Frank Fan Frank Fan - 4 years ago 236
R Question

multinomial logistic regression in R: multinom in nnet package result different from mlogit in mlogit package?

Both R functions,

) and
) can be used for multinomial logistic regression. But why this example returns different result of p values of coefficients?

#prepare data

mydata <- read.csv("")
mydata$rank <- factor(mydata$rank)
mydata$gre[1:10] = rnorm(10,mean=80000)


test = multinom(admit ~ gre + gpa + rank, data = mydata)
z <- summary(test)$coefficients/summary(test)$standard.errors
# For simplicity, use z-test to approximate t test.
pv <- (1 - pnorm(abs(z)))*2
# (Intercept) gre gpa rank2 rank3 rank4
# 0.00000000 0.04640089 0.00000000 0.00000000 0.00000000 0.00000000


mldata =,choice = 'admit', shape = "wide")

mlogit.model1 <- mlogit(admit ~ 1 | gre + gpa + rank, data = mldata)
# Coefficients :
# Estimate Std. Error t-value Pr(>|t|)
# 1:(intercept) -3.5826e+00 1.1135e+00 -3.2175 0.0012930 **
# 1:gre 1.7353e-05 8.7528e-06 1.9825 0.0474225 *
# 1:gpa 1.0727e+00 3.1371e-01 3.4195 0.0006274 ***
# 1:rank2 -6.7122e-01 3.1574e-01 -2.1258 0.0335180 *
# 1:rank3 -1.4014e+00 3.4435e-01 -4.0697 4.707e-05 ***
# 1:rank4 -1.6066e+00 4.1749e-01 -3.8482 0.0001190 ***

Why the p values from
are so different? I guess it is because of the outliers I added using
mydata$gre[1:10] = rnorm(10,mean=80000)
. If outlier is an inevitable issue (for example in genomics, metabolomics, etc.), which R function should I use?

Answer Source

The difference here is the difference between the Wald $z$ test (what you calculated in pv) and the Likelihood Ratio test (what is returned by summary(mlogit.model). The Wald test is computationally simpler, but in general has less desirable properties (e.g., its CIs are not scale-invariant). You can read more about the two procedures here.

To perform LR tests on your nnet model coefficents, you can load the car and lmtest packages and call Anova(test) (though you'll have to do a little more work for the single df tests).

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