Compute Precision Weights from Estimated Scale Parameters

Given the estimated log-scale intercept (gamma_0) and slope (gamma_1), computes the per-observation residual SD (sigma_i), raw precision weight (w_saturated), and mean-normalised weight (w_saturated_norm).

Usage

compute_saturated_weights(df, gamma_0, gamma_1 = 0)

Arguments

df

Data frame with a log_cv column (from prepare_cv()).

gamma_0

Numeric: estimated intercept of the log-sigma model (log(phi)).

gamma_1

Numeric: estimated slope of the log-sigma model (beta1). Set to 0 for intercept-only (uniform weights). Default 0.

Value

The input data frame with additional columns:

sigma_i

Estimated residual SD for each observation.

w_saturated

Raw precision weight: 1 / sigma_i^2.

w_saturated_norm

Mean-normalised weight: w_saturated / mean(w_saturated). The shape is identical to w_saturated; normalisation to mean = 1 is applied only for cross-group comparability.

Details

The transformation is: $$\sigma_i = \exp(\gamma_0 + \gamma_1 \cdot \log(\mathrm{cv}_i))$$ $$w_i = 1 / \sigma_i^2$$

Examples

data(example_assay)
dat_sub <- example_assay[example_assay$antigen == "prn" &
                         example_assay$feature == "IgG1", ]
d <- prepare_cv(dat_sub, pcov_col = "pcov")

# Apply hypothetical scale estimates
d <- compute_saturated_weights(d, gamma_0 = 0.5, gamma_1 = 1.2)
summary(d$w_saturated_norm)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.      NA's 
#> 0.0005172 0.5825621 1.1687081 1.0000000 1.4015256 1.7504343         6 
weight_diagnostics(d$w_saturated)
#> $n_obs
#> [1] 512
#> 
#> $n_valid
#> [1] 506
#> 
#> $n_eff
#> [1] 402.3
#> 
#> $eff_ratio
#> [1] 0.795
#> 
#> $weight_ratio
#> [1] 3384
#> 
#> $gini
#> [1] 0.284
#>