Animal response-column slopes

Adds slope-only predictor deviations across response columns, with an additive-genetic relationship matrix \(A\) relating those columns. If B is the response-column by predictor coefficient matrix, the model is $$\mathrm{Cov}(\mathrm{vec}(B^\mathsf{T})) = A \otimes \Sigma_\mathrm{predictor}.$$ The RHS must be the response-column factor resolved from trait =, and the pedigree or matrix labels must match its levels. A single | estimates a full predictor covariance; || gives separate predictor variances with zero covariance. The term never adds a random intercept.

Usage

animal_slope(formula, pedigree = NULL, A = NULL, Ainv = NULL)

Arguments

formula

An lme4-bar formula. With one or more bare predictors and the resolved response-column factor on the RHS, x1 + x2 | trait is the full column-slope covariance alias and x1 + x2 || trait is its diagonal alias. For one predictor the two bars fit the same 1 x 1 covariance.

pedigree, A, Ainv

One relatedness input for the column-slope aliases: a pedigree, additive-genetic covariance matrix, or its precision.

Value

A formula marker; never evaluated.

Details

This route is covered for Gaussian long-format data with bare finite numeric predictors. Wide-format column slopes, non-Gaussian responses, transformed or factor bases, latent predictor covariance, and intervals are not supported in this release. Use extract_Sigma(fit, level = "column_slope") for \(\Sigma_\mathrm{predictor}\).

Historical non-trait RHS forms remain accepted to preserve existing fits. They are compatibility behaviour, not the teaching API; new code uses the resolved response-column factor on the RHS.

See also

slope(), phylo_slope(), kernel_slope(), spatial_slope(), animal_dep(), animal_indep(), extract_Sigma().

Examples

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