Fixed-kernel response-column slopes

Adds slope-only response-column deviations coupled by a supplied labelled covariance matrix K. With response-column by predictor coefficient matrix B, the model is $$\mathrm{Cov}(\mathrm{vec}(B^\mathsf{T})) = K \otimes \Sigma.$$ A single | estimates a full predictor covariance Sigma; || makes it diagonal. For one predictor these are the same model. K must be finite, symmetric, positive definite, and have row and column names matching the levels of the response-column factor. Its storage order need not match the factor order because labels are used for alignment.

Usage

kernel_slope(formula, K, name = "kernel")

Arguments

formula: A slope-only bar formula with bare numeric predictor names on the left and the resolved response-column factor on the right.
K: A labelled positive-definite covariance matrix for the response columns.
name: A non-empty label retained in extractor source metadata.

Value

A formula marker; never evaluated.

Details

Scope

This route is covered for one labelled positive-definite kernel, Gaussian long-format data, and one or more bare, finite numeric predictors. The supplied matrix is used on its original scale. Wide-format column slopes, non-Gaussian responses, transformed/factor bases, and a random intercept inside this term are not supported in this release.

Examples

if (FALSE) { # \dontrun{
set.seed(1); dat <- expand.grid(unit = factor(1:12), trait = factor(paste0("sp", 1:4)))
dat$lat <- rnorm(nrow(dat)); dat$temp <- rnorm(nrow(dat)); dat$value <- rnorm(nrow(dat))
K <- diag(nlevels(dat$trait)); dimnames(K) <- list(levels(dat$trait), levels(dat$trait))
fit <- gllvmTMB(
  value ~ 0 + trait + kernel_slope(lat + temp | trait, K = K),
  data = dat, trait = "trait", unit = "unit",
  family = gaussian()
)
extract_Sigma(fit, level = "column_slope")
} # }