nct: Network Comparison Test
In GGMncv: Gaussian Graphical Models with Nonconvex Regularization

Description Usage Arguments Details Value Note References Examples

A re-implementation and extension of the permutation based network comparison test introduced in \insertCitevan2017comparing;textualGGMncv. Such extensions include scaling to networks with many nodes and the option to use custom test-statistics.

nct(
  Y_g1,
  Y_g2,
  iter = 1000,
  desparsify = TRUE,
  method = "pearson",
  FUN = NULL,
  cores = 1,
  progress = TRUE,
  update_progress = 4,
  ...
)

`Y_g1`	A matrix (or data.frame) of dimensions n by p, corresponding to the first dataset (p must be the same for `Y_g1` and `Y_g2`).
`Y_g2`	A matrix of dimensions n by p, corresponding to the second dataset (p must be the same for `Y_g1` and `Y_g2`).
`iter`	Numeric. Number of (Monte Carlo) permutations (defaults to `1000`).
`desparsify`	Logical. Should the de-sparsified glasso estimator be computed (defaults to `TRUE`)? This is much faster, as the tuning parameter is fixed to \mjseqn\lambda = \sqrtlog(p)/n.
`method`	character string. Which correlation coefficient (or covariance) is to be computed. One of "pearson" (default), "kendall", or "spearman".
`FUN`	A function or list of functions (defaults to `NULL`), specifying custom test-statistics. See Examples.
`cores`	Numeric. Number of cores to use when executing the permutations in parallel (defaults to `1`).
`progress`	Logical. Should a progress bar be included (defaults to `TRUE`)?
`update_progress`	How many times should the progress bar be updated (defaults to `4`)? Note that setting this to a large value should result in the worse performance, due to additional overhead communicating among the parallel processes.
`...`	Additional arguments passed to `ggmncv`.

User-Defined Functions

These functions must have two arguments, corresponding to the partial correlation network for each group. An example is provided below.

For user-defined functions (FUN), absolute values are used to compute the p-value, assuming more than one value is returned (e.g., centrality). This is done to mimic the R package NCT.

A fail-safe method to ensure the p-value is computed correctly is to access the permutations and observed values from the nct object.

Finally, comparing edges is not implemented. The most straightforward way to do this is with compare_edges, which uses the de-sparsified estimator.

A list of class nct, including the following

glstr_pvalue: Global strength p-value.
sse_pvalue: Sum of square error p-value.
jsd_pvalue: Jensen-Shannon divergence p-value.
max_pvalue: Maximum difference p-value.
glstr_obs: Global strength observed.
sse_obs: Sum of square error observed.
jsd_obs: Jensen-Shannon divergence observed.
max_obs: Maximum difference observed.
glstr_perm: Global strength permutations.
sse_perm: Sum of square error permutations.
jsd_perm: Jensen-Shannon divergence permutations.
max_perm: Maximum difference permutations.

For user-defined functions, i.e., those provided to FUN, the function name is pasted to _pvalue, _obs, and _perm.

In \insertCitevan2017comparing;textualGGMncv, it was suggested that these are tests of invariance. To avoid confusion, that terminology is not used in GGMncv. This is because these tests assume invariance or the null is true, and thus can only be used to detect differences. Hence, it would be incorrect to suggest networks are the same, or evidence for invariance, by merely failing to reject the null hypothesis \insertCitewilliams_nullGGMncv.

For the defaults, Jensen-Shannon divergence is a symmetrized version of Kullback-Leibler divergence (the average of both directions).

Computational Speed

This implementation has two key features that should make it scale to larger networks: (1) parallel computation and (2) the R package glassoFast is used under the hood (as opposed to glasso). CPU (time) comparisons are provided in \insertCitesustik2012glassofast;textualGGMncv.

Non-regularized

Non-regularized can be implemented by setting lambda = 0. Note this is provided to ggmncv via ....

\insertAllCited

# generate network
main <- gen_net(p = 10)

# assume groups are equal
y1 <- MASS::mvrnorm(n = 500,
                    mu = rep(0, 10),
                    Sigma = main$cors)

y2 <- MASS::mvrnorm(n = 500,
                    mu = rep(0, 10),
                    Sigma = main$cors)

compare_ggms <- nct(y1, y2, iter = 500,
                    progress = FALSE)

compare_ggms

# custom function
# note: x & y are partial correlation networks

# correlation
Correlation <- function(x, y){
cor(x[upper.tri(x)], y[upper.tri(y)])
}

compare_ggms <- nct(y1, y2,iter = 100,
                    FUN = Correlation,
                    progress = FALSE)

compare_ggms

# correlation and strength

Strength <- function(x, y){
NetworkToolbox::strength(x) - NetworkToolbox::strength(y)
}

compare_ggms <- nct(y1, y2, iter = 100,
                    FUN = list(Correlation = Correlation,
                               Strength = Strength),
                    progress = FALSE)

compare_ggms