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 | |
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;
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 | |
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 |
"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;
"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;
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