The dimensionality is the number of components the test is measuring.
Usage
Dimensionality(U, na = NULL, Z = NULL, w = NULL)
# Default S3 method
Dimensionality(U, na = NULL, Z = NULL, w = NULL)
# S3 method for class 'binary'
Dimensionality(U, na = NULL, Z = NULL, w = NULL)
# S3 method for class 'rated'
Dimensionality(U, na = NULL, Z = NULL, w = NULL)
# S3 method for class 'ordinal'
Dimensionality(U, na = NULL, Z = NULL, w = NULL)Arguments
- U
Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the
dataFormatfunction.- na
Values to be treated as missing values.
- Z
Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.
- w
Item weight vector specifying the relative importance of each item.
Value
Returns a list of class c("exametrika", "Dimensionality") containing:
- Component
Sequence of component numbers
- Eigenvalue
Eigenvalues of the tetrachoric correlation matrix
- PerOfVar
Percentage of variance explained by each component
- CumOfPer
Cumulative percentage of variance explained
- first_loading
Loadings of the items on the first principal component, \(v_1 \sqrt{\lambda_1}\), named by item. The sign of an eigenvector is arbitrary, so it is oriented to make the loadings sum to a positive value. An item loading with the opposite sign to the rest is a candidate for a reverse-keyed item that has not been recoded.