I am trying to work on a Dirichlet regression problem where I look at three true proportions the first two are actually measured while the third is computed as the complement:
The issue that I have is that $p_1$ and $p_2$ are measured with error and hence $p_3$ will sometimes be negative i.e. when $p_1+p_2>1$.
Is there any way to “correct” for this problem? I know there might be a way to do this with a Bayesian approach where you model the measurement error. But I would rather look at a simpler approach such as a proper way to normalise the data.