find_ (get_?) algorithm

Although the fitting algorithm plays an important role, it is often unreported/uncared about. Surprisingly, its access is not really straightforward.

What do you think about a function that does that?

Here's a draft:

#' @export
find_algorithm <- function(model, ...) {
  UseMethod("find_algorithm")
}


#' @export
find_algorithm.merMod <- function(model) {
  if(model@resp$REML == 0){
    algorithm <- "ML"
  } else{
    algorithm <- "REML"
  }

  out <- list(
    "algorithm" = algorithm,
    "optimizer" = as.character(model@optinfo$optimizer)
  )

  return(out)
  }



#' @export
find_algorithm.stanreg <- function(model) {

  info <- model$stanfit@sim

  out <- list(
    "algorithm" = model$algorithm,
    "chains" = info$chains,
    "iterations" = info$iter,
    "warmup" = info$warmup
  )

  return(out)
}

Start from the proposed find_algorithm generic and its merMod and stanreg methods in the issue body. Check how these model classes expose fitting and sampling details; done means a documented function consistently reports the requested algorithm information for the supported classes, with tests covering the results.