Draw whole cross-spectral matrices from a fitted coupling model

stats::simulate() refuses on a cross_wishart() fit, because a draw is a Hermitian matrix and the response slot carries one of its four numbers. This returns all four, so a simulated data frame can be refitted or compared against the observed one.

Usage

frm_cross_simulate(
  fit,
  nsim = 1L,
  seed = NULL,
  newdata = NULL,
  re_formula = NULL
)

Arguments

fit

A cross_wishart() fit.

nsim

Number of replicate data frames.

seed

Optional seed, set with set.seed() before drawing.

newdata

Optional data frame of predictor values.

re_formula

Passed to stats::predict(); NULL keeps the random effects.

Value

A list of nsim data frames, each with the columns frm_cross_spectrum() produces: w11, w22, w12r, w12i, n.

How a draw is made

Each row's fitted spectral matrix is factored as L L^H and n independent complex normal vectors are drawn through L; the returned matrix is their outer-product sum. That is the definition of the complex Wishart rather than a transformation of it, so a simulated row and the density are one statement of the model. Checked against the density's own first moment: over 20000 draws the mean of the simulated matrix divided by n matches the fitted matrix to 0.0011 at n = 16.

Examples

set.seed(6)
src <- rnorm(2048)
xs <- frm_cross_spectrum(src + rnorm(2048), 0.9 * src + rnorm(2048),
                         segments = 16)
xs <- xs[xs$freq < 0.1, ]
fit <- frmtmb::frm(
  frmtmb::bf(w11 | vreal(w22, w12r, w12i) + vint(n) ~ 1,
             pow2 ~ 1, coh ~ 1, phase ~ 1),
  family = cross_wishart(), data = xs)
str(frm_cross_simulate(fit, nsim = 2, seed = 1)[[1]])
#> 'data.frame':	12 obs. of  5 variables:
#>  $ w11 : num  27.7 28.1 37.8 37.6 38 ...
#>  $ w22 : num  24.3 19.9 28.2 33.5 33.2 ...
#>  $ w12r: num  13.3 12.1 12.9 18.5 23.5 ...
#>  $ w12i: num  -5.8 2.4 -1.17 -13.35 3.03 ...
#>  $ n   : num  16 16 16 16 16 16 16 16 16 16 ...