7

我正在为iris数据集做多项逻辑回归模型，

library(VGAM)
mlog1 <- vglm(Species ~ ., data=iris, family=multinomial())
coef(mlog1)

系数为：

 (Intercept):1  (Intercept):2 Sepal.Length:1 Sepal.Length:2  Sepal.Width:1 
     34.243397      42.637804      10.746723       2.465220      12.815353 
 Sepal.Width:2 Petal.Length:1 Petal.Length:2  Petal.Width:1  Petal.Width:2 
      6.680887     -25.042636      -9.429385     -36.060294     -18.286137

然后我使用multinom()函数并做同样的事情：

library(nnet)
mlog2 <- multinom(Species ~ ., data=iris)

系数：

Coefficients:
           (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width
versicolor    18.69037    -5.458424   -8.707401     14.24477   -3.097684
virginica    -23.83628    -7.923634  -15.370769     23.65978   15.135301

这两个结果之间似乎差距很大？我哪里做错了？我怎样才能修复它们并获得类似的结果？

4

1 回答 1

10

The gap is due to two factors: (1) The multinomial() family in VGAM chooses the reference to be the last level of the response factor by default while multinom() in nnet always uses the first level as the reference. (2) The species categories in the iris data can be separated linearly, thus leading to very large coefficients and huge standard errors. Where exactly the numeric optimization stops when the log-likelihood virtually doesn't change further, can be somewhat different across implementations but is practically irrelevant.

As an example without separation consider a school choice regression model based on data from the German Socio-Economic Panel (1994-2002) in the AER package:

data("GSOEP9402", package = "AER")
library("nnet")
m1 <- multinom(school ~ meducation + memployment + log(income) + log(size),
  data = GSOEP9402)
m2 <- vglm(school ~ meducation + memployment + log(income) + log(size),
  data = GSOEP9402, family = multinomial(refLevel = 1))

Then, both models lead to esssentially the same coefficients:

coef(m1)
##                (Intercept) meducation memploymentparttime memploymentnone
## Realschule   -6.366449  0.3232377           0.4422277       0.7322972
## Gymnasium   -22.476933  0.6664295           0.8964440       1.0581122
##            log(income) log(size)
## Realschule   0.3877988 -1.297537
## Gymnasium    1.5347946 -1.757441

coef(m2, matrix = TRUE)
##                     log(mu[,2]/mu[,1]) log(mu[,3]/mu[,1])
## (Intercept)                 -6.3666257        -22.4778081
## meducation                   0.3232500          0.6664550
## memploymentparttime          0.4422720          0.8964986
## memploymentnone              0.7323156          1.0581625
## log(income)                  0.3877985          1.5348495
## log(size)                   -1.2975203         -1.7574912
于 2015-04-26T13:56:31.857 回答