Calculate Selectivity — Get

Selectivity-at-bin under any of the parametric, semi-parametric and non-parametric forms, constant or time-varying. Equations are in the model equations vignette.

Usage

Get_Selex(
  Selex_Model,
  TimeVary_Model,
  pars,
  ln_seldevs,
  Region,
  Year,
  Bin,
  Sex,
  Wbin_bicubic = NULL,
  Wyr_bicubic = NULL,
  n_bin_nodes_bicubic = NULL,
  n_yr_nodes_bicubic = NULL,
  bin_devs = NULL,
  bin_dev_bins = NULL,
  sel_norm_bins = NULL,
  n_sel_bins = NULL,
  apical = 1,
  dbnrml_raw = c(0, 0),
  dbnrml_startbin = 1
)

Arguments

Selex_Model: Integer selectivity form. 0 logistic (b50, slope), 1 gamma dome (bin-at-peak, curvature), 2 power \(1/\text{bin}^{p}\), 3 logistic (b50, b95), 4 double normal with plateau and flexible tails (six parameters, \(p_1\) the bin the plateau starts at on the bin scale, \(p_5\) and \(p_6\) the selectivity at the first and last bins), 6 and 7 the two logistics scaled by an asymptote \(\alpha \in (0,1)\), 5 non-parametric on the logit scale through plogis, standardized over years and bins jointly, 9 non-parametric on the log scale with the level free and each year centered over sel_norm_bins, and 8 a bicubic spline over a bin-node by year-node grid, which takes no TimeVary_Model deviations.
TimeVary_Model: Integer temporal structure. 0 none, 1 iid and 2 random walk deviations on the model parameters, 3 and 4 a 3D GMRF on the marginal or conditional variance and 5 a separable 2D AR(1), all three applied at bin level.
pars: Numeric vector of selectivity parameters on the transformed scale, in the order the form expects: c(ln_b50, ln_slope) for model 0, c(ln_bmax, ln_delta) for 1, c(ln_power) for 2, c(ln_b50, ln_b95) for 3, c(p1, ..., p6) for 4, one logit value per bin for 5, c(logit_alpha, ln_b50, ln_k) for 6, c(logit_alpha, ln_b50, ln_b95) for 7, one log value per bin for 9, and for 8 the flattened bin-node by year-node grid, filled column-major into a n_yr_nodes by n_bin_nodes matrix.
ln_seldevs: Array of log-scale deviations [n_regions, n_years, n_parameters_or_bins, n_sexes, 1]. Under TimeVary_Model 1 and 2 they apply to the parameters after exponentiation; under 3 to 5 they apply multiplicatively at bin level to the constructed curve; under Selex_Model = 5 they act on the bin-level logit parameters before the transformation.
Region: Integer region index.
Year: Integer absolute year index, a row index into Wyr_bicubic. Read directly by Selex_Model == 8, and otherwise only to index ln_seldevs.
Bin: Numeric vector of bins (ages or lengths).
Sex: Integer sex index.
Wbin_bicubic: Numeric length(Bin) x n_bin_nodes natural cubic spline weight matrix (see Get_Natural_Cubic_Spline_Weights) mapping bin-node log-selectivity onto Bin. Read under Selex_Model == 8 only, and may be NULL otherwise. Zero padding in unused columns contributes nothing.
Wyr_bicubic: Numeric n_yrs_total x n_yr_nodes weight matrix mapping year-node log-selectivity onto every absolute model year; row Year is used for this call. Read under Selex_Model == 8 only. A single column of ones gives a time-invariant bin-only spline.
n_bin_nodes_bicubic, n_yr_nodes_bicubic: Integer, this fleet and block's own node counts. Supply them whenever Wbin_bicubic or Wyr_bicubic may have been zero-padded wider than this block's grid, because another block shares the storage array: the padded width would misassign which flattened parameter lands in which cell. NULL (default) falls back to ncol(), which is right when no padding is possible.
bin_devs: Array of log-scale bin-override deviations [n_regions, n_years, n_bins, n_sexes, 1], or NULL. Supplies the value for every bin named in bin_dev_bins.
bin_dev_bins: Integer vector of the bins whose selectivity is replaced by exp(bin_devs[...]) rather than taken from the functional form, or NULL for none. Applied after everything else, including any standardization, so the named bins are governed by their own deviations while the rest of the curve keeps its parametric shape.
sel_norm_bins: Integer vector of the bins the mean-one standardization averages over under Selex_Model = 9, or NULL for every bin. A gear whose catchability is defined against part of the age range standardizes over that part, which shifts the scale absorbed by q.
n_sel_bins: Integer, or NULL/0 for none. Bins beyond this one are kept at its computed value rather than evaluated through the functional form, the NSelBins plateau convention several assessments apply. Applied after the form and its parameter deviations, but before the bin-level semi-parametric deviations and the bin overrides.
apical: Numeric, the height the double normal's limbs are built up to and the plateau sits at. 1 (default) is the ordinary curve; a sex with an apical offset takes exp(ln_*sel_sex_scale) here, which moves the middle of its curve and leaves the first and last bins where their own parameters put them. Ignored by every other form.
dbnrml_raw: Integer vector of length two (0/1) for the double normal: whether the ascending and descending limbs are left as raw Gaussians, \(\exp(-(x - peak)^2 / width)\) built up to the apical value, rather than anchored to p5 and p6 at the first and last bins. Default c(0, 0).
dbnrml_startbin: Integer, the bin the double normal's ascending limb is anchored at and built up from. 1 (default) anchors at the first bin. Anchor later when the compositions start above the population's first length bin: p5 is then the selectivity at that bin, and every bin below takes \((b / b_{start})^2\) times the selectivity there.

Value

Numeric vector of selectivity at Bin, on the natural scale and not normalized unless a downstream component says so.