SSCP: Get diagonality (bartlett)...

Tests the hypothesis that the selected SSCP matrix object is diagonal.

Setting

Number of constraints
modifies the number of independent observations. The default value is 1.

Algorithm

The test statistic is |R|N/2, the N/2-th power of the determinant of the correlation matrix. Bartlett (1954) developed the following approximation to the limiting distribution:

χ2 = -(N - numberOfConstraints - (2p + 5) /6) ln |R|

In the formula's above, p is the dimension of the correlation matrix, N-numberOfConstraints is the number of independent observations. Normally numberOfConstraints would equal 1, however, if the matrix has been computed in some other way, e.g., from within-group sums of squares and cross-products of k independent groups, numberOfConstraints would equal k.

We return the probability α as

α = chiSquareQ (χ2 , p(p-1)/2).

A very low α indicates that it is very improbable that the matrix is diagonal.

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© djmw, November 11, 2001