mds_test function

Test optimal number of MDS dimensions.

Generate bootstrapped confidence intervals and permutation based null distribution for MDS analysis. Output shows how much stress is reduced by adding an additional dimension to the MDS analysis of similarity_matrix, and bootstrapped iterations of similarity_matrix, compared with the stress reduction expected from a matrix with no meaningful structure. This function is inspired by pca_test(), but is less connected with statistical literature than that function. We currently reject additional dimensions is they reduce less stress than we would expect by chance. That is, when the distribution from the boostrapped analyses sits notably lower than the permuted distribution when plotted by plot_mds_test()

mds_test(
  similarity_matrix,
  n_boots = 50,
  n_perms = 50,
  test_dimensions = 5,
  principal = TRUE,
  mds_type = "ordinal",
  spline_degree = 2,
  spline_int_knots = 2
)

Arguments

• similarity_matrix: Square matrix of speaker similarity scores.
• n_boots: Number of bootstrapping iterations (default: 25).
• n_perms: Number of permutations (default: 25).
• test_dimensions: Number of MDS dimensions to test for stress reduction (default: 5).
• principal: Whether to apply principal axis transform to MDS (default: TRUE)
• mds_type: What kind of MDS to apply, see smacof::smacofSym() (default: 'ordinal')
• spline_degree: How many spline degrees when type is 'mspline' (default: 2)
• spline_int_knots: How many internal knots when type is 'mspline' (default: 2)

Returns

object of class mds_test_results, containing:

• $stress_reduction a tibble containing
• $n_boots Number of bootstrapping iterations.
• $n_perms Number of permutation iterations
• $mds_type Type of MDS analysis (type argument passed to smacof::smacofSym())
• $principal Whether principal axis transformation is applied (passed to smacof::smacofSym())

Examples

# Apply interval MDS to `sim_matrix`, with 5 permutations and bootstraps
# testing up to 3 dimensions. In real usage, increase `n_boots` and `n_perms`
# to at least 50.
mds_test(
 sim_matrix,
 n_boots = 5,
 n_perms = 5,
 test_dimensions = 3,
 mds_type = 'interval'
)