Function for term / parameter-wise deletion

Original thread posted by @bwiernik in https://github.com/easystats/parameters/issues/570#issuecomment-926944548

Current version take a model, re-fits models with term\parameter deletion on the fixed effects, and applies a function(s) to each subset vs the full model.

#' @param m A model
#' @fn A function or list of functions. Each function takes two arguments: the
#'   model and the subset model (in that order).
#' @param by Should subsetting bedone by term or by parameter?
compare_nested <- function(m, fn, by = c("term", "parameter")) {
  by <- match.arg(by)
  if (!is.list(fn)) fn <- list(fn)
  
  mf <- insight::get_data(m)
  m_formula <- insight::find_formula(m)
  mm <- insight::get_modelmatrix(m)
  
  if ("random" %in% names(m_formula)) {
    m_formula[["random"]] <- gsub("~", "", format(m_formula[["random"]]))
  }
  
  if (colnames(mm)[1] == "(Intercept)") {
    colnames(mm)[1] <- "Intercept"
  }
  new_dat <- cbind(mf, mm)
  
  if (by == "term") {
    v_assign <- attr(mm, "assign")
    k_assign <- unique(v_assign)
    subset_formula <- vector("list", length(k_assign))
    
    for (k in seq_along(k_assign)) {
      tmp_formula <- m_formula
      tmp_cond <- stats::update.formula(
        tmp_formula$conditional,
        paste(". ~ 0 +", paste0("`", colnames(mm)[v_assign!=k_assign[k]], "`", collapse = " + "))
      )
      tmp_formula$conditional <- paste(as.character(tmp_cond)[c(2, 1, 3)], collapse = " ")
      subset_formula[k] <- format(tmp_formula)
    }
    
    term_nm <- attr(terms(m_formula$conditional),"term.labels")
    if (colnames(mm)[1] == "Intercept") term_nm <- c("Intercept", term_nm)
    names(subset_formula) <- term_nm
  } else {
    subset_formula <- vector("list", ncol(mm))
    v_pars <- colnames(mm)
    
    for (k in seq_along(v_pars)) {
      tmp_formula <- m_formula
      tmp_cond <- stats::update.formula(
        tmp_formula$conditional,
        paste(". ~ 0 +", paste0("`", v_pars[-k], "`", collapse = " + "))
      )
      tmp_formula$conditional <- paste(as.character(tmp_cond)[c(2, 1, 3)], collapse = " ")
      subset_formula[k] <- format(tmp_formula)
    }
    names(subset_formula) <- v_pars
  }
  
  
  res <- lapply(subset_formula, function(sf) {
    s_mod <- update(m, formula = sf, data = new_dat)
    .out <- lapply(fn, function(.f) .f(m, s_mod))
    if (length(.out)==1L) .out <- .out[[1]]
    .out
  })
  return(res)
}

m2 <- glm(count ~ spp * mined, family = "poisson", data = glmmTMB::Salamanders)
#> Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
#> TMB was built with Matrix version 1.3.3
#> Current Matrix version is 1.3.4
#> Please re-install 'TMB' from source using install.packages('TMB', type = 'source') or ask CRAN for a binary version of 'TMB' matching CRAN's 'Matrix' package

do_LRT <- function(m, sub_m) {
  ll1 <- logLik(m)
  ll2 <- logLik(sub_m)
  
  chisq <- -2 * (ll2[1] - ll1[1])
  df <- attr(ll1, "df") - attr(ll2, "df")
  p <- pchisq(chisq, df, lower.tail = FALSE)
  
  data.frame(chisq, df, p)
}

do_spR2 <- function(m, sub_m) {
  data.frame(
    spR2 = performance::r2(m)[[1]] - performance::r2(sub_m)[[1]]  
  )
}


(term_res <- compare_nested(m2, list(LRT = do_LRT, spR2 = do_spR2)))
#> $Intercept
#> $Intercept$LRT
#>      chisq df           p
#> 1 71.63583  1 2.58814e-17
#> 
#> $Intercept$spR2
#>                        spR2
#> Nagelkerke's R2 0.007306225
#> 
#> 
#> $spp
#> $spp$LRT
#>     chisq df            p
#> 1 49.6665  6 5.483212e-09
#> 
#> $spp$spR2
#>                         spR2
#> Nagelkerke's R2 -0.002198223
#> 
#> 
#> $mined
#> $mined$LRT
#>      chisq df            p
#> 1 120.9563  1 3.906445e-28
#> 
#> $mined$spR2
#>                       spR2
#> Nagelkerke's R2 0.02986212
#> 
#> 
#> $`spp:mined`
#> $`spp:mined`$LRT
#>      chisq df            p
#> 1 34.55771  6 5.248732e-06
#> 
#> $`spp:mined`$spR2
#>                         spR2
#> Nagelkerke's R2 -0.008548994

term_res |>
  lapply(do.call, what = cbind) |>
  do.call(what = rbind)
#>           LRT.chisq LRT.df        LRT.p         spR2
#> Intercept  71.63583      1 2.588140e-17  0.007306225
#> spp        49.66650      6 5.483212e-09 -0.002198223
#> mined     120.95629      1 3.906445e-28  0.029862123
#> spp:mined  34.55771      6 5.248732e-06 -0.008548994

^{Created on 2021-09-26 by the reprex package (v2.0.1)}

Start with the compare_nested prototype and examples in this issue, including its term- and parameter-wise deletion paths. Determine where this functionality belongs in the parameters package, then verify that it can refit the reduced models and apply one or more supplied functions while preserving the demonstrated result structure.