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Construct a logistic-normal covariance matrix

get_logistN_Sigma.Rd

Builds the covariance matrix \(\Sigma\) used in logistic-normal composition likelihoods for a given correlation structure. Three structures are supported, matching the comp_like codes used throughout SPoRC: iid (2), AR(1) across bins (3), and AR(1) across bins with constant correlation across sexes via a Kronecker product (4).

Usage

get_logistN_Sigma(
  comp_like,
  n_bins,
  n_sexes,
  theta,
  corr_b = NULL,
  corr_s = NULL
)

Arguments

comp_like

Integer. Covariance structure: 2 = iid (diagonal \(\theta^2 I\)), 3 = AR(1) across bins (\(\theta^2 C_{\text{AR1}}\)), 4 = Kronecker product of constant sex correlation and AR(1) bin correlation (\(\theta^2 (C_{\text{sex}} \otimes C_{\text{AR1}})\)).

n_bins

Integer. Number of composition categories (ages or lengths). The resulting matrix has dimension n_bins for comp_like 2 and 3, or n_bins × n_sexes for comp_like = 4.

n_sexes

Integer. Number of sexes. Required for comp_like = 4; ignored otherwise.

theta

Numeric. Marginal standard deviation \(\theta > 0\) controlling the overall scale of \(\Sigma\).

corr_b

Numeric. AR(1) correlation across bins in \((-1, 1)\). Required for comp_like 3 and 4; ignored for comp_like = 2.

corr_s

Numeric. Constant (exchangeable) correlation across sexes in \((-1, 1)\). Required for comp_like = 4; ignored otherwise.

Value

Numeric covariance matrix \(\Sigma\) of dimension n_bins × n_bins (comp_like 2, 3) or (n_bins × n_sexes) × (n_bins × n_sexes) (comp_like = 4).

See also

Other Utility: fit_model(), get_par_est_info(), post_optim_sanity_checks(), rho_trans(), set_data_indicator_unused()

Examples

if (FALSE) { # \dontrun{
# iid
get_logistN_Sigma(comp_like = 2, n_bins = 5, n_sexes = NULL, theta = 0.5)

# AR(1) across bins
get_logistN_Sigma(comp_like = 3, n_bins = 5, n_sexes = NULL,
                  theta = 0.5, corr_b = 0.3)

# AR(1) across bins x constant across sexes
get_logistN_Sigma(comp_like = 4, n_bins = 5, n_sexes = 2,
                  theta = 0.5, corr_b = 0.3, corr_s = 0.2)
} # }