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In maximum likelihood estimation, including an additional parameter in the model usually results in a higher likelihood value. It is possible, though, to add an additional parameter that doesn't change the likelihood.

A trivial example would be the model $\mu_i = \theta_1 \theta_2$, where clearly either one of the $\theta_1$ or $\theta_2$ is superfluous.

Is there a technical term for such a parameter, or can I call it simply a redundant parameter?

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  • $\begingroup$ So which one of the parameters $\theta_1,\theta_2$ you want to call a name? What I'm alluding to is in your example you can't just single out one of them. The problem is not in one of the parameters but in the model specification itself $\endgroup$ – Aksakal Apr 29 '17 at 15:35
  • $\begingroup$ @Aksakal Yes, you're right, but you could speak of the model as "having a ____ parameter," without referring to any parameter in particular. $\endgroup$ – Ernest A Apr 29 '17 at 15:44
  • $\begingroup$ The model could be under-identified (other alternatives: just identified and over-identified). I don't know about the parameters, though. $\endgroup$ – Richard Hardy Apr 29 '17 at 18:40
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You would call such a model non-identifiable, or you might call the problematic parameter(s) itself non-identifiable.

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