Stata 多项式回归 - post-估计 Wald 检验

Question

我在 Stata 中进行了多项逻辑回归分析，然后进行了 Wald 测试，希望有人可以确认我的代码正在做我认为正在做的事情。

注意：我正在使用一些 Stata 的示例数据来说明。我运行对此图的分析完全没有意义，但使用与我的 'real' 分析相同的程序，除了我的实际分析还包括一些概率权重和其他协变量这一事实。

sysuse auto.dta

首先，我运行一个多项逻辑回归，从'Foreign'和'Price'预测'Repair Record'：

mlogit rep78 i.foreign price, base(1) rrr nolog

Multinomial logistic regression                 Number of obs     =         69
                                                LR chi2(8)        =      31.15
                                                Prob > chi2       =     0.0001
Log likelihood = -78.116372                     Pseudo R2         =     0.1662

------------------------------------------------------------------------------
       rep78 |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |  (base outcome)
-------------+----------------------------------------------------------------
2            |
     foreign |
    Foreign  |   .7822853   1672.371    -0.00   1.000            0           .
       price |   1.000414   .0007027     0.59   0.556     .9990375    1.001792
       _cons |   .5000195   1.669979    -0.21   0.836      .000718    348.2204
-------------+----------------------------------------------------------------
3            |
     foreign |
    Foreign  |     686842   1.30e+09     0.01   0.994            0           .
       price |   1.000462   .0006955     0.66   0.507     .9990996    1.001826
       _cons |   1.254303   4.106511     0.07   0.945     .0020494    767.6863
-------------+----------------------------------------------------------------
4            |
     foreign |
    Foreign  |    6177800   1.17e+10     0.01   0.993            0           .
       price |   1.000421   .0006999     0.60   0.547     .9990504    1.001794
       _cons |   .5379627     1.7848    -0.19   0.852     .0008067    358.7452
-------------+----------------------------------------------------------------
5            |
     foreign |
    Foreign  |   2.79e+07   5.29e+10     0.01   0.993            0           .
       price |   1.000386   .0007125     0.54   0.587     .9989911    1.001784
       _cons |    .146745   .5072292    -0.56   0.579     .0001676    128.4611
------------------------------------------------------------------------------

其次，我想知道结果类别 4 的 'Foreign' 系数是否显着不同于结果类别 5 的 'Foreign' 系数。因此，我运行 Wald 检验:

test [4]1.foreign = [5]1.foreign

 ( 1)  [4]1.foreign - [5]1.foreign = 0

           chi2(  1) =    2.72
         Prob > chi2 =    0.0988

据此，我得出结论，结果类别 4 的 'Foreign' 系数与结果类别 5 的 'Foreign' 系数没有显着差异。更简单地说，[=28= 之间的关联]和'Repair 4'（相对于'Repair 1'）等于'Foreign'和'Repair 5'之间的关联（相对于'Repair 1'）。

我的 Wald 测试代码以及我对它所做和显示的推断是否正确？

Answer 1

此外，对于评论中讨论的内容，您还可以使用以下代码执行似然比检验。

sysuse auto.dta

qui mlogit rep78 i.foreign price, base(1) rrr nolog 
estimate store unrestricted

constraint 1 [4]1.foreign = [5]1.foreign

qui mlogit rep78 i.foreign price, base(1) rrr nolog constraints(1)
estimate store restricted

lrtest unrestricted restricted

测试的输出显示与 Wald 测试相同的结论，但它具有更好的属性，如下所述。

Likelihood-ratio test                                 LR chi2(1)  =      3.13
(Assumption: restricted nested in unrestricted)       Prob > chi2 =    0.0771

引用官方documentation 来自mlogit

The results produced by test are an approximation based on the estimated covariance matrix of the coefficients. Because the probability of being uninsured is low, the log-likelihood may be nonlinear for the uninsured. Conventional statistical wisdom is not to trust the asymptotic answer under these circumstances but to perform a likelihood-ratio test instead.

Stata 多项式回归 - post-估计 Wald 检验

Stata multinomial regression - post-estimation Wald test

stata

logistic-regression

multinomial