QAP regression — qap

Regression between matrices, with a test based on the permutation of the nodes (Krackhardt, 1988; Dekker, Krackhardt and Snijders, 2007).

Usage

qap_lm(
  Y,
  X,
  reps = 1000,
  family = c("gaussian", "binomial"),
  method = c("dsp", "y"),
  diag = FALSE
)

Arguments

Y: A square matrix with the dependent relation
X: A list of square matrices with the independent relations
reps: Number of permutations
family: gaussian for a linear regression (default) or binomial for a logistic regression
method: Whether to permute the dependent matrix (y) or the residuals of each predictor (dsp, default)
diag: Whether the diagonal is considered

Value

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

Details

The coefficients are those of an ordinary regression (or a logistic regression when family = "binomial") of the ties of Y on the ties of the matrices in X. As the ties are not independent, the standard errors of the regression do not apply, and the coefficients are compared with the ones obtained after permuting the nodes.

With method = "y" the rows and columns of Y are permuted. With method = "dsp" (default) the double semi-partialling of Dekker et al. (2007) is used: each predictor is regressed on the other predictors, and the residuals of that regression are permuted, which behaves better when the predictors are correlated with each other. The intercept is not permuted by the double semi-partialling, so its p-values are not returned.

References

Dekker, D., Krackhardt, D. and Snijders, T. A. B. (2007). Sensitivity of MRQAP tests to collinearity and autocorrelation conditions. Psychometrika, 72(4), 563–581. doi:10.1007/s11336-007-9016-1

Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4), 359–381. doi:10.1016/0378-8733(88)90004-4

Author

Alejandro Espinosa-Rada

Examples

set.seed(18051889)
Y <- matrix(c(
  0, 1, 1, 0, 0,
  1, 0, 1, 0, 0,
  1, 1, 0, 1, 0,
  0, 0, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
X1 <- matrix(c(
  0, 1, 0, 0, 0,
  1, 0, 1, 0, 0,
  0, 1, 0, 1, 0,
  0, 0, 1, 0, 1,
  0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)

qap_lm(Y, list(distance = X1), reps = 100)
#> $coefficients
#>           coefficient p_greater p_lower p_two_sided
#> intercept   0.1666667        NA      NA          NA
#> distance    0.8333333      0.03       1        0.04
#> 
#> $fit
#> [1] 0.6666667
#> 
#> $distribution
#>        intercept      distance
#>   [1,] 0.6666667 -4.166667e-01
#>   [2,] 0.5000000 -2.239957e-17
#>   [3,] 0.6666667 -4.166667e-01
#>   [4,] 0.5000000  1.364684e-17
#>   [5,] 0.5000000  4.902545e-17
#>   [6,] 0.5000000  1.114879e-16
#>   [7,] 0.6666667 -4.166667e-01
#>   [8,] 0.3333333  4.166667e-01
#>   [9,] 0.6666667 -4.166667e-01
#>  [10,] 0.3333333  4.166667e-01
#>  [11,] 0.5000000  8.025668e-17
#>  [12,] 0.1666667  8.333333e-01
#>  [13,] 0.6666667 -4.166667e-01
#>  [14,] 0.5000000  6.718253e-18
#>  [15,] 0.5000000 -1.947467e-17
#>  [16,] 0.6666667 -4.166667e-01
#>  [17,] 0.5000000 -1.947467e-17
#>  [18,] 0.5000000  4.902545e-17
#>  [19,] 0.5000000  1.114879e-16
#>  [20,] 0.5000000  1.114879e-16
#>  [21,] 0.3333333  4.166667e-01
#>  [22,] 0.6666667 -4.166667e-01
#>  [23,] 0.6666667 -4.166667e-01
#>  [24,] 0.5000000  1.114879e-16
#>  [25,] 0.3333333  4.166667e-01
#>  [26,] 0.6666667 -4.166667e-01
#>  [27,] 0.6666667 -4.166667e-01
#>  [28,] 0.5000000  6.718253e-18
#>  [29,] 0.3333333  4.166667e-01
#>  [30,] 0.8333333 -8.333333e-01
#>  [31,] 0.6666667 -4.166667e-01
#>  [32,] 0.3333333  4.166667e-01
#>  [33,] 0.5000000  1.114879e-16
#>  [34,] 0.5000000  6.718253e-18
#>  [35,] 0.5000000  6.718253e-18
#>  [36,] 0.5000000  1.364684e-17
#>  [37,] 0.5000000  1.114879e-16
#>  [38,] 0.5000000  1.364684e-17
#>  [39,] 0.5000000  1.100837e-16
#>  [40,] 0.3333333  4.166667e-01
#>  [41,] 0.3333333  4.166667e-01
#>  [42,] 0.6666667 -4.166667e-01
#>  [43,] 0.6666667 -4.166667e-01
#>  [44,] 0.5000000  6.718253e-18
#>  [45,] 0.5000000  6.718253e-18
#>  [46,] 0.5000000  4.902545e-17
#>  [47,] 0.5000000  6.718253e-18
#>  [48,] 0.5000000  1.364684e-17
#>  [49,] 0.5000000  4.902545e-17
#>  [50,] 0.5000000  8.025668e-17
#>  [51,] 0.1666667  8.333333e-01
#>  [52,] 0.3333333  4.166667e-01
#>  [53,] 0.5000000  6.718253e-18
#>  [54,] 0.3333333  4.166667e-01
#>  [55,] 0.3333333  4.166667e-01
#>  [56,] 0.6666667 -4.166667e-01
#>  [57,] 0.6666667 -4.166667e-01
#>  [58,] 0.5000000  1.114879e-16
#>  [59,] 0.5000000  4.902545e-17
#>  [60,] 0.6666667 -4.166667e-01
#>  [61,] 0.5000000  8.025668e-17
#>  [62,] 0.6666667 -4.166667e-01
#>  [63,] 0.5000000  4.676835e-17
#>  [64,] 0.8333333 -8.333333e-01
#>  [65,] 0.5000000  6.718253e-18
#>  [66,] 0.6666667 -4.166667e-01
#>  [67,] 0.3333333  4.166667e-01
#>  [68,] 0.5000000  6.718253e-18
#>  [69,] 0.6666667 -4.166667e-01
#>  [70,] 0.1666667  8.333333e-01
#>  [71,] 0.3333333  4.166667e-01
#>  [72,] 0.5000000  1.364684e-17
#>  [73,] 0.5000000  4.902545e-17
#>  [74,] 0.5000000  1.114879e-16
#>  [75,] 0.5000000  1.114879e-16
#>  [76,] 0.5000000  1.364684e-17
#>  [77,] 0.5000000  1.364684e-17
#>  [78,] 0.3333333  4.166667e-01
#>  [79,] 0.3333333  4.166667e-01
#>  [80,] 0.3333333  4.166667e-01
#>  [81,] 0.6666667 -4.166667e-01
#>  [82,] 0.5000000 -1.947467e-17
#>  [83,] 0.5000000  6.718253e-18
#>  [84,] 0.6666667 -4.166667e-01
#>  [85,] 0.5000000  1.114879e-16
#>  [86,] 0.3333333  4.166667e-01
#>  [87,] 0.5000000  1.364684e-17
#>  [88,] 0.5000000  6.718253e-18
#>  [89,] 0.5000000  1.364684e-17
#>  [90,] 0.6666667 -4.166667e-01
#>  [91,] 0.6666667 -4.166667e-01
#>  [92,] 0.5000000  4.902545e-17
#>  [93,] 0.6666667 -4.166667e-01
#>  [94,] 0.6666667 -4.166667e-01
#>  [95,] 0.5000000  4.902545e-17
#>  [96,] 0.5000000 -1.947467e-17
#>  [97,] 0.6666667 -4.166667e-01
#>  [98,] 0.6666667 -4.166667e-01
#>  [99,] 0.5000000  4.902545e-17
#> [100,] 0.6666667 -4.166667e-01
#>