## Reverse parameters in multinomial logit regression

Frequent Contributor
Posts: 113

# Reverse parameters in multinomial logit regression

[ Edited ]

Hello,

I have this multinomial logit model:

``````proc logistic data=edu.educationClean;
class Langue(ref='0')  /param=ref;
weight pond / norm;
where model=1;
run;``````

With the following output:

Analysis of Maximum Likelihood Estimates
Parameter   edu3 DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept   0 1 -0.7505 0.0134 3131.3792 <.0001
Intercept   1 1 0.1590 0.0103 236.5849 <.0001
Langue 1 0 1 -0.0533 0.0841 0.4021 0.5260
Langue 1 1 1 -0.2527 0.0677 13.9402 0.0002
Langue 2 0 1 1.5045 0.0729 426.1495 <.0001
Langue 2 1 1 0.2267 0.0773 8.6057 0.0034

In addition to this, I would like to have reverse parameters (I mean edu3=2 vs other) and their p values. I think I can do it manually (but maybe I'm wrong), for example, for langue=1, by doing -(-0.0533+-0.2527) to get the parameter for edu3=2 compared to other categories. However, with this method, I don't get p values. Is there a way to produce this automacially in the output?

SAS Employee
Posts: 307

## Re: Reverse parameters in multinomial logit regression

That implies that you want to model a logit defined as log[ Pr(Edu3=2)/(1-Pr(Edu3=2) ].  To do this, simply create a new response variable: new=(edu3=2); and fit a binary logistic model using it as the response.

Frequent Contributor
Posts: 113

## Re: Reverse parameters in multinomial logit regression

[ Edited ]

That is what I tried.

``````data edu.educationClean;
set edu.educationClean;
HIGH=0;
if edu3=2 then HIGH=1;
run;

proc logistic data=edu.educationClean;
class Langue(ref='0')  /param=ref;
weight pond / norm;
where model=1;
run;``````

It gives this output:

SAS Output

Analysis of Maximum Likelihood Estimates
Parameter   HIGH DF Estimate Standard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept   1 1 -0.4974 0.00963 2667.2291 <.0001
Langue 1 1 1 0.1913 0.0616 9.6420 0.0019
Langue 2 1 1 -0.7824 0.0675 134.4464 <.0001

Which is not what I expected as parameters. From the multinomial outputs, in my mind, the parameter for edu3=2 when langue=1 should be -(-0.0533+-0.2527)=0.306. However, it is 0.1913 when using a binomial regression. Maybe something is wrong with my reasoning.

SAS Employee
Posts: 307

## Re: Reverse parameters in multinomial logit regression

The generalized logit model you fit originaly is:

l0=log(p0/p2)=int0+lang01+lang02
l1=log(p1/p2)=int1+lang11+lang12

You now fit the model l2=log(p2/(p0+p1))=int+lang1+lang2.

When lang=1, under that first model:

l0=int0+lang01
l1=int1+lang11

And in the second model:

l2=int+lang1

Algebraically, I don't see that -(lang01+lang11) as you want to do, gets you to the lang1 parameter in the second model.

Frequent Contributor
Posts: 113

## Re: Reverse parameters in multinomial logit regression

So there is no way to get log(p2/(p0+p1)) directly from the multinomial logit parameters?

Frequent Contributor
Posts: 113