                                    |
                              _cons |  -1.263463   .0798439   -15.82   0.000    -1.419954   -1.106972
-----------------------------------------------------------------------------------------------------


margins, dydx(*) post

Average marginal effects                          Number of obs   =        958
Model VCE    : OIM

Expression   : Pr(move_right), predict()
dy/dx w.r.t. : real_income_change_percent 1.gender

--------------------------------------------------------------------------------------------
                           |            Delta-method
                           |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
real_income_change_percent |   .0002846   .0001454     1.96   0.050    -4.15e-07    .0005697
                           |
                    gender |
                   Female  |  -.0102626   .0207666    -0.49   0.621    -.0509643    .0304392
--------------------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Answer 1

这听起来像是一个特定于某个软件 (Stata) 的问题，因此票数接近，但这里潜伏着一个统计问题：交互效应的边际效应是什么样的？

此类边际效应并非微不足道，并且往往强烈依赖于其他协变量的值，请参见this article. Often this marginal effect is so variable that it makes no sense to try to summarize it with one number. In my opinion, this is a major weakness. To the extend that in general I tend to prefer using logistic regression and interpret the interaction term as a ratio of odds ratios, see this article。

Answer 2

我觉得你的问题很奇怪。您询问了虚拟交互，但您的示例涉及连续虚拟交互。

执行任一操作的方法如下：

webuse union, clear

/* dummy-dummy iteraction */
probit union i.south##i.black grade, nolog
margins r.south#r.black

/* continuous-dummy iteraction */
probit union i.south##c.grade
margins r.south, dydx(grade)

您应该尝试通过 "hand" 重现这些（使用 predicts 的差异）以了解边距命令在幕后做了什么。

使用Stata的probit回归中交互变量的边际效应

Marginal effect of interaction variable in probit regression using Stata

stata