# Multivariable Wald to test equality of multinomial coefficients

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## Multivariable Wald to test equality of multinomial coefficients

 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.         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariable Wald to test equality of multinomial coefficients

 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 <[hidden email]> 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. > > > >         [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Multivariable Wald to test equality of multinomial coefficients

 Thanks Bert, I realise that and am not distilling it down to the p value. I am primarily considering the issue of collapsing down in the larger context of the added value/information that the extra categories give. However, I am curious to see (as I said from a statistical standpoint) whether the coefficients are sufficiently dissimilar. Regards, Paul Sanfilippo  On 4 October 2016 at 10:08:12 am, Bert Gunter ([hidden email]) wrote: 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 <[hidden email]> 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.   >   >   >   > [[alternative HTML version deleted]]   >   > ______________________________________________   > [hidden email] mailing list -- To UNSUBSCRIBE and more, see   > https://stat.ethz.ch/mailman/listinfo/r-help  > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html  > and provide commented, minimal, self-contained, reproducible code.           [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.