Linear combinations of theta

Computes posterior draws for linear combinations of subgroup effects. Useful for pairwise contrasts (e.g., treatment vs control), weighted averages, or any custom linear estimand involving theta parameters.

Usage

theta_contrasts(fit, contrast_matrix, labels = NULL)

Arguments

fit

A shrinkr_fit object from shrink().

contrast_matrix

A numeric matrix L with ncol(L) = G (number of groups) and nrow(L) = M (number of contrasts). Each row defines one linear combination: $$contrast_i = L_{i1}\theta_1 + L_{i2}\theta_2 + \ldots + L_{iG}\theta_G$$

labels

Optional character vector of length M to name the contrasts. If NULL, uses "contrast1", "contrast2", etc.

Value

A posterior::draws_df with columns .chain, .iteration, .draw, and one column per contrast.

See also

shrink() for fitting models, summarise_theta() for basic theta summaries

Examples

set.seed(1)
draws <- data.frame(
  mu = rnorm(20, 0.2, 0.05),
  tau = abs(rnorm(20, 0.3, 0.03)),
  `theta[1]` = rnorm(20, 0.0, 0.1),
  `theta[2]` = rnorm(20, 0.3, 0.1),
  `theta[3]` = rnorm(20, 0.5, 0.1),
  check.names = FALSE
)
draws$tau_squared <- draws$tau^2
fit <- list(
  fit = posterior::as_draws_df(draws),
  data = list(
    G = 3, K = 1, centered = FALSE,
    vars = c("group1", "group2", "group3"),
    quantiles = data.frame(
      q2.5 = c(-0.20, 0.10, 0.30),
      q50 = c(0.00, 0.30, 0.50),
      q97.5 = c(0.20, 0.50, 0.70)
    )
  ),
  summary = posterior::summarise_draws(
    posterior::as_draws_df(draws),
    "mean", "sd",
    ~posterior::quantile2(., probs = c(0.025, 0.5, 0.975))
  ),
  diagnostics = list(n_divergent = 0, max_treedepth = 0, n_leapfrog = 0)
)
class(fit) <- "shrinkr_fit"
L <- matrix(c(-1, 1, 0), nrow = 1)
contrast <- theta_contrasts(fit, L, labels = "group2_vs_group1")
posterior::summarise_draws(contrast)
#> # A tibble: 1 × 10
#>   variable         mean median    sd    mad     q5   q95  rhat ess_bulk ess_tail
#>   <chr>           <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>    <dbl>    <dbl>
#> 1 group2_vs_grou… 0.296  0.304 0.118 0.0756 0.0805 0.436  1.06     17.1     20.4