Compute various measures of internal consistencies
applied to (sub)scales, which items were extracted using
parameters::principal_components().
Arguments
- x
An object of class
parameters_pca, as returned byparameters::principal_components(), 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.
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(), 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.
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, acceptable values are 0.20 or higher; the closer to 1.00 the better. See
item_reliability()for more details.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