tsme_model_select — tsme_model

Fit tsme over a grid of copula families, measurement error distributions, and mixture component counts, then rank the specifications by AIC and BIC.

The log-likelihood is computed as the sum of three components:

ll_y: log-likelihood of the outcome ME model
ll_t: log-likelihood of the treatment ME model
ll_cop: copula log-likelihood

$$AIC = -2 \ell + 2k, \quad BIC = -2 \ell + k \log n$$ where $k = k_Y + k_T + 1$ is computed per grid row, with $k_m = 2$ for $m = 1$ and $k_m = 3m - 1$ for $m \ge 2$, plus one copula parameter.

Laplace ME does not support mixture models (n_mix > 1); any grid row combining Laplace with y_n_mix > 1 or t_n_mix > 1 is dropped automatically with a message.

Usage

tsme_model_select(
  data,
  y_formula,
  t_formula,
  tau,
  t_values,
  copulas = c("gaussian", "clayton", "gumbel", "frank"),
  me_distributions = c("gaussian", "laplace"),
  y_n_mix = 1L,
  t_n_mix = 1L,
  n_cores = 1L,
  return_fits = FALSE,
  ...
)

Arguments

data: data.frame passed to tsme
y_formula: formula for the outcome model
t_formula: formula for the treatment model
tau: quantile levels for the first-stage QR (passed to tsme)
t_values: treatment values for conditional distribution summaries
copulas: character vector of copula families to try. Any subset of c("gaussian","clayton","gumbel","frank") (default: all four).
me_distributions: character vector of ME distributions to try. Any subset of c("gaussian","laplace") (default: both).
y_n_mix: integer or integer vector of ME mixture component counts to try for the outcome equation (default 1L). When a vector is supplied, all values are crossed with the other grid dimensions.
t_n_mix: integer or integer vector of ME mixture component counts to try for the treatment equation (default 1L).
n_cores: number of parallel workers (default 1)
return_fits: logical; if TRUE the fitted tsme objects are returned alongside the table (default FALSE)
...: additional arguments passed to tsme for every cell in the grid (e.g. n_copula_me_draws, mcmc_draws)

Value

a list with element table (a data.frame sorted by BIC with columns copula, me_distribution, y_n_mix, t_n_mix, k_params, ll_y, ll_t, ll_cop, ll, aic, bic) and, if return_fits = TRUE, element fits (a list of tsme objects in the same order as table)

Examples

if (FALSE) { # \dontrun{
  tau      <- seq(0.05, 0.95, length.out = 15)
  t_values <- quantile(nlsy97$lpi, probs = seq(0.1, 0.9, by = 0.1))
  sel <- tsme_model_select(
    data             = nlsy97,
    y_formula        = lci ~ ageC_97 + ageF,
    t_formula        = lpi ~ ageC_97 + ageF,
    tau              = tau,
    t_values         = t_values,
    y_n_mix          = 1:2,
    t_n_mix          = 1:2,
    n_cores          = 4L,
    mcmc_draws       = 200L,
    mcmc_burn_in     = 20L
  )
  print(sel)
} # }