congru {multiway} | R Documentation |
Tucker's Congruence Coefficient
Description
Calculates Tucker's congruence coefficient (uncentered correlation) between x
and y
if these are vectors. If x
and y
are matrices then the congruence between the columns of x
and y
are computed.
Usage
congru(x, y = NULL)
Arguments
x |
Numeric vector, matrix or data frame. |
y |
NULL (default) or a vector, matrix or data frame with compatible dimensions to |
Details
Tucker's congruence coefficient is defined as
r = \frac{\sum_{i=1}^{n}x_{i}y_{i}}{ \sqrt{\sum_{i=1}^{n}x_{i}^{2}\sum_{i=1}^{n}y_{i}^{2}} }
where x_{i}
and y_{i}
denote the i
-th elements of x
and y
.
Value
Returns a scalar or matrix with congruence coefficient(s).
Note
If x
is a vector, you must also enter y
.
Author(s)
Nathaniel E. Helwig <helwig@umn.edu>
References
Tucker, L.R. (1951). A method for synthesis of factor analysis studies (Personnel Research Section Report No. 984). Washington, DC: Department of the Army.
Examples
########## EXAMPLE 1 ##########
set.seed(1)
A <- rnorm(100)
B <- rnorm(100)
C <- A*5
D <- A*(-0.5)
congru(A,B)
congru(A,C)
congru(A,D)
########## EXAMPLE 2 ##########
set.seed(1)
A <- cbind(rnorm(20),rnorm(20))
B <- cbind(A[,1]*-0.5,rnorm(20))
congru(A)
congru(A,B)