Support experimental designs

[capnrefsmmat]

Instead of sampling X from the population, fix it according to a design, i.e. a data frame specifying the combinations of predictors to set. Something like this:

design <- some_design_function(...)

pop <- population(
  y = response(x1 + 2 * x2, error_scale = 1)
)

pop |>
  design_x(design) |>
  sample_y()

[capnrefsmmat]

On second thought, for pedagogical purposes, using a design package isn't as good as making students do it themselves.

Say you want a full factorial of x1 and x2. Make students write a full_factorial() function that returns a data frame of values for x1 and x2. Then:

design <- full_factorial(x1 = c("foo", "bar"), x2 = c("ham", "spam"), n_reps = 4)

pop |>
  design_x(design)

yields a population with the chosen x.

Next problem: That doesn't support sampling_distribution(..., fixed_x = FALSE). We would, ideally, allow the regressinator to regenerate designs, so students can see the difference between e.g. variance with the design fixed and variance under repeated resamples from the population.

However, repeated resampling here is conceptually different from in regression. In principle, every person in the population has a potential outcome function. We observe a sample from the population. We then perform our treatment assignment, which effectively takes a sample from the potential outcomes.

We might want to:

• Simulate many treatment assignments in the same population, holding the potential outcomes fixed
• Simulate many samples from the population, with a new treatment assignment each time

How do we make an API for that?