This function computes Tau-Equivalent Measurement, also known as Cronbach's alpha coefficient, for a given data set.
Arguments
- x
This should be a data matrix or a Covariance/Phi/Tetrachoric matrix.
- na
This parameter identifies the numbers or characters that should be treated as missing values when 'x' is a data matrix.
- Z
This parameter represents a missing indicator matrix. It is only needed if 'x' is a data matrix.
- w
This parameter is an item weight vector. It is only required if 'x' is a data matrix.
Value
For a correlation/covariance matrix input, returns a single numeric value representing the alpha coefficient. For binary data, returns a list with three components:
- AlphaCov
Alpha coefficient calculated from covariance matrix
- AlphaPhi
Alpha coefficient calculated from phi coefficient matrix
- AlphaTetrachoric
Alpha coefficient calculated from tetrachoric correlation matrix
For ordinal data, returns a list with AlphaCov (from the covariance
matrix of the category scores) and AlphaPolychoric (from the
polychoric correlation matrix, the ordinal alpha of Zumbo et al., 2007).
Rated and nominal data are not supported.
References
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of a test. Psychometrika, 16,297-334.
Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21–29.