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Construct logistic-normal covariance matrix

get_logistN_Sigma.Rd

Helper function to generate the covariance matrix (\(\Sigma\)) used in logistic-normal composition models. The structure depends on the specification of comp_like:

  • comp_like = 2: independent and identically distributed (iid) across categories (\(n_\mathrm{categories}\)).

  • comp_like = 3: first-order autoregressive (AR1) correlation across categories (\(n_\mathrm{categories}\)).

  • comp_like = 4: two-dimensional AR1 correlation across categories and sexes (\(n_\mathrm{categories} \times n_\mathrm{sexes}\)).

Usage

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

Arguments

comp_like

Integer specifying the logistic-normal correlation structure:

  • 2 = iid across categories

  • 3 = AR1 across categories

  • 4 = AR1 across categories and sexes

n_bins

Number of composition categories (e.g., age or length bins). For comp_like = 2, 3, the covariance matrix is dimensioned n_bins. For comp_like = 4, it is dimensioned n_bins * n_sexes.

n_sexes

Number of sexes. Required when comp_like = 4.

theta

Standard deviation parameter controlling the overall scale of the covariance.

corr_b

Correlation parameter across categories, in the interval \((-1, 1)\). Used when comp_like = 3 or 4.

corr_s

Correlation parameter across sexes, in the interval \((-1, 1)\). Used when comp_like = 4.

Value

A covariance matrix \(\Sigma\) with dimension:

  • n_bins (comp_like = 2, 3)

  • 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{
n_cat <- 5
n_sexes <- 2

# iid example (categories only)
get_logistN_Sigma(comp_like = 2, n_bins = n_cat, n_sexes = NULL, theta = 0.5)

# AR1 across categories
get_logistN_Sigma(comp_like = 3, n_bins = n_cat, n_sexes = NULL, theta = 0.5,
                  corr_b = 0.3)

# AR1 across categories and sexes
get_logistN_Sigma(comp_like = 4, n_bins = n_cat, n_sexes = n_sexes, theta = 0.5,
                  corr_b = 0.3, corr_s = 0.2)
} # }