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 by`parameters::principal_components()`

.

## 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). See`item_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

Trochim WMK (2008) Types of Reliability. (web)

## Examples

```
# data generation from '?prcomp', slightly modified
C <- chol(S <- toeplitz(.9^(0:15)))
set.seed(17)
X <- matrix(rnorm(1600), 100, 16)
Z <- X %*% C
if (require("parameters") && require("psych")) {
pca <- principal_components(as.data.frame(Z), rotation = "varimax", n = 3)
pca
check_itemscale(pca)
}
#> Loading required package: psych
#>
#> Attaching package: ‘psych’
#> The following object is masked from ‘package:randomForest’:
#>
#> outlier
#> # Description of (Sub-)ScalesComponent 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 | -0.03 | 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 | 0.03 | 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 | 0.02 | 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
```