congru: Tucker's Congruence Coefficient
In multiway: Component Models for Multi-Way Data

Description Usage Arguments Details Value Note Author(s) References Examples

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.

1	congru(x, y = NULL)

`x`	Numeric vector, matrix or data frame.
`y`	NULL (default) or a vector, matrix or data frame with compatible dimensions to `x`. The default is equivalent to `y = x` (but more efficient).

Tucker's congruence coefficient is defined as

r = \frac{∑_{i=1}^{n}x_{i}y_{i}}{ √{∑_{i=1}^{n}x_{i}^{2}∑_{i=1}^{n}y_{i}^{2}} }

where x_{i} and y_{i} denote the i-th elements of x and y.

Returns a scalar or matrix with congruence coefficient(s).

If x is a vector, you must also enter y.

Nathaniel E. Helwig <helwig@umn.edu>

Tucker, L.R. (1951). A method for synthesis of factor analysis studies (Personnel Research Section Report No. 984). Washington, DC: Department of the Army.

##########   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)