## Relation between multinomial and binomial logit parameters

Solved
Frequent Contributor
Posts: 111

# Relation between multinomial and binomial logit parameters

Hello,

Hello,
I have those parameters from a multinomial logit regression that explains Education (L/M/H) by language (Dominant/Other Europe/Non-European).

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

 Analysis of Maximum Likelihood Estimates Parameter edu3 DF Estimate Standard Wald Pr > ChiSq Error Chi-Square Intercept L 1 -0.7505 0.0134 3131.38 <.0001 Intercept M 1 0.159 0.0103 236.585 <.0001 Language Europe L 1 -0.0533 0.0841 0.4021 0.526 Language Europe M 1 -0.2527 0.0677 13.9402 0.0002 Language Non-Europe L 1 1.5045 0.0729 426.15 <.0001 Language Non-Europe M 1 0.2267 0.0773 8.6057 0.0034

The parameter (-0.0533) thus compares L to H for Other Euoprean compared to Dominant (reference category). Now I want to know what is the parameter for L compared to all others (M+H), so I was going to do -0.0533-(-0.2527)=0.1994.

1-Is this correct?

2-If so, why, when I perform a binominal logit regression (L vs Other), I get these parameters. In my mind, it should give the same.

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

 Analysis of Maximum Likelihood Estimates Parameter LOW DF Estimate Standard Wald Pr > ChiSq Error Chi-Square Intercept 1 1 -1.5263 0.0122 15662.1 <.0001 Language Europe 1 1 0.0751 0.0776 0.9348 0.3336 Language Non-Europe 1 1 1.3759 0.0566 591.027 <.0001

Accepted Solutions
Solution
‎07-13-2017 11:47 AM
SAS Employee
Posts: 242

## Re: Relation between multinomial and binomial logit parameters

"L compared to all others (M+H)" defines a cumulative logit. The relationship between the parameters of the nominal and ordinal models is a much more complex nonlinear function.  But, to get the parameters on a model using cumulative logits like you want, all you need to do is change your model from a generalized logit model to an ordinal logit model that allows unequal slopes for the two cumulative logits, like so:

``````proc logistic data=edu.educationClean;
class Language(ref='Dom')  /param=ref;
model edu3(ref='H')= Language / unequalslopes;
weight pond / norm;
where model=1;
run;``````

All Replies
Solution
‎07-13-2017 11:47 AM
SAS Employee
Posts: 242

## Re: Relation between multinomial and binomial logit parameters

"L compared to all others (M+H)" defines a cumulative logit. The relationship between the parameters of the nominal and ordinal models is a much more complex nonlinear function.  But, to get the parameters on a model using cumulative logits like you want, all you need to do is change your model from a generalized logit model to an ordinal logit model that allows unequal slopes for the two cumulative logits, like so:

``````proc logistic data=edu.educationClean;
class Language(ref='Dom')  /param=ref;
model edu3(ref='H')= Language / unequalslopes;
weight pond / norm;
where model=1;
run;``````
☑ This topic is solved.