Per-edge posterior summary of a group difference

Summarizes the posterior of \(D_{ij} = X_{k,ij} - X_{m,ij}\) for every edge \(i < j\): mean, standard deviation, credible interval, the sign probability and the exceedance probabilities \(P(|D_{ij}| > c)\).

Usage

diff_summary(
  fit,
  groups = c(1, 2),
  scale = c("pcor", "precision"),
  deltas = c(0.01, 0.02, 0.05, 0.1),
  probs = c(0.025, 0.975),
  chain = NULL
)

Arguments

fit: A multiggm_fit or multiggm_fit_list object.
groups: Integer vector of length 2, the groups c(k, m) to compare. Default c(1, 2).
scale: "pcor" (default) for partial correlations or "precision" for precision-matrix entries.
deltas: Numeric vector of magnitude thresholds c for the exceedance probabilities \(P(|D| > c)\), on the scale given by scale.
probs: Numeric vector of length 2 with the credible-interval quantiles, or NULL to skip the interval (faster).
chain: NULL (default) pools all chains; an integer vector selects chains of a multiggm_fit_list.

Value

A data frame with one row per edge \(i < j\) and columns i, j, mean, sd, lower, median, upper, excludes_zero, p_sign, and one p_exceed_<c> column per entry of deltas. Rows are in R's upper.tri() order. Attributes record groups, scale, deltas, probs and n_draws.

Details

Do not use excludes_zero or p_sign for FDR control. A credible interval that excludes zero is equivalent to p_sign \(\ge 1 - \alpha/2\), where p_sign \(= \max\{P(D > 0), P(D < 0)\}\). Whenever the posterior of \(D\) is continuous, \(P(D = 0) = 0\), so p_sign is not a probability that the edge differs. This holds for the SSVS sampler (normal spike), for the mGHS sampler (continuous shrinkage), and for G-Wishart edges present in both groups. Edges with identical true values in both groups then get p_sign near 1 from sampling noise alone. In a simulation with mGHS (p = 100, n = 1000 per group), Bayesian FDR on p_sign gave an achieved FDR of about 0.50 at a nominal 0.05. Use \(P(|D| > c)\) with a practically meaningful c instead (see select_diff_edges()).

For mGHS fits with save_draws = FALSE, the summary is read from running sums kept by the sampler over every post-burn-in iteration. Then deltas must be a subset of the grid given at fit time, and the credible-interval columns are NA.

Examples

sim <- simulate_multiggm(K = 2, p = 8, n = 80, seed = 1)
fit <- multiggm_mcmc(data_list = sim$data_list, burnin = 200, nsave = 100)
ds <- diff_summary(fit, deltas = c(0.05, 0.1))
head(ds)
#>   i j         mean         sd        lower     median      upper excludes_zero
#> 1 1 2 -0.545838605 0.11333604 -0.762861810 -0.5249929 -0.3813812          TRUE
#> 2 1 3  0.007934572 0.08006625 -0.178854518  0.0000000  0.1858638         FALSE
#> 3 2 3  0.019830943 0.10398023 -0.154502805  0.0000000  0.2663474         FALSE
#> 4 1 4  0.008392163 0.04324758 -0.007186162  0.0000000  0.1475525         FALSE
#> 5 2 4  0.419292562 0.09993498  0.245943073  0.4058617  0.6534092          TRUE
#> 6 3 4  0.499296070 0.16104462  0.239851834  0.4925896  0.7949466          TRUE
#>   p_sign p_exceed_0.05 p_exceed_0.1
#> 1   1.00          1.00         1.00
#> 2   0.15          0.16         0.14
#> 3   0.21          0.27         0.19
#> 4   0.09          0.08         0.04
#> 5   1.00          1.00         1.00
#> 6   0.98          0.98         0.98