Restrictions when using Likelihood Ratio test

[Ahmed Sappa]

I am using a random effects (panel data) ordered probit model in the form: Y = X1 X2 X3 D1 D2 D3 D5 where D1, D2, D3, D4 and D5 are binary, mutually exclusive dummy variables with D4 as the "base"/"reference" category to avoid a dummy variable trap. I want to test the joint significance of the dummy variables by conducting a likelihood-ratio test between the following models:

Y = X1 X2 X3 D1 D2 D3 D5
Y = X1 X2 X3

My question here is there 4 or 5 restrictions in the likelihood-ratio test? As although I am imposing restrictions on the 4 included dummy variables by setting them equal to zero, is the base category variable D4 not being restricted to a value of zero too?

Thanks for any help.

[Joseph Coveney]

. . . is the base category variable D4 not being restricted to a value of zero too?

It is indeed being constrained to zero in the restricted model.

But it was already being constrained to zero in the unrestricted model. So, you have only four additional constraints, hence four degrees of freedom in the likelihood-ratio test.

[Ahmed Sappa]

Ah okay, thank you for your help!