如何在 mlogit 中获取由 effects() 计算的边际效应的标准误差

Question

我目前正在使用 R 中的 mlogit 包进行（条件）多项逻辑回归分析。这些模型的标准输出是系数、标准误差及其显着性水平。由于这些系数可能难以解释，我还使用包中包含的 effects() 函数计算边际效应。然而，effects() 函数只提供边际效应（或弹性），而没有提供其他信息。理想情况下，我还会提供一些关于显着性和置信区间的信息。 有没有一种函数或简单的方法可以计算通过 effects() 计算的边际效应的标准误和显着性水平？

使用 mlogit 包中包含的 MC 数据集的示例

    # loading packages
    library(mlogit)
    library(Formula)
    
    # loading dataset on mode of travel from mlogit package
    data("ModeCanada", package = "mlogit")
    
    # only include choice sets with all four alternatives
    MC <- dfidx(ModeCanada, subset = noalt == 4)
    
    # formula of a multinomial model with income as a predictor of 
    # the mode of travel
    ml.MC1 <- mlogit(choice ~ 1 | income | 1, MC)
    
    # calculate model
    summary(ml.MC1)

    # output includes coefficients of the model but also standard 
    # error, z-values, and level of significance
    
    Coefficients :
                      Estimate Std. Error z-value  Pr(>|z|)
    (Intercept):air -1.5035093  0.1963055 -7.6590 1.865e-14 ***
    (Intercept):bus -1.7715605  0.6643887 -2.6665  0.007666 **
    (Intercept):car  0.7371313  0.1572490  4.6877 2.763e-06 ***
    income:air       0.0414857  0.0034315 12.0896 < 2.2e-16 ***
    income:bus      -0.0510644  0.0181427 -2.8146  0.004884 **
    income:car       0.0053445  0.0029496  1.8120  0.069991 .
    ---
    Signif. codes:
    0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    Log-Likelihood: -2779.2

    # calculate marginal effects (an absolute increase of predictor as absolute
    # change in predicted outcome probability)(at sample means). 
    # However, the output only includes the marginal effect of changes in 
    # income, but no info on standard errors, etc.

    effects(ml.MC1, covariate = "income", type = "aa")

            train           air           bus           car 
    -0.0029162845  0.0086781323 -0.0001209537 -0.0056408941 

Answer 1

我没有R 解决方案，但这里有一个Stata 解决方案，可能有助于比较未来的R 答案或您自己的例程。在任何情况下，“手动”R 解决方案是将Delta Theorem 应用于Kenneth's Book 的第 3.6 节（导数和弹性）中导出的弹性表达式。我希望这可以帮助您入门。

有条件的 logit 复制

. asclogit choice  if noalt==4  ,case(case)   casev(income) alternatives(alt)  base(train) nolog

Alternative-specific conditional logit         Number of obs      =     11,116
Case ID variable: case                         Number of cases    =       2779

Alternatives variable: alt                     Alts per case: min =          4
                                                              avg =        4.0
                                                              max =          4

                                                  Wald chi2(3)    =     212.63
Log likelihood = -2779.2424                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
      choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
air          |
      income |   .0414857   .0034315    12.09   0.000       .03476    .0482113
       _cons |  -1.503509   .1963055    -7.66   0.000    -1.888261   -1.118758
-------------+----------------------------------------------------------------
bus          |
      income |  -.0510649   .0181427    -2.81   0.005    -.0866239   -.0155059
       _cons |  -1.771551   .6643887    -2.67   0.008    -3.073729   -.4693731
-------------+----------------------------------------------------------------
car          |
      income |   .0053445   .0029496     1.81   0.070    -.0004365    .0111255
       _cons |   .7371313    .157249     4.69   0.000     .4289289    1.045334
-------------+----------------------------------------------------------------
train        |  (base alternative)
------------------------------------------------------------------------------

边际效应

. margins  ,dydx(income)

Average marginal effects                        Number of obs     =     11,116
Model VCE    : OIM

Expression   : Pr(alt|1 selected), predict()
dy/dx w.r.t. : income

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
income       |
    _outcome |
        air  |   .0081304   .0004962    16.38   0.000     .0071578     .009103
        bus  |  -.0002234   .0000904    -2.47   0.014    -.0004007   -.0000461
        car  |  -.0052056   .0005082   -10.24   0.000    -.0062017   -.0042095
      train  |  -.0027014    .000358    -7.55   0.000    -.0034031   -.0019997
------------------------------------------------------------------------------