Compute various measures of internal consistencies
applied to (sub)scales, which items were extracted using
parameters::principal_components() or parameters::factor_analysis().
Arguments
- x
An object of class
parameters_pca, as returned byparameters::principal_components(), of classparameters_efa, as returned byparameters::factor_analysis(), or a data frame.- factor_index
If
xis a data frame,factor_indexmust be specified. It must be a numeric vector of same length as number of columns inx, where each element is the index of the factor to which the respective column inx.- verbose
Toggle warnings and messages. If
TRUE, messages are printed.
Details
check_itemscale() calculates various measures of internal consistencies,
such as Cronbach's alpha, item difficulty or discrimination etc. on subscales
which were built from several items. Subscales are retrieved from the results
of parameters::principal_components() or parameters::factor_analysis(),
i.e. based on how many components were extracted from the PCA, respectively
how many factors were extracted from the factor analysis. 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 is
p+(1-p)/2(which mostly is between 0.5 and 0.8). Seeitem_difficulty()for details.For item discrimination, also known as corrected item-total correlations, acceptable values are 0.20 or higher; the closer to 1.00 the better. See
item_discrimination()for more details. If an item discrimination is negative, the corresponding item probably need to be reverse-coded (which can be done withdatawizard::reverse()).In case the total Cronbach's alpha value is below the acceptable cut-off of 0.7 (mostly if an index has few items), the mean inter-item-correlation is an alternative measure to indicate acceptability. Satisfactory range lies between 0.2 and 0.4. See also
item_intercor().
References
Briggs SR, Cheek JM (1986) The role of factor analysis in the development and evaluation of personality scales. Journal of Personality, 54(1), 106-148. doi: 10.1111/j.1467-6494.1986.tb00391.x
Examples
# data generation from '?prcomp', slightly modified
C <- chol(S <- toeplitz(0.9^(0:15)))
set.seed(17)
X <- matrix(rnorm(1600), 100, 16)
Z <- X %*% C
pca <- parameters::principal_components(
as.data.frame(Z),
rotation = "varimax",
n = 3
)
pca
#> # Rotated loadings from Principal Component Analysis (varimax-rotation)
#>
#> Variable | RC3 | RC1 | RC2 | Complexity | Uniqueness | MSA
#> --------------------------------------------------------------
#> V1 | 0.85 | 0.17 | 0.20 | 1.20 | 0.21 | 0.90
#> V2 | 0.89 | 0.25 | 0.22 | 1.28 | 0.11 | 0.90
#> V3 | 0.91 | 0.26 | 0.17 | 1.23 | 0.07 | 0.89
#> V4 | 0.88 | 0.33 | 0.13 | 1.33 | 0.10 | 0.91
#> V5 | 0.82 | 0.41 | 0.14 | 1.55 | 0.14 | 0.94
#> V6 | 0.68 | 0.59 | 0.18 | 2.12 | 0.15 | 0.92
#> V7 | 0.57 | 0.74 | 0.20 | 2.04 | 0.09 | 0.93
#> V8 | 0.44 | 0.81 | 0.20 | 1.67 | 0.11 | 0.95
#> V9 | 0.33 | 0.84 | 0.32 | 1.61 | 0.09 | 0.93
#> V10 | 0.29 | 0.85 | 0.33 | 1.55 | 0.09 | 0.92
#> V11 | 0.30 | 0.79 | 0.42 | 1.86 | 0.11 | 0.92
#> V12 | 0.27 | 0.68 | 0.57 | 2.28 | 0.15 | 0.90
#> V13 | 0.20 | 0.55 | 0.71 | 2.06 | 0.15 | 0.90
#> V14 | 0.21 | 0.36 | 0.86 | 1.48 | 0.09 | 0.91
#> V15 | 0.20 | 0.23 | 0.91 | 1.23 | 0.08 | 0.88
#> V16 | 0.11 | 0.15 | 0.90 | 1.09 | 0.15 | 0.87
#>
#> The 3 principal components (varimax rotation) accounted for 88.19% of the total variance of the original data (RC3 = 32.81%, RC1 = 31.24%, RC2 = 24.14%).
#>
check_itemscale(pca)
#> # Description of (Sub-)Scales
#> Component 1
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V1 | 0 | -0.02 | 1.06 | -0.49 | -0.01 | 0.80 | 0.96
#> V2 | 0 | -0.05 | 1.05 | -0.29 | -0.02 | 0.90 | 0.95
#> V3 | 0 | 0.00 | 1.10 | -0.77 | 0.00 | 0.94 | 0.95
#> V4 | 0 | 0.00 | 1.10 | -0.82 | 0.00 | 0.92 | 0.95
#> V5 | 0 | -0.07 | 1.09 | -0.29 | -0.02 | 0.90 | 0.95
#> V6 | 0 | -0.04 | 1.13 | -0.27 | -0.01 | 0.83 | 0.96
#>
#> Mean inter-item-correlation = 0.813 Cronbach's alpha = 0.963
#>
#> Component 2
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V7 | 0 | -0.01 | 1.07 | 0.01 | 0.00 | 0.87 | 0.97
#> V8 | 0 | 0.02 | 0.96 | 0.23 | 0.01 | 0.89 | 0.96
#> V9 | 0 | 0.04 | 0.98 | 0.37 | 0.01 | 0.93 | 0.96
#> V10 | 0 | 0.08 | 1.00 | 0.18 | 0.02 | 0.93 | 0.96
#> V11 | 0 | 0.02 | 1.03 | 0.18 | 0.01 | 0.92 | 0.96
#> V12 | 0 | 0.00 | 1.04 | 0.27 | 0.00 | 0.84 | 0.97
#>
#> Mean inter-item-correlation = 0.840 Cronbach's alpha = 0.969
#>
#> Component 3
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V13 | 0 | 0.04 | 0.95 | 0.10 | 0.01 | 0.81 | 0.95
#> V14 | 0 | -0.02 | 0.96 | 0.24 | -0.01 | 0.93 | 0.91
#> V15 | 0 | -0.03 | 0.94 | 0.41 | -0.01 | 0.92 | 0.91
#> V16 | 0 | 0.03 | 0.96 | 0.28 | 0.01 | 0.82 | 0.94
#>
#> Mean inter-item-correlation = 0.811 Cronbach's alpha = 0.945
# as data frame
check_itemscale(
as.data.frame(Z),
factor_index = parameters::closest_component(pca)
)
#> # Description of (Sub-)Scales
#> Component 1
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V1 | 0 | -0.02 | 1.06 | -0.49 | -0.01 | 0.80 | 0.96
#> V2 | 0 | -0.05 | 1.05 | -0.29 | -0.02 | 0.90 | 0.95
#> V3 | 0 | 0.00 | 1.10 | -0.77 | 0.00 | 0.94 | 0.95
#> V4 | 0 | 0.00 | 1.10 | -0.82 | 0.00 | 0.92 | 0.95
#> V5 | 0 | -0.07 | 1.09 | -0.29 | -0.02 | 0.90 | 0.95
#> V6 | 0 | -0.04 | 1.13 | -0.27 | -0.01 | 0.83 | 0.96
#>
#> Mean inter-item-correlation = 0.813 Cronbach's alpha = 0.963
#>
#> Component 2
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V7 | 0 | -0.01 | 1.07 | 0.01 | 0.00 | 0.87 | 0.97
#> V8 | 0 | 0.02 | 0.96 | 0.23 | 0.01 | 0.89 | 0.96
#> V9 | 0 | 0.04 | 0.98 | 0.37 | 0.01 | 0.93 | 0.96
#> V10 | 0 | 0.08 | 1.00 | 0.18 | 0.02 | 0.93 | 0.96
#> V11 | 0 | 0.02 | 1.03 | 0.18 | 0.01 | 0.92 | 0.96
#> V12 | 0 | 0.00 | 1.04 | 0.27 | 0.00 | 0.84 | 0.97
#>
#> Mean inter-item-correlation = 0.840 Cronbach's alpha = 0.969
#>
#> Component 3
#>
#> Item | Missings | Mean | SD | Skewness | Difficulty | Discrimination | alpha if deleted
#> ------------------------------------------------------------------------------------------
#> V13 | 0 | 0.04 | 0.95 | 0.10 | 0.01 | 0.81 | 0.95
#> V14 | 0 | -0.02 | 0.96 | 0.24 | -0.01 | 0.93 | 0.91
#> V15 | 0 | -0.03 | 0.94 | 0.41 | -0.01 | 0.92 | 0.91
#> V16 | 0 | 0.03 | 0.96 | 0.28 | 0.01 | 0.82 | 0.94
#>
#> Mean inter-item-correlation = 0.811 Cronbach's alpha = 0.945