跨数据比较回归系数技巧
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跨数据比较回归系数之OLS：
https://stats.idre.ucla.edu/stata/code/comparing-regression-coefficients-across-groups-using-suest/
Comparing Regression Coefficients Across Groups using Suest | Stata Code Fragments
The FAQ at https://stats.idre.ucla.edu/stat/stata/faq/compreg3.htm shows how you can compare regression coefficients across three groups using xi and by forming interactions. This can also be done using suest as shown below.（这里的链接给了用哑变量交互项来比较不同数据的回归系数的方法，下面的方法用suest命令来实现。）
*从互联网读入数据
use https://stats.idre.ucla.edu/stat/stata/faq/compreg3
*用年龄为1 的数据组进行回归
regress weight height if age==1
*存储第一组回归的结果到age1中
est store age1
*用年龄为2 的数据组进行回归
regress weight height if age==2
*存储第一组回归的结果到age2中
est store age2
*用年龄为3 的数据组进行回归
regress weight height if age==3
*存储第一组回归的结果到age3中
est store age3
*利用suest进行这三个模型的同时估计
suest age1 age2 age3
*利用test检验不同模型的beta是否相等
test [age1_mean]height=[age2_mean]height
( 1) [age1_mean]height - [age2_mean]height = 0
chi2( 1) = 24.04
Prob > chi2 = 0.0000
*利用test检验不同模型的beta是否相等，多个模型可以用accum参数
test [age2_mean]height=[age3_mean]height, accum
跨数据比较回归系数之Binary Choice（Logit and Probit）：
参考文献：
Williams R. Using Heterogenous Choice Models to Compare Logit and Probit Coefficients Across Groups[J]. Sociological Methods & Research, 2009, 37(4):531-559.
*首先安装oglm的第三方程序
ssc install oglm
Appendix: Stata Code
The following code replicates parts of the analysis in this paper. The user-written oglm and mfx2 commands must be installed; from within Stata type help findit. For more information, see the author‟s web page at http://www.nd.edu/~rwilliam/oglm/index.html.
Stata Code for Tables 1 & 2:
* Step 1. 无约束模型，所有的回归系数可以随性别而改变 Unconstrained models, all coefficients can differ by gender.
use "http://www.indiana.edu/~jslsoc/stata/spex_data/tenure01.dta", clear
* Allison（原文作者）将样本限制在前10年会获得终身教职的 Allison limited the sample to the first 10 years untenured
keep if pdasample
* 选择男性样本进行模型估计 Males Only
oglm tenure year yearsq select articles prestige if male, store(step1male)
* 选择女性样本进行模型估计 Females Only
oglm tenure year yearsq select articles prestige if female, store(step1fem)
* 采用了交互项的等价的混合模型 Equivalent pooled model, using interactions.
oglm tenure year yearsq select articles prestige f_year f_yearsq f_select f_articles f_prestige female, store(step1)
* Step 2. 混合模型，只有截距项因性别而改变 Pooled model; only the intercepts differ by gender.
* Allison提到了该模型但并未在文中汇报 Allison refers to this model but does not present it in the paper.
oglm tenure year yearsq select articles prestige female, store(step2)
* Step 3. 残差方差允许根据性别而改变 Residual variances allowed to differ by gender.
* Allison的模型实际上是异质选择模型的一个特例，用oglm包可以很方便的计算delta
* Allison’s model is actually a special case of a heterogeneous choice model,
* and it is easy to compute Allison’s delta using oglm.
* 与Allison文章中的表2的结果进行对比 Compare these results with the first half of Allison’s Table 2.
oglm tenure female year yearsq select articles prestige , het(female) store(step3)
* 计算delta Compute delta
display (1 - exp(.3022305))/ exp(.3022305)
* Step 4A. 检验残差方差不同时alphas是否相等 Test that the Alphas are = but residual variances differ.
lrtest step2 step3, stats
* Step 4B. 检验跨组的alpha在残差方差不同时alpha是否相等
* Test whether any Alphas differ across groups given that residual variances differ.
lrtest step1 step3, stats
* Step 4C. 检验文章的效果是否存在组间差异 Test whether the effect of articles differs across groups.
*首先需要估计带交互项的模型 First have to estimate the model with the interaction term added.
* 与Allison文章中的表2结果进行对比 Compare this with the second half of Allison’s Table 2.
oglm tenure female year yearsq select articles prestige f_articles, het(female) store(step4c)
* 计算delta Compute delta
display (1 - exp(.1774193))/ exp(.1774193)
*现在进行female*articles交互项的检验 Now do the formal test of the female*articles interaction term.
lrtest step3 step4c, stats
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