qrme_start_search — qrme_start

Run qrme from multiple random starting values and return the fit with the highest log-likelihood. Use this to assess whether the EM algorithm converges to a unique solution or is sensitive to starting values.

For each restart, start_sigma is drawn uniformly from sigma_range, start_mu is drawn from \(N(0, 0.01)\), and mixture weights start_pi are drawn from a symmetric Dirichlet (i.e., uniform on the simplex).

Usage

qrme_start_search(
  formula,
  data,
  tau,
  n_starts = 10L,
  sigma_range = c(0.1, 2),
  return_fits = FALSE,
  ...
)

Arguments

formula: formula for the outcome model (passed to qrme)
data: data.frame
tau: quantile levels for QR
n_starts: number of random restarts (default 10)
sigma_range: length-2 numeric vector giving the \([\min, \max]\) interval from which start_sigma is drawn for each component (default c(0.1, 2.0))
return_fits: logical; if TRUE the fitted qrme objects for all successful restarts are returned (default FALSE)
...: additional arguments passed to qrme for every restart (e.g. n_mix, me_distribution, mcmc_draws). Arguments start_sigma, start_mu, start_pi, and se are set internally and should not be passed via ....

Value

a list with:

table: data.frame of start index and log-likelihood for each successful restart, sorted descending by log-likelihood
best_fit: the qrme fit with the highest log-likelihood
fits: (only when return_fits = TRUE) list of all successful qrme fits

Examples

if (FALSE) { # \dontrun{
  set.seed(1)
  n <- 300; X <- runif(n)
  Y <- 1 + 2 * X + rnorm(n) + rnorm(n, sd = 0.5)
  best <- qrme_start_search(
    Y ~ X, data.frame(Y, X),
    tau         = c(0.25, 0.5, 0.75),
    n_starts    = 5L,
    mcmc_draws  = 100L,
    mcmc_burn_in = 50L,
    max_em_iters = 20L
  )
  best$table
} # }