[R] Multivariable Wald to test equality of multinomial coefficients

[Paul Sanfilippo]

Hi,

I am trying to replicate a test in the Hosmer - Applied Logistic regression text (pp 289, 3rd ed) that uses a Multivariable Wald test to test the equality of coefficients across the 2 logits of a 3 category response multinomial model. I’d like to see whether (from a  statistical standpoint) it is acceptable to collapse the 2 response categories and then simply use a binary logistic regression. The idea is that if the coefficients across the 2 logits are similar (non-significant p value with Wald test), then it is reasonable to pool the categories.

There does not seem to be a built in way to do this in R?

Using the mtcars dataset as an example (for the sake of the example, using cyl as a 3-factor response), does anyone have any ideas how to do this

library(nnet)
data(mtcars)
mtcars$cyl <- as.factor(mtcars$cyl)  
mtcars$am <- as.factor(mtcars$am)  
mod <- multinom(cyl ~ am + hp, data=mtcars)
summary(mod)

> summary(mod)
Call:
multinom(formula = cyl ~ am + hp, data = mtcars)

Coefficients:
  (Intercept)       am1        hp
6   -42.03847  -3.77398 0.4147498
8   -92.30944 -26.27554 0.7836576

So, I want to simultaneously test whether the 3 coefficients across the 2 logits are similar.

Thank you.



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