The cross-spectra of several channel pairs, stacked with a pair factor

cross_wishart() models ONE channel pair. A recording with more channels has a pair for every two of them, and the questions asked of it are about all of those pairs at once. frm_cross_pairs() runs frm_cross_spectrum() on each pair and stacks the results, one block per pair, with a pair factor that a model can use.

Usage

frm_cross_pairs(X, pairs = NULL, ...)

Arguments

X

The recording: a numeric matrix or a data frame of numeric columns whose COLUMNS ARE CHANNELS and whose rows are samples, or a list of such matrices, one per epoch, each with the same channels. Channel names come from the column names, or are ch1, ch2, and so on when there are none.

pairs

Which pairs to form. NULL, the default, forms every pair of two different channels, in column order. Otherwise a two-column matrix or data frame, one row per pair, naming each channel by name or by column number.

...

Passed to frm_cross_spectrum(): sfreq, segments, tapers, smooth, window, frange and, for a list of epochs, group.

Value

The rows of frm_cross_spectrum() for every pair, with the factors pair ("a-b" for channels a and b), ch1 and ch2 in front. ch1 is the signal frm_cross_spectrum() takes as x, so the fitted phase is the lead of ch1 over ch2.

Many pairs in one model

Fitting each pair on its own and correcting the p-values afterwards treats the pairs as unrelated. One model over the stacked frame lets them share information instead:

• coh ~ 1 + (1 | pair) gives each pair its own coherence, shrunk toward the pairs' common level by as much as the data say the pairs differ. A pair that stands out after shrinkage stands out against the others, which is the comparison a multiple-comparison correction tries to make after the fact.

• coh ~ s(freq, by = pair) with pair also a fixed effect gives each pair its own coherence spectrum, and frm_coherence() reads each one off with a band.

• coh ~ 0 + pair, with mu, pow2 and phase also by pair, is the separate fits in one call: the likelihood is then a sum of one term per pair, so each pair's estimate is the one its own fit gives.

The power of a channel appears in every pair that includes it, so the blocks share channels. Each block is still a correct likelihood for its own pair; what the stacked likelihood does not model is the dependence between two blocks that share a channel. Read the standard errors of a stacked fit with that in mind.

See also

frm_cross_spectrum(), cross_wishart().

Examples

set.seed(2)
src <- rnorm(2048)
X <- cbind(Fz = src + rnorm(2048), Cz = 0.8 * src + rnorm(2048),
           Pz = rnorm(2048))
xp <- frm_cross_pairs(X, sfreq = 256, segments = 8)
table(xp$pair)
#> 
#> Fz-Cz Fz-Pz Cz-Pz 
#>   127   127   127