Relation between multinomial and binomial logit parameters

Demographer — Wed, 10 May 2017 14:06:28 GMT

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;
model edu3(ref='H')= Language /link=glogit rsquare;
weight pond / norm;
where model=1;
run;

Analysis of Maximum Likelihood Estimates
Parameter		edu3	DF	Estimate	Standard	Wald	Pr > ChiSq
Parameter		edu3	DF	Estimate	Error	Chi-Square	Pr > ChiSq
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;
model LOW(ref='0')= Language /link=glogit rsquare;
weight pond / norm;
where model=1;
run;

Analysis of Maximum Likelihood Estimates
Parameter		LOW	DF	Estimate	Standard	Wald	Pr > ChiSq
Parameter		LOW	DF	Estimate	Error	Chi-Square	Pr > ChiSq
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

Re: Relation between multinomial and binomial logit parameters

StatDave — Thu, 13 Jul 2017 15:25:44 GMT

"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;

topic Relation between multinomial and binomial logit parameters in Statistical Procedures

Relation between multinomial and binomial logit parameters

Re: Relation between multinomial and binomial logit parameters