Fitting all two-way interactions when some scale parameters are shared

[haziqj]

It is impossible to fit the following model

y ~ (x1 + x2) + x3 + x1:x2 + x1:x3 + x2:x3

We can only fit y ~ (x1 + x2) + x3 via non-formula, or assign separate scale parameters for each of the interactions. The reason is that (x1 + x2) is treated as H = H1 + H2 and the individual kernel matrices H1 and H2 are not saved to process the Hadamard interactions.

It is possible to code this to make it work, but need to think of how the user inputs the iprior call. Perhaps need to work on the formula parsing before this can be implemented.

On the bright side, it is not probable that a model would have shared scale parameters and interactions at the same time... Not that I've encountered yet anyway.