em.algo — em.algo • qrme

A pseudo EM algorithm for quantile regression with measurement error. The measurement error here follows a mixture of normals.

Usage

em.algo(
  formula,
  data,
  betmatguess,
  tau,
  me_distribution = "gaussian",
  m = 1,
  piguess = 1,
  muguess = 0,
  sigguess = 1,
  mcmc_method = "MH",
  tol = NULL,
  conv_criterion = "params",
  loglik_draws = 100L,
  conv_patience = 1L,
  mcmc_draws = 200,
  mcmc_burn_in = 100,
  proposal_sd = NULL,
  n_cores = 1,
  max_em_iters = 100,
  verbose = FALSE
)

Arguments

formula: y ~ x
data: a data.frame that contains y and x
betmatguess: Initial values for the beta parameters. This should be an LxK matrix where L is the number of quantiles and K is the dimension of the covariates
tau: An L-vector indicating which quantiles have been estimated
me_distribution: The distribution of the measurement error. "gaussian" is the default and supports a mixture of normals. "laplace" is also supported.
m: The number of components of the mixture distribution for the measurement error
piguess: Starting value for the probabilities of each mixture distribution (should have length equal to k)
muguess: Starting value for the mean of each mixture component (should have length equal to k)
sigguess: Starting value for the standard deviation of each mixture component (should have length equal to k)
mcmc_method: Simulation step to use in the EM algorithm. Currently only "MH" is supported.
tol: Convergence tolerance. When NULL (default), 1e-2 is used for both criteria. For "params", tol is compared against max(|theta_new - theta_old| / (1 + |theta_old|)), the maximum scaled parameter change across all parameters; this is dimensionless and application-invariant. For "loglik", it is compared against the relative log-likelihood change |ll_new - ll_old| / |ll_old|. Tighten to 1e-3 or smaller for higher accuracy at the cost of more iterations.
conv_criterion: Convergence criterion. "params" (default) stops when the maximum scaled parameter change falls below tol (see tol above). "loglik" stops when the relative change in the observed-data log-likelihood, |ll_new - ll_old| / |ll_old|, falls below tol; the log-likelihood is evaluated using Monte Carlo integration with loglik_draws draws per outer iteration.
loglik_draws: Number of Monte Carlo draws used to evaluate the log-likelihood at each outer EM iteration when conv_criterion = "loglik". More draws reduce noise in the convergence check at the cost of speed. Default is 100.
conv_patience: Integer. Number of consecutive iterations that must satisfy the convergence criterion before the algorithm stops. Default is 1 (current behaviour). Setting this to 2 requires two back-to-back iterations below tol, guarding against false convergence caused by Monte Carlo noise in the log-likelihood or parameter updates.
mcmc_draws: Total number of MCMC draws per EM step (default 200)
mcmc_burn_in: Number of MCMC draws to discard as burnin (default 100)
proposal_sd: Standard deviation of the Metropolis-Hastings proposal (random-walk step size). When NULL (default), initialised to the SD of the ME mixture from the starting parameters and updated after each M-step to track the current ME scale: sqrt(sum(pi_k * (sig_k^2 + mu_k^2))). Pass a positive numeric to fix the proposal at that value for all iterations.
n_cores: Number of cores for parallel bootstrap computation (default 1)
max_em_iters: Maximum number of EM outer iterations. If convergence is not reached, the estimates from the final iteration are returned (default is 100)
verbose: Logical or nonnegative integer. If FALSE (default), suppresses progress output. If TRUE or 1, reports major computational stages, EM iteration numbers, and convergence diagnostics. If 2, also reports qrme-native details such as pi, mu, sigma, tolerance, and finite-mixture summaries. If 3 or larger, also reports raw normalmixEM() output, which uses lambda for mixture probabilities.

Value

QRME object