I want to know how we can refer to the parameters of a model that was constrained to be equal to another parameter of this model.
For example: Consider a parametric model (wiki definition) $\mathcal{P}_{\mathbf{\theta}} = \{f_\mathbf{\theta} | \mathbf{\theta} \in \Theta\}$ ,where $ \mathbf{\theta} = (\theta_1, \theta_2, \theta_3, \theta_4)$, $\Theta = \mathbb{R}^4$ and $f_\mathbf{\theta}$ is a probability density function (pdf) with parameter $\mathbf{\theta}$.
Now consider that we have a model $\mathcal{M}_{\mathbf{\theta}'}$ with the same pdf of $\mathcal{P}$, except for the fact that the parameters of $\mathcal{M}$ are constrained such that $\theta'_1 = \theta'_2$.
In this case, how do we call the variable $\theta'_2$ ?
Notes:
It seems to me that it is not correct to call $\theta'_2$ as a parameter.
I know that, in this case, I could rewrite the model $\mathcal{M}$ as $\mathcal{M}_{\mathbf{\lambda}'} = \{g_\mathbf{\lambda} | \mathbf{\lambda} \in \mathbb{R}^3\}$, where $\mathbf{\lambda} = (\lambda_1, \lambda_2,\lambda_3)$ and $g_\mathbf{\lambda} \equiv p_{(\lambda_1,\lambda_1, \lambda_2,\lambda_3)}$. But in this specific case, I don't want to remove any original variables due to the convenience of notation for my specific problem.
I can provide more details of the model in question if someone feels it is necessary.