简介 虚拟变量（Dummy variables）和交乘项(Interaction)
在对有组别或者等级的数据进行处理时，常常需要利用虚拟变量和交乘项来探究各组之间或各等级之间的结构性的差异（Structural Difference）
例： 探究婚姻对女性工资造成的结构性的差异
sysuse nlsw88.dta, clear
sum
Variable | Obs Mean Std. Dev. Min Max
-------------+------------------------------------------------
idcode | 2,246 2612.654 1480.864 1 5159
age | 2,246 39.15316 3.060002 34 46
race | 2,246 1.282725 .4754413 1 3
married | 2,246 .6420303 .4795099 0 1
never_marr~d | 2,246 .1041852 .3055687 0 1
-------------+------------------------------------------------
grade | 2,244 13.09893 2.521246 0 18
collgrad | 2,246 .2368655 .4252538 0 1
south | 2,246 .4194123 .4935728 0 1
smsa | 2,246 .7039181 .4566292 0 1
c_city | 2,246 .2916296 .4546139 0 1
-------------+------------------------------------------------
industry | 2,232 8.189516 3.010875 1 12
occupation | 2,237 4.642825 3.408897 1 13
union | 1,878 .2454739 .4304825 0 1
wage | 2,246 7.766949 5.755523 1.004952 40.74659
hours | 2,242 37.21811 10.50914 1 80
-------------+------------------------------------------------
ttl_exp | 2,246 12.53498 4.610208 .1153846 28.88461
tenure | 2,231 5.97785 5.510331 0 25.91667
基础模型（Basic Model）
添加虚拟变量及交乘项的复杂方法
gen marriedtenure = married*tenure
gen marriedhours = married*hours
gen marriedttl = married*ttl_exp
reg wage tenure hours ttl_exp married*
test marriedtenure marriedhours marriedttl
Source | SS df MS
-------------+----------------------------------
Model | 6140.31754 7 877.188219
Residual | 67880.4931 2,219 30.5905782
-------------+----------------------------------
Total | 74020.8106 2,226 33.2528349
Number of obs = 2,227
F(7, 2219) = 28.68
Prob > F = 0.0000
R-squared = 0.0830
Adj R-squared = 0.0801
Root MSE = 5.5309
-----------------------------------------------
wage | Coef. Std. Err. t
--------------+--------------------------------
tenure | .1048823 .0412746 2.54
hours | .0874067 .0222925 3.92
ttl_exp | .2183548 .0515089 4.24
married | 1.029717 1.12407 0.92
marriedtenure | -.110726 .0532406 -2.08
marriedhours | -.0418236 .0261311 -1.60
marriedttl | .0869538 .0652744 1.33
_cons | 1.208404 .9551692 1.27
-----------------------------------------------
------------------------------------------------
wage | P>|t| [95% Conf. Interval]
--------------+---------------------------------
tenure | 0.011 .0239415 .1858232
hours | 0.000 .0436904 .1311231
ttl_exp | 0.000 .1173441 .3193655
married | 0.360 -1.174622 3.234056
marriedtenure | 0.038 -.2151326 -.0063194
marriedhours | 0.110 -.0930675 .0094204
marriedttl | 0.183 -.0410515 .214959
_cons | 0.206 -.6647154 3.081522
------------------------------------------------
( 1) marriedtenure = 0
( 2) marriedhours = 0
( 3) marriedttl = 0
F( 3, 2219) = 2.31
Prob > F = 0.0748
利用Factor Indicator 的便捷方法
Factor Indicator 的更多应用及详情请见于fvvarlist。
help fvvarlist
简便方式
global cx "tenure hours ttl_exp"
reg wage i.married##c.($cx)
testparm married married#c.($cx)
Source | SS df MS
-------------+----------------------------------
Model | 6140.31754 7 877.188219
Residual | 67880.4931 2,219 30.5905782
-------------+----------------------------------
Total | 74020.8106 2,226 33.2528349
Number of obs = 2,227
F(7, 2219) = 28.68
Prob > F = 0.0000
R-squared = 0.0830
Adj R-squared = 0.0801
Root MSE = 5.5309
----------------------------------------------------
wage | Coef. Std. Err. t
------------------+---------------------------------
married |
married | 1.029717 1.12407 0.92
tenure | .1048823 .0412746 2.54
hours | .0874067 .0222925 3.92
ttl_exp | .2183548 .0515089 4.24
|
married#c.tenure |
married | -.110726 .0532406 -2.08
|
married#c.hours |
married | -.0418236 .0261311 -1.60
|
married#c.ttl_exp |
married | .0869538 .0652744 1.33
|
_cons | 1.208404 .9551692 1.27
----------------------------------------------------
---------------------------------------------------
wage | P>|t| [95% Conf. Interval]
------------------+--------------------------------
married |
married | 0.360 -1.174622 3.234056
tenure | 0.011 .0239415 .1858232
hours | 0.000 .0436904 .1311231
ttl_exp | 0.000 .1173441 .3193655
|
married#c.tenure |
married | 0.038 -.2151326 -.0063194
|
married#c.hours |
married | 0.110 -.0930675 .0094204
|
married#c.ttl_exp |
married | 0.183 -.0410515 .214959
|
_cons | 0.206 -.6647154 3.081522
---------------------------------------------------
( 1) 1.married#c.tenure = 0
( 2) 1.married#c.hours = 0
( 3) 1.married#c.ttl_exp = 0
F( 3, 2219) = 2.31
Prob > F = 0.0748
注意此处应使用命令 testparm 而非 test
test 不支持 factor indicator 的#语法
若要用test，则需要改写为
test married married#c.tenture married#c.hours married#c.ttl_exp
这样则极为冗长和复杂。
总结
- 利用factor indicator 的语法极大的方便了虚拟变量交乘项的生成
- 在回归和检验中均可使用，注意test应用testparm命令替代
- 在自变量多的时候，该方法的便捷性更加明显
- 可以利用global 命令将其他需要交乘变量，放入一个全局暂元中，之后直接$引用就好，极大地减少代码的书写量
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