diff --git a/R/binned_residuals.R b/R/binned_residuals.R
index 7d9ec9803..d7461c8c7 100644
--- a/R/binned_residuals.R
+++ b/R/binned_residuals.R
@@ -13,9 +13,15 @@
 #'   taken.
 #' @param ci Numeric, the confidence level for the error bounds.
 #' @param ci_type Character, the type of error bounds to calculate. Can be
-#'   `"gaussian"` (default), `"exact"` or `"boot"`.
+#'   `"exact"` (default), `"gaussian"` or `"boot"`. `"exact"` calculates the
+#'   error bounds based on the exact binomial distribution, using [`binom.test()`].
+#'   `"gaussian"` uses the Gaussian approximation, while `"boot"` uses a simple
+#'   bootstrap method, where confidence intervals are calculated based on the
+#'   quantiles of the bootstrap distribution.
 #' @param residuals Character, the type of residuals to calculate. Can be
-#'   `"response"` (default), `"pearson"` or `"deviance"`.
+#'   `"deviance"` (default), `"pearson"` or `"response"`. It is recommended to
+#'   use `"response"` only for those models where other residuals are not
+#'   available.
 #' @param iterations Integer, the number of iterations to use for the
 #'   bootstrap method. Only used if `ci_type = "boot"`.
 #' @param show_dots Logical, if `TRUE`, will show data points in the plot. Set
@@ -74,8 +80,8 @@ binned_residuals <- function(model,
                              n_bins = NULL,
                              show_dots = NULL,
                              ci = 0.95,
-                             ci_type = c("gaussian", "exact", "boot"),
-                             residuals = c("response", "pearson", "deviance"),
+                             ci_type = c("exact", "gaussian", "boot"),
+                             residuals = c("deviance", "pearson", "response"),
                              iterations = 1000,
                              ...) {
   # match arguments
@@ -106,6 +112,11 @@ binned_residuals <- function(model,
     deviance = .safe(stats::residuals(model, type = "deviance"))
   )
 
+  # make sure we really have residuals
+  if (is.null(y)) {
+    insight::format_error("Could not calculate residuals. Try using `residuals = \"response\"`.")
+  }
+
   if (is.null(n_bins)) n_bins <- round(sqrt(length(pred)))
 
   breaks.index <- floor(length(pred) * (1:(n_bins - 1)) / n_bins)
@@ -124,7 +135,7 @@ binned_residuals <- function(model,
     r <- switch(ci_type,
       gaussian = stats::qnorm(c((1 - ci) / 2, (1 + ci) / 2), mean = ybar, sd = sdev / sqrt(n)),
       exact = {
-        out <- stats:::binom.test(sum(y0[items]), n)$conf.int
+        out <- stats::binom.test(sum(y0[items]), n)$conf.int
         out <- out - (min(out) - ybar) - (diff(out) / 2)
         out
       },
@@ -138,8 +149,7 @@ binned_residuals <- function(model,
       n = n,
       x.lo = model.range[1],
       x.hi = model.range[2],
-      se = stats::qnorm((1 + ci) / 2) * sdev / sqrt(n),
-      ci_range = sdev / sqrt(n)
+      se = stats::qnorm((1 + ci) / 2) * sdev / sqrt(n)
     )
     cbind(d0, rbind(r))
   }))
diff --git a/R/check_model.R b/R/check_model.R
index bbf6c6a84..5e7567d7f 100644
--- a/R/check_model.R
+++ b/R/check_model.R
@@ -35,7 +35,8 @@
 #'   tries to guess whether performance will be poor due to a very large model
 #'   and thus automatically shows or hides dots.
 #' @param verbose If `FALSE` (default), suppress most warning messages.
-#' @param ... Currently not used.
+#' @param ... Arguments passed down to the individual check functions, especially
+#'   to `check_predictions()` and `binned_residuals()`.
 #' @inheritParams check_predictions
 #'
 #' @return The data frame that is used for plotting.
@@ -185,11 +186,11 @@ check_model.default <- function(x,
   ca <- tryCatch(
     {
       if (minfo$is_bayesian) {
-        suppressWarnings(.check_assumptions_stan(x))
+        suppressWarnings(.check_assumptions_stan(x, ...))
       } else if (minfo$is_linear) {
-        suppressWarnings(.check_assumptions_linear(x, minfo, verbose))
+        suppressWarnings(.check_assumptions_linear(x, minfo, verbose, ...))
       } else {
-        suppressWarnings(.check_assumptions_glm(x, minfo, verbose))
+        suppressWarnings(.check_assumptions_glm(x, minfo, verbose, ...))
       }
     },
     error = function(e) {
@@ -346,7 +347,7 @@ check_model.model_fit <- function(x,
     threshold <- NULL
   }
   dat$INFLUENTIAL <- .influential_obs(model, threshold = threshold)
-  dat$PP_CHECK <- .safe(check_predictions(model))
+  dat$PP_CHECK <- .safe(check_predictions(model, ...))
 
   dat <- insight::compact_list(dat)
   class(dat) <- c("check_model", "see_check_model")
@@ -357,7 +358,7 @@ check_model.model_fit <- function(x,
 
 # compile plots for checks of generalized linear models  ------------------------
 
-.check_assumptions_glm <- function(model, model_info, verbose = TRUE) {
+.check_assumptions_glm <- function(model, model_info, verbose = TRUE, ...) {
   dat <- list()
 
   dat$VIF <- .diag_vif(model, verbose = verbose)
@@ -371,9 +372,9 @@ check_model.model_fit <- function(x,
     threshold <- NULL
   }
   dat$INFLUENTIAL <- .influential_obs(model, threshold = threshold)
-  dat$PP_CHECK <- .safe(check_predictions(model))
+  dat$PP_CHECK <- .safe(check_predictions(model, ...))
   if (isTRUE(model_info$is_binomial)) {
-    dat$BINNED_RESID <- binned_residuals(model)
+    dat$BINNED_RESID <- binned_residuals(model, ...)
   }
   if (isTRUE(model_info$is_count)) {
     dat$OVERDISPERSION <- .diag_overdispersion(model)
diff --git a/man/binned_residuals.Rd b/man/binned_residuals.Rd
index b913ec53a..33e710f11 100644
--- a/man/binned_residuals.Rd
+++ b/man/binned_residuals.Rd
@@ -10,8 +10,8 @@ binned_residuals(
   n_bins = NULL,
   show_dots = NULL,
   ci = 0.95,
-  ci_type = c("gaussian", "exact", "boot"),
-  residuals = c("response", "pearson", "deviance"),
+  ci_type = c("exact", "gaussian", "boot"),
+  residuals = c("deviance", "pearson", "response"),
   iterations = 1000,
   ...
 )
@@ -37,10 +37,16 @@ and thus automatically shows or hides dots.}
 \item{ci}{Numeric, the confidence level for the error bounds.}
 
 \item{ci_type}{Character, the type of error bounds to calculate. Can be
-\code{"gaussian"} (default), \code{"exact"} or \code{"boot"}.}
+\code{"exact"} (default), \code{"gaussian"} or \code{"boot"}. \code{"exact"} calculates the
+error bounds based on the exact binomial distribution, using \code{\link[=binom.test]{binom.test()}}.
+\code{"gaussian"} uses the Gaussian approximation, while \code{"boot"} uses a simple
+bootstrap method, where confidence intervals are calculated based on the
+quantiles of the bootstrap distribution.}
 
 \item{residuals}{Character, the type of residuals to calculate. Can be
-\code{"response"} (default), \code{"pearson"} or \code{"deviance"}.}
+\code{"deviance"} (default), \code{"pearson"} or \code{"response"}. It is recommended to
+use \code{"response"} only for those models where other residuals are not
+available.}
 
 \item{iterations}{Integer, the number of iterations to use for the
 bootstrap method. Only used if \code{ci_type = "boot"}.}
diff --git a/man/check_model.Rd b/man/check_model.Rd
index 2bf82af92..d5ead9420 100644
--- a/man/check_model.Rd
+++ b/man/check_model.Rd
@@ -28,7 +28,8 @@ check_model(x, ...)
 \arguments{
 \item{x}{A model object.}
 
-\item{...}{Currently not used.}
+\item{...}{Arguments passed down to the individual check functions, especially
+to \code{check_predictions()} and \code{binned_residuals()}.}
 
 \item{dot_size, line_size}{Size of line and dot-geoms.}