3
$\begingroup$

I'm currently performing the following analysis :

  1. Computing $r_j(Y_{ij}, X_{ij})$ for each design cell (factor with level 1 or 0 for each unit)

  2. Estimating effect of factor on $r(Y,X)$ with a linear model :
    $r_j(Y,X) \sim \mathcal{N}(\mu, \sigma) $
    where
    $\mu = \alpha + \mathbf{\beta} \mathbf{X}$ with $\mathbf{X} = \matrix{1, 0}$
    Additionally I include random effects but for the sake of simplicity I don't write it down.

My question is whether one can build an integrated model simultaneously computing the correlation (preserving its uncertainty) and test for the effect of the factor. I have guessed the following but I can't find any relevant literature to back up my thought :

$\mathbf{Y} \sim \mathcal{MVN}(\mathbf{M}, \Sigma)$ with $\mathbf{Y} = \matrix{X, Y} $
where
$\mathbf{M} = \mathbf{A} + \mathbf{B} \mathbf{X}$ with $\mathbf{A}$ and $\mathbf{B}$ being vectors of corresponding parameters for $X$ and $Y$
and $\Sigma = \pmatrix{\sigma_X & \sigma_X \sigma_Y \rho \\ \sigma_X \sigma_Y \rho & \sigma_Y}$ where (at least) $\rho \sim \alpha + \mathbf{\beta} \mathbf{X}$

I would like to make inferences for $\mathbf{A}$, $\mathbf{B}$ and $\rho$ in the same model. Naively the logic seems OK but I guess that I might miss some assumptions or other potential source of problems by building such a model.

New contributor
S-Oxyde is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
$\endgroup$

Your Answer

S-Oxyde is a new contributor. Be nice, and check out our Code of Conduct.

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.