Info objective

[kaibagley]

Fisher information based objective function, with A and D optimality criterion, and optimises spatially using a user-supplied covariance structure. It is calculated from treatment contrasts, adjusted for nuisance fixed effects like block and intercept.

$$ I = X_1^{\intercal} L X_1 $$

And L removes nuisance effects under a spatial correlation structure from user-supplied $n \times n$ covariance $\Sigma$ and nuisance effects $X_2$

$$ L = \Sigma^{-1} - \Sigma^{-1} X_2 (X_2^{\intercal} \Sigma^{-1} X_2)^{-1} X_2^{\intercal}\Sigma^{-1} $$

With A-optimality $\mathrm{tr}(I^-)$ or contrast-space D-optimality (pseudo determinant since I has rank $\nu - 1$) $-\log \left| I \right|$.

So basically the user specifies the correlation structure they want to use at analysis, such as $AR1 \times AR1$, and the design is optimised to be efficient under that spatial structure. So it should be directly targeting the Cramér-Rao lower bound rather than the adjacency proxy currently used in speed.

[wvjgsuhp]

Thank you for additional objective function.
Please have a look at _pkgdown.yml and see if new functions could be populated where appropriate.
Also, I'd mark helper functions with #' @keywords internal instead of #' @export if they're not expected for users.

[kaibagley]

Thanks, i updated the yaml so the new public functions are in the index. The low level helpers are already @noRd, so they shouldn't be exported, and I left some of the functions like compute_L_projection and others because I thought they might be useful for users who might want to inspect the information objective workflow. But I'm happy to hide them if you want!

[rogerssam]

Hi @kaibagley,
We've done quite a bit of work since you opened this PR. Can I help with updating the current state of the code in this PR and addressing some of the issues raised by Wasin so we can get it merged?

[kaibagley]

Hey, sorry for the delay! I'll get to work on addressing some of these issues now, but please feel free to make any changes you'd like if you need things to move a bit faster. I've been quite busy with PhD stuff recently, sorry!

[kaibagley]

Alright made a couple changes + merged. Please let me know what you think