compute.qrme

does the heavy lifting on computing quantile regression with left hand side measurement error

Usage

compute.qrme(
  formula,
  tau = 0.5,
  data,
  me_distribution = "gaussian",
  n_mix = 1,
  start_beta = NULL,
  start_mu = NULL,
  start_sigma = NULL,
  start_pi = NULL,
  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

tau

vector for which quantiles to compute quantile regression

data

a data.frame that contains y and x

me_distribution

Distribution of the measurement error: "gaussian" (default, supports a mixture of normals) or "laplace".

n_mix

The number of mixture components of the measurement error (default 1). Increase this for more flexible measurement-error distributions.

start_beta

an LxK matrix of starting values for beta where L is the dimension of tau and K is the number of covariates (default is NULL and in this case, the starting values are set to be the QR coefficients coming from QR that ignores measurment error)

start_mu

A vector of length n_mix of starting values for the mean of each mixture component. When NULL (default), set to 0 for n_mix = 1 and to evenly-spaced values on [-0.25 * sd(y), 0.25 * sd(y)] for n_mix > 1, mean-centered to satisfy the mean-zero ME constraint.

start_sigma

A vector of length n_mix of starting values for the standard deviation of each mixture component. When NULL (default), backed out from the mixture variance identity assuming equal weights and equal component SDs targeting a mixture SD of 0.5 * sd(y): sigma = sqrt(max(target^2 - mean(start_mu^2), (target/sqrt(n_mix))^2)). This gives 0.5 * sd(y) for n_mix = 1 and slightly larger values for n_mix > 1 (since the component means absorb some variance).

start_pi

A vector of length n_mix of starting values for the fraction of observations in each component of the mixture of normals distribution for the measurement error (default is NULL and in this case, the starting values are all set to be 1/n_mix)

mcmc_method

The type of simulation step to use in the EM algorithm. Currently only "MH" for Metropolis-Hastings is supported.

tol

Convergence tolerance. When NULL (default), a value is chosen automatically based on conv_criterion. See em.algo for details.

conv_criterion

Convergence criterion: "params" (default) uses the Euclidean norm of parameter changes; "loglik" uses the relative change in the observed-data log-likelihood. See em.algo.

loglik_draws

Number of Monte Carlo draws for the log-likelihood convergence check when conv_criterion = "loglik" (default 100). Ignored when conv_criterion = "params".

conv_patience

Integer. Consecutive iterations that must satisfy the convergence criterion before stopping (default 1). Setting to 2 guards against false convergence from Monte Carlo noise. See em.algo.

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. 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.