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Compute Selectivity Process Error Log-Likelihood (Positive Scale)

Get_sel_PE_loglik.Rd

Calculates the positive log-likelihood contribution for selectivity process error deviations under a variety of temporal/spatiotemporal structures.

Usage

Get_sel_PE_loglik(
  PE_model,
  PE_pars,
  ln_devs,
  map_sel_devs,
  sel_vals,
  pen_wts,
  min_sel_devs_shared_bins
)

Arguments

PE_model

Integer specifying the process error structure:

  • 1 = IID: deviations drawn independently as \(N(0, \sigma^2)\).

  • 2 = Random walk: deviations follow a first-order random walk initialized with a diffuse prior (\(\sigma = 5\)) at y = 1.

  • 3 = 3D GMRF with marginal variance parameterization.

  • 4 = 3D GMRF with conditional variance parameterization.

  • 5 = Separable 2D AR(1) across bins and years.

PE_pars

Array of process error parameters dimensioned [1, par_index, sex, 1]. The par_index slot meaning depends on PE_model:

  • Models 1–2: [1,1,s,1] = log standard deviation (\(\log \sigma\)) for sex s, indexed by bin/age.

  • Models 3–4: [1,1,s,1] = unconstrained partial correlation by age/bin; [1,2,s,1] = unconstrained partial correlation by year; [1,3,s,1] = unconstrained partial correlation by cohort; [1,4,s,1] = log variance.

  • Model 5: [1,1,s,1] = unconstrained bin correlation (transformed via \(2/(1+e^{-2x})-1\)); [1,2,s,1] = unconstrained year correlation; [1,4,s,1] = log standard deviation.

ln_devs

Array of log-scale selectivity deviations dimensioned [1, year, bin, sex, 1].

map_sel_devs

Integer array dimensioned [fleet, year, bin, sex] mapping deviations to unique estimated parameters. Shared deviations carry the same integer value; NA entries are treated as fixed and excluded from likelihood evaluation.

sel_vals

Array of selectivity values dimensioned [1, year, bin, sex, 1], used on the log scale when computing bin and year smoothness penalties (do_sel_pen = TRUE).

pen_wts

Named numeric vector with elements "yr_devs", "bin_curve", "yr_curve" (any missing name is treated as 0). Independently weights the additional regularization penalties applied beyond the process error likelihood: "yr_devs" weights a first-difference-across-years penalty on ln_devs (models 1–2 only); "bin_curve" and "yr_curve" weight second-difference (curvature) penalties on log-selectivity across bins and across years, respectively (models 3–5 only, via Get_Selex_Smoothness_Penalty). A weight of 0 disables that term.

min_sel_devs_shared_bins

Integer vector. Indices of the reference (minimum) bin within each shared deviation group, used to subset the bin dimension when evaluating GMRF or 2D AR(1) likelihoods (PE models 3-5). When no bin sharing is specified, defaults to 1:n_bins (i.e., all bins are included).

Value

Numeric scalar: the positive log-likelihood contribution from selectivity process error. Negated externally to form the negative log-likelihood.

Details

The function supports:

  • IID process error

  • Random walk process error

  • 3D Gaussian Markov Random Field (GMRF) models (marginal or conditional variance)

  • Separable 2D AR(1) models

Independently-weighted regularization penalties can also be applied via pen_wts (see Get_Selex_Smoothness_Penalty for the bin/year curvature terms, which this function delegates to for PE_model 3–5):

  • For PE_model 1–2: pen_wts["yr_devs"] weights a first-difference penalty on log-deviations across years.

  • For PE_model 3–5: pen_wts["bin_curve"] and pen_wts["yr_curve"] independently weight second-difference (smoothness) penalties on log-selectivity across bins and across years, respectively.

Each weight defaults to 0 (off); set any subset of them to apply only the penalty terms desired, rather than one shared on/off flag.

Note: The returned value is on the positive log-likelihood scale. It must be negated to obtain a negative log-likelihood contribution, which is handled outside this function.