QAP correlation

Correlation between two matrices, with a test based on the permutation of the nodes (Hubert and Schultz, 1976; Krackhardt, 1987).

Usage

qap_cor(
  A,
  B,
  reps = 1000,
  diag = FALSE,
  method = c("pearson", "spearman", "kendall")
)

Arguments

A

A square matrix

B

A square matrix of the same order

reps

Number of permutations

diag

Whether the diagonal is considered

method

Correlation coefficient: pearson (default), spearman or kendall

Value

This function returns the observed correlation and the proportion of permutations with a correlation greater or equal, lower or equal, and larger in absolute value, than the observed one.

Details

The ties of a network are not independent, so the usual test of a correlation does not apply. The quadratic assignment procedure compares the observed correlation with the correlations obtained after permuting the rows and the columns of one of the matrices at the same time, which keeps its structure while breaking its association with the other matrix.

References

Hubert, L. and Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 29(2), 190–241. doi:10.1111/j.2044-8317.1976.tb00714.x

Krackhardt, D. (1987). QAP partialling as a test of spuriousness. Social Networks, 9(2), 171–186. doi:10.1016/0378-8733(87)90012-8

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0,
  1, 0, 1, 0,
  1, 1, 0, 1,
  0, 0, 1, 0
), byrow = TRUE, ncol = 4)
B <- matrix(c(
  0, 1, 0, 0,
  1, 0, 1, 0,
  0, 1, 0, 1,
  0, 0, 1, 0
), byrow = TRUE, ncol = 4)

set.seed(18051889)
qap_cor(A, B, reps = 100)
#> $correlation
#> [1] 0.7071068
#> 
#> $p_greater
#> [1] 0.22
#> 
#> $p_lower
#> [1] 1
#> 
#> $p_two_sided
#> [1] 0.38
#> 
#> $distribution
#>   [1]  0.0000000  0.0000000  0.0000000  0.7071068  0.7071068  0.0000000
#>   [7]  0.0000000  0.0000000  0.7071068  0.7071068  0.0000000  0.0000000
#>  [13] -0.7071068 -0.7071068 -0.7071068  0.0000000  0.0000000 -0.7071068
#>  [19]  0.0000000  0.7071068 -0.7071068  0.0000000  0.0000000  0.7071068
#>  [25]  0.0000000  0.7071068  0.0000000  0.0000000 -0.7071068  0.0000000
#>  [31] -0.7071068  0.0000000  0.0000000 -0.7071068  0.0000000  0.0000000
#>  [37]  0.0000000  0.0000000  0.7071068  0.0000000  0.0000000 -0.7071068
#>  [43]  0.0000000 -0.7071068 -0.7071068  0.0000000  0.0000000  0.7071068
#>  [49]  0.7071068  0.7071068  0.0000000  0.0000000  0.0000000  0.0000000
#>  [55] -0.7071068  0.0000000  0.7071068  0.7071068  0.7071068  0.0000000
#>  [61]  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.7071068
#>  [67]  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000  0.0000000
#>  [73] -0.7071068  0.7071068  0.0000000  0.7071068  0.0000000  0.0000000
#>  [79]  0.0000000 -0.7071068  0.0000000  0.0000000  0.7071068 -0.7071068
#>  [85]  0.0000000  0.7071068  0.0000000  0.7071068  0.7071068  0.0000000
#>  [91]  0.0000000 -0.7071068  0.0000000  0.0000000  0.0000000  0.7071068
#>  [97]  0.0000000  0.0000000  0.0000000  0.0000000
#>