# [R] Multivariable Wald to test equality of multinomial coefficients

Bert Gunter bgunter.4567 at gmail.com
Tue Oct 4 01:08:11 CEST 2016

```See inline.

-- Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Mon, Oct 3, 2016 at 3:30 PM, Paul Sanfilippo <prseye at gmail.com> wrote:
> 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."

IMHO, this is a bad idea. See
http://www.nature.com/news/statisticians-issue-warning-over-misuse-of-p-values-1.19503.

Significance or lack of it is not a legitimate criterion on which to
base scientific decisions.

>
> 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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