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Test optimal number of MDS dimensions.

Source: R/mds_test.R
mds_test.Rd

[Experimental] 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()

Usage

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)

Value

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'
)
#> $stress_reduction
#> # A tibble: 33 × 6
#>    source    dims stress_dist cumulative lag_stress  diff
#>    <chr>    <int>       <dbl>      <dbl>      <dbl> <dbl>
#>  1 permuted     1       0.535          1      1     0.465
#>  2 permuted     1       0.531          2      1     0.469
#>  3 permuted     1       0.531          3      1     0.469
#>  4 permuted     1       0.531          4      1     0.469
#>  5 permuted     1       0.526          5      1     0.474
#>  6 permuted     2       0.357          1      0.535 0.178
#>  7 permuted     2       0.352          2      0.531 0.179
#>  8 permuted     2       0.350          3      0.531 0.180
#>  9 permuted     2       0.356          4      0.531 0.175
#> 10 permuted     2       0.353          5      0.526 0.173
#> # ℹ 23 more rows
#> 
#> $n_boots
#> [1] 5
#> 
#> $n_perms
#> [1] 5
#> 
#> $mds_type
#> [1] "interval"
#> 
#> $principal
#> [1] TRUE
#> 
#> attr(,"class")
#> [1] "mds_test_results"