Draft McDonald's Omega

NAMESPACE

@@ -139,6 +139,9 @@ S3method(logLik,iv_robust)
 S3method(logLik,ivreg)
 S3method(logLik,plm)
 S3method(logLik,svycoxph)
+S3method(mcdonalds_omega,data.frame)
+S3method(mcdonalds_omega,matrix)
+S3method(mcdonalds_omega,parameters_pca)
 S3method(model_performance,Arima)
 S3method(model_performance,BFBayesFactor)
 S3method(model_performance,DirichletRegModel)
@@ -294,6 +297,7 @@ S3method(print,icc_decomposed)
 S3method(print,item_difficulty)
 S3method(print,item_discrimination)
 S3method(print,looic)
+S3method(print,mcdonalds_omega)
 S3method(print,performance_accuracy)
 S3method(print,performance_cv)
 S3method(print,performance_hosmer)
@@ -547,6 +551,7 @@ export(item_reliability)
 export(item_split_half)
 export(looic)
 export(mae)
+export(mcdonalds_omega)
 export(model_performance)
 export(mse)
 export(multicollinearity)

NEWS.md

@@ -1,5 +1,9 @@
 # performance 0.10.9
 
+## New functions
+
+* `mcdonalds_omega()` to calculate McDonald's Omega for a scale.
+
 ## Changes
 
 * `r2()` for models of class `glmmTMB` without random effects now returns the
@@ -12,6 +16,11 @@
 
 * `check_itemscale()` gets a `print_html()` method.
 
+* `check_itemscale()` and `item_reliability()` gain a `type` argument, to
+  specify the type of reliability to be computed. The default is `"alpha"`,
+  which computes Cronbach's alpha, the other option is `"omega"` (McDonald's
+  Omega).
+
 * Clarification in the documentation of the `estimator` argument for
   `performance_aic()`.
 

R/check_itemscale.R

@@ -10,19 +10,19 @@
 #' @param factor_index If `x` is a data frame, `factor_index` must be specified.
 #' It must be a numeric vector of same length as number of columns in `x`, where
 #' each element is the index of the factor to which the respective column in `x`.
+#' @inheritParams item_reliability
 #'
 #' @return A list of data frames, with related measures of internal
 #'   consistencies of each subscale.
 #'
 #' @details
-#'
-#' `check_itemscale()` calculates various measures of internal
-#' consistencies, such as Cronbach's alpha, item difficulty or discrimination
+#' `check_itemscale()` calculates various measures of internal consistencies,
+#' such as Cronbach's Alpha (or McDonald's Omega), item difficulty or discrimination
 #' etc. on subscales which were built from several items. Subscales are
 #' retrieved from the results of [`parameters::principal_components()`], i.e.
-#' based on how many components were extracted from the PCA,
-#' `check_itemscale()` retrieves those variables that belong to a component
-#' and calculates the above mentioned measures.
+#' based on how many components were extracted from the PCA, `check_itemscale()`
+#' retrieves those variables that belong to a component and calculates the above
+#' mentioned measures.
 #'
 #' @note
 #' - *Item difficulty* should range between 0.2 and 0.8. Ideal value
@@ -65,7 +65,7 @@
 #'   factor_index = parameters::closest_component(pca)
 #' )
 #' @export
-check_itemscale <- function(x, factor_index = NULL) {
+check_itemscale <- function(x, factor_index = NULL, type = "alpha") {
   # check for valid input
   if (!inherits(x, c("parameters_pca", "data.frame"))) {
     insight::format_error(
@@ -89,6 +89,9 @@
     }
   }
 
+  # alpha or omega?
+  type <- match.arg(type, c("alpha", "omega"))
+
   # assign data and factor index
   if (inherits(x, "parameters_pca")) {
     insight::check_if_installed("parameters")
@@ -102,12 +105,15 @@
   out <- lapply(sort(unique(subscales)), function(.subscale) {
     columns <- names(subscales)[subscales == .subscale]
     items <- dataset[columns]
-    reliability <- item_reliability(items)
+    reliability <- item_reliability(items, type = type)
 
     .item_discr <- reliability$item_discrimination
     if (is.null(.item_discr)) .item_discr <- NA
-    .item_alpha <- reliability$alpha_if_deleted
-    if (is.null(.item_alpha)) .item_alpha <- NA
+    .item_rel_estimate <- switch(type,
+      alpha = reliability$alpha_if_deleted,
+      omega = reliability$omega_if_deleted
+    )
+    if (is.null(.item_rel_estimate)) .item_rel_estimate <- NA
 
     s_out <- data.frame(
       Item = columns,
@@ -117,13 +123,22 @@
       Skewness = vapply(items, function(i) as.numeric(datawizard::skewness(i)), numeric(1)),
       Difficulty = item_difficulty(items)$Difficulty,
       Discrimination = .item_discr,
-      `alpha if deleted` = .item_alpha,
+      reliability_if_deleted = .item_rel_estimate,
       stringsAsFactors = FALSE,
       check.names = FALSE
     )
 
+    # fix column name
+    colnames(s_out)[8] <- switch(type,
+      alpha = "alpha if deleted",
+      omega = "omega if deleted"
+    )
+
     attr(s_out, "item_intercorrelation") <- item_intercor(items)
     attr(s_out, "cronbachs_alpha") <- cronbachs_alpha(items)
+    if (type == "omega") {
+      attr(s_out, "mcdonalds_omega") <- mcdonalds_omega(items, ci = NULL)
+    }
 
     s_out
   })
@@ -144,31 +159,43 @@
     lapply(seq_along(x), function(i) {
       out <- x[[i]]
       attr(out, "table_caption") <- c(sprintf("\nComponent %i", i), "red")
+      if (!is.null(attributes(out)$mcdonalds_omega)) {
+        omega <- sprintf("  McDonald's omega = %.3f", attributes(out)$mcdonalds_omega)
+      } else {
+        omega <- ""
+      }
       attr(out, "table_footer") <- c(sprintf(
-        "\nMean inter-item-correlation = %.3f  Cronbach's alpha = %.3f",
+        "\nMean inter-item-correlation = %.3f  Cronbach's alpha = %.3f%s",
         attributes(out)$item_intercorrelation,
-        attributes(out)$cronbachs_alpha
+        attributes(out)$cronbachs_alpha,
+        omega
       ), "yellow")
-
       out
     }),
     digits = digits,
     format = "text",
     missing = "<NA>",
     zap_small = TRUE
   ))
+  cat("\n")
 }
 
 
 #' @export
 print_html.check_itemscale <- function(x, digits = 2, ...) {
   x <- lapply(seq_along(x), function(i) {
     out <- x[[i]]
+    if (!is.null(attributes(out)$mcdonalds_omega)) {
+      omega <- sprintf(", McDonald's omega = %.3f", attributes(out)$mcdonalds_omega)
+    } else {
+      omega <- ""
+    }
     attr(out, "table_caption") <- sprintf(
-      "Component %i: Mean inter-item-correlation = %.3f, Cronbach's alpha = %.3f",
+      "Component %i: Mean inter-item-correlation = %.3f, Cronbach's alpha = %.3f%s",
       i,
       attributes(out)$item_intercorrelation,
-      attributes(out)$cronbachs_alpha
+      attributes(out)$cronbachs_alpha,
+      omega
     )
     out
   })

R/cronbachs_alpha.R

@@ -4,7 +4,8 @@
 #' @description Compute various measures of internal consistencies
 #'    for tests or item-scales of questionnaires.
 #'
-#' @param x A matrix or a data frame.
+#' @param x A matrix or a data frame, or an object returned by
+#' `[parameters::principal_components()]`.
 #' @param ... Currently not used.
 #'
 #' @return The Cronbach's Alpha value for `x`.
@@ -50,14 +51,12 @@ cronbachs_alpha.data.frame <- function(x, verbose = TRUE, ...) {
 }
 
 
-
 #' @export
 cronbachs_alpha.matrix <- function(x, verbose = TRUE, ...) {
   cronbachs_alpha(as.data.frame(x), verbose = verbose, ...)
 }
 
 
-
 #' @export
 cronbachs_alpha.parameters_pca <- function(x, verbose = TRUE, ...) {
   # fetch data used for the PCA

R/item_reliability.R

@@ -5,21 +5,25 @@
 #'    for tests or item-scales of questionnaires.
 #'
 #' @param x A matrix or a data frame.
+#' @param type Type of reliability estimate. Either `"alpha"` (default, see
+#' [`cronbachs_alpha()`]) or `"omega"` (see [`mcdonalds_omega()`]). Note that
+#' computing McDonald's Omega is more computationally intensive than Cronbach's
+#' Alpha.
 #' @param standardize Logical, if `TRUE`, the data frame's vectors will be
 #'   standardized. Recommended when the variables have different measures /
 #'   scales.
 #' @param digits Amount of digits for returned values.
 #'
 #' @return A data frame with the corrected item-total correlations (*item
-#'      discrimination*, column `item_discrimination`) and Cronbach's Alpha
-#'      (if item deleted, column `alpha_if_deleted`) for each item
-#'      of the scale, or `NULL` if data frame had too less columns.
+#' discrimination*, column `item_discrimination`) and Cronbach's Alpha
+#' (if item deleted, column `alpha_if_deleted`) resp. McDonald's Omega for each
+#' item of the scale, or `NULL` if data frame had too few columns.
 #'
 #' @details
-#'
 #' This function calculates the item discriminations (corrected item-total
 #' correlations for each item of `x` with the remaining items) and the
-#' Cronbach's alpha for each item, if it was deleted from the scale. The
+#' Cronbach's alpha (when `type = "alpha"`) resp. McDonald's Omega (when
+#' `type = "omega"`) for each item, if it was deleted from the scale. The
 #' absolute value of the item discrimination indices should be above 0.2. An
 #' index between 0.2 and 0.4 is considered as "fair", while an index above 0.4
 #' (or below -0.4) is "good". The range of satisfactory values is from 0.4 to
@@ -28,18 +32,23 @@
 #' determine why a negative value was obtained (e.g. reversed answer categories
 #' regarding positive and negative poles).
 #'
-#' @examples
+#' @examplesIf requireNamespace("lavaan", quietly = TRUE)
 #' data(mtcars)
-#' x <- mtcars[, c("cyl", "gear", "carb", "hp")]
-#' item_reliability(x)
+#' item_reliability(mtcars[, c("cyl", "gear", "carb", "hp")])
+#'
+#' data(iris)
+#' item_reliability(iris[1:4], type = "omega")
 #' @export
-item_reliability <- function(x, standardize = FALSE, digits = 3) {
+item_reliability <- function(x, type = "alpha", standardize = FALSE, digits = 3) {
   # check param
   if (!is.matrix(x) && !is.data.frame(x)) {
     insight::format_alert("`x` needs to be a data frame or matrix.")
     return(NULL)
   }
 
+  # alpha or omega?
+  type <- match.arg(type, c("alpha", "omega"))
+
   # remove missings, so correlation works
   x <- stats::na.omit(x)
 
@@ -58,20 +67,33 @@ item_reliability <- function(x, standardize = FALSE, digits = 3) {
     # when items have different measures / scales
     if (standardize) x <- .std(x)
 
-    # calculate cronbach-if-deleted
-    cronbachDeleted <- vapply(seq_len(ncol(x)), function(i) cronbachs_alpha(x[, -i]), numeric(1L))
-
     # calculate corrected total-item correlation
     totalCorr <- vapply(seq_len(ncol(x)), function(i) {
       stats::cor(x[, i], rowSums(x[, -i]), use = "pairwise.complete.obs")
     }, numeric(1L))
 
-    ret.df <- data.frame(
-      term = df.names,
-      alpha_if_deleted = round(cronbachDeleted, digits),
-      item_discrimination = round(totalCorr, digits),
-      stringsAsFactors = FALSE
-    )
+    # reliability estimate alpha or omega?
+    if (type == "alpha") {
+      # calculate cronbach-if-deleted
+      cronbachDeleted <- vapply(seq_len(ncol(x)), function(i) cronbachs_alpha(x[, -i]), numeric(1L))
+
+      ret.df <- data.frame(
+        term = df.names,
+        alpha_if_deleted = round(cronbachDeleted, digits),
+        item_discrimination = round(totalCorr, digits),
+        stringsAsFactors = FALSE
+      )
+    } else {
+      # calculate omega-if-deleted
+      omegaDeleted <- vapply(seq_len(ncol(x)), function(i) mcdonalds_omega(x[, -i], ci = NULL), numeric(1L))
+
+      ret.df <- data.frame(
+        term = df.names,
+        omega_if_deleted = round(omegaDeleted, digits),
+        item_discrimination = round(totalCorr, digits),
+        stringsAsFactors = FALSE
+      )
+    }
   } else {
     insight::format_warning("Data frame needs at least three columns for reliability-test.")
   }