diff --git a/R/check_model.R b/R/check_model.R
index 576f483e4..11562a351 100644
--- a/R/check_model.R
+++ b/R/check_model.R
@@ -462,35 +462,35 @@ check_model.DHARMa <- check_model.performance_simres
 
   # multicollinearity --------------
   if (any(c("all", "vif") %in% check)) {
-    dat$VIF <- .diag_vif(model, verbose = verbose)
+    dat$VIF <- .model_diagnostic_vif(model, verbose = verbose)
   }
 
   # Q-Q plot (normality/uniformity of residuals) --------------
   if (any(c("all", "qq") %in% check)) {
     dat$QQ <- switch(residual_type,
       simulated = .safe(simulate_residuals(model, ...)),
-      .diag_qq(model, model_info = model_info, verbose = verbose)
+      .model_diagnostic_qq(model, model_info = model_info, verbose = verbose)
     )
   }
 
   # Random Effects Q-Q plot (normality of BLUPs) --------------
   if (any(c("all", "reqq") %in% check)) {
-    dat$REQQ <- .diag_reqq(model, level = 0.95, model_info = model_info, verbose = verbose)
+    dat$REQQ <- .model_diagnostic_ranef_qq(model, level = 0.95, model_info = model_info, verbose = verbose)
   }
 
   # normal-curve plot (normality of residuals) --------------
   if (any(c("all", "normality") %in% check)) {
-    dat$NORM <- .diag_norm(model, verbose = verbose)
+    dat$NORM <- .model_diagnostic_normality(model, verbose = verbose)
   }
 
   # non-constant variance (heteroskedasticity, liniearity) --------------
   if (any(c("all", "ncv", "linearity") %in% check)) {
-    dat$NCV <- .diag_ncv(model, verbose = verbose)
+    dat$NCV <- .model_diagnostic_ncv(model, verbose = verbose)
   }
 
   # homogeneity of variance --------------
   if (any(c("all", "homogeneity") %in% check)) {
-    dat$HOMOGENEITY <- .diag_homogeneity(model, verbose = verbose)
+    dat$HOMOGENEITY <- .model_diagnostic_homogeneity(model, verbose = verbose)
   }
 
   # outliers --------------
@@ -501,7 +501,7 @@ check_model.DHARMa <- check_model.performance_simres
     } else {
       threshold <- attributes(dat$OUTLIERS)$threshold$cook
     }
-    dat$INFLUENTIAL <- .influential_obs(model, threshold = threshold)
+    dat$INFLUENTIAL <- .safe(.model_diagnostic_outlier(model, threshold = threshold))
   }
 
   # posterior predictive checks --------------
@@ -523,25 +523,25 @@ check_model.DHARMa <- check_model.performance_simres
 
   # multicollinearity --------------
   if (any(c("all", "vif") %in% check)) {
-    dat$VIF <- .diag_vif(model, verbose = verbose)
+    dat$VIF <- .model_diagnostic_vif(model, verbose = verbose)
   }
 
   # Q-Q plot (normality/uniformity of residuals) --------------
   if (any(c("all", "qq") %in% check)) {
     dat$QQ <- switch(residual_type,
       simulated = .safe(simulate_residuals(model, ...)),
-      .diag_qq(model, model_info = model_info, verbose = verbose)
+      .model_diagnostic_qq(model, model_info = model_info, verbose = verbose)
     )
   }
 
   # homogeneity of variance --------------
   if (any(c("all", "homogeneity") %in% check)) {
-    dat$HOMOGENEITY <- .diag_homogeneity(model, verbose = verbose)
+    dat$HOMOGENEITY <- .model_diagnostic_homogeneity(model, verbose = verbose)
   }
 
   # Random Effects Q-Q plot (normality of BLUPs) --------------
   if (any(c("all", "reqq") %in% check)) {
-    dat$REQQ <- .diag_reqq(model, level = 0.95, model_info = model_info, verbose = verbose)
+    dat$REQQ <- .model_diagnostic_ranef_qq(model, level = 0.95, model_info = model_info, verbose = verbose)
   }
 
   # outliers --------------
@@ -552,7 +552,7 @@ check_model.DHARMa <- check_model.performance_simres
     } else {
       threshold <- attributes(dat$OUTLIERS)$threshold$cook
     }
-    dat$INFLUENTIAL <- .influential_obs(model, threshold = threshold)
+    dat$INFLUENTIAL <- .safe(.model_diagnostic_outlier(model, threshold = threshold))
   }
 
   # posterior predictive checks --------------
@@ -567,7 +567,7 @@ check_model.DHARMa <- check_model.performance_simres
 
   # misspecified dispersion and zero-inflation --------------
   if (isTRUE(model_info$is_count) && any(c("all", "overdispersion") %in% check)) {
-    dat$OVERDISPERSION <- .diag_overdispersion(model)
+    dat$OVERDISPERSION <- .model_diagnostic_overdispersion(model)
   }
 
   dat <- insight::compact_list(dat)
diff --git a/R/check_model_diagnostics.R b/R/check_model_diagnostics.R
index 8897c685e..9595ed968 100644
--- a/R/check_model_diagnostics.R
+++ b/R/check_model_diagnostics.R
@@ -1,6 +1,6 @@
 # prepare data for VIF plot ----------------------------------
 
-.diag_vif <- function(model, verbose = TRUE) {
+.model_diagnostic_vif <- function(model, verbose = TRUE) {
   out <- check_collinearity(model, verbose = verbose)
   dat <- insight::compact_list(out)
   if (is.null(dat)) {
@@ -35,7 +35,7 @@
 
 # prepare data for QQ plot ----------------------------------
 
-.diag_qq <- function(model, model_info = NULL, verbose = TRUE) {
+.model_diagnostic_qq <- function(model, model_info = NULL, verbose = TRUE) {
   if (inherits(model, c("lme", "lmerMod", "merMod", "gam"))) {
     res_ <- stats::residuals(model)
   } else if (inherits(model, "geeglm")) {
@@ -98,7 +98,7 @@
 
 # prepare data for random effects QQ plot ----------------------------------
 
-.diag_reqq <- function(model, level = 0.95, model_info = NULL, verbose = TRUE) {
+.model_diagnostic_ranef_qq <- function(model, level = 0.95, model_info = NULL, verbose = TRUE) {
   # check if we have mixed model
   if (is.null(model_info) || !model_info$is_mixed) {
     return(NULL)
@@ -161,7 +161,7 @@
 
 # prepare data for normality of residuals plot ----------------------------------
 
-.diag_norm <- function(model, verbose = TRUE) {
+.model_diagnostic_normality <- function(model, verbose = TRUE) {
   r <- try(as.numeric(stats::residuals(model)), silent = TRUE)
 
   if (inherits(r, "try-error")) {
@@ -181,7 +181,7 @@
 
 # prepare data for influential obs plot ----------------------------------
 
-.diag_influential_obs <- function(model, threshold = NULL) {
+.model_diagnostic_outlier <- function(model, threshold = NULL) {
   s <- summary(model)
 
   if (inherits(model, "lm", which = TRUE) == 1) {
@@ -220,7 +220,7 @@
 
 # prepare data for non-constant variance plot ----------------------------------
 
-.diag_ncv <- function(model, verbose = TRUE) {
+.model_diagnostic_ncv <- function(model, verbose = TRUE) {
   ncv <- tryCatch(
     data.frame(
       x = as.numeric(stats::fitted(model)),
@@ -248,7 +248,7 @@
 
 # prepare data for homogeneity of variance plot ----------------------------------
 
-.diag_homogeneity <- function(model, verbose = TRUE) {
+.model_diagnostic_homogeneity <- function(model, verbose = TRUE) {
   faminfo <- insight::model_info(model)
   r <- tryCatch(
     if (inherits(model, "merMod")) {
@@ -367,7 +367,7 @@
 
 
 
-.diag_overdispersion <- function(model, ...) {
+.model_diagnostic_overdispersion <- function(model, ...) {
   faminfo <- insight::model_info(model)
 
   # data for poisson models
diff --git a/R/check_normality.R b/R/check_normality.R
index 7ea6970ec..ffd4ba824 100644
--- a/R/check_normality.R
+++ b/R/check_normality.R
@@ -231,7 +231,7 @@ check_normality.merMod <- function(x, effects = c("fixed", "random"), ...) {
           p.val <- c(p.val, .check_normality(re[[i]][[j]], x, "random effects"))
         }
       }
-      attr(p.val, "re_qq") <- .diag_reqq(x, level = 0.95, model_info = info)
+      attr(p.val, "re_qq") <- .model_diagnostic_ranef_qq(x, level = 0.95, model_info = info)
       attr(p.val, "type") <- "random effects"
       attr(p.val, "re_groups") <- re_groups
     }
diff --git a/R/check_outliers.R b/R/check_outliers.R
index 071bd39a3..7729f9931 100644
--- a/R/check_outliers.R
+++ b/R/check_outliers.R
@@ -588,7 +588,7 @@ check_outliers.default <- function(x,
   attr(outlier, "threshold") <- thresholds
   attr(outlier, "method") <- method
   attr(outlier, "text_size") <- 3
-  attr(outlier, "influential_obs") <- .influential_obs(x, threshold = unlist(thresholds))
+  attr(outlier, "influential_obs") <- .safe(.model_diagnostic_outlier(x, threshold = unlist(thresholds))) # nolint
   attr(outlier, "variables") <- "(Whole model)"
   attr(outlier, "raw_data") <- my_data
   attr(outlier, "outlier_var") <- outlier_var
@@ -2036,14 +2036,6 @@ check_outliers.DHARMa <- check_outliers.performance_simres
 
 
 
-# influential observations data --------
-
-.influential_obs <- function(x, threshold = NULL) {
-  .safe(.diag_influential_obs(x, threshold = threshold))
-}
-
-
-
 # Non-supported model classes ---------------------------------------
 
 #' @export
diff --git a/R/check_overdispersion.R b/R/check_overdispersion.R
index 0d877b0ad..fc8e25e32 100644
--- a/R/check_overdispersion.R
+++ b/R/check_overdispersion.R
@@ -101,7 +101,7 @@ plot.check_overdisp <- function(x, ...) {
     }
   }
   if (!is.null(model)) {
-    x <- .diag_overdispersion(model)
+    x <- .model_diagnostic_overdispersion(model)
     class(x) <- c("see_check_overdisp", "data.frame")
     attr(x, "colors") <- list(...)$colors
     attr(x, "line_size") <- list(...)$size_line