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Profile Likelihood for mars Models

profile_likelihood.Rd

Compute one-dimensional profile-likelihood curves and confidence intervals for selected parameters by fixing one parameter at a time and re-optimizing the remaining parameters.

Usage

profile_likelihood(
  object,
  parameters = NULL,
  level = 0.95,
  n_points = 21,
  span = 3,
  grid = NULL,
  optim_method = "L-BFGS-B",
  control = list(factr = 1e+07, maxit = 400),
  parameter_pairs = NULL
)

Arguments

object

A fitted mars or pub_bias object. mars profiling currently excludes LASSO fits.

parameters

Optional parameter specification. May be NULL (default: all random-effects parameters), numeric indices into the optimizer parameter vector, or parameter names. Fixed-effect parameters use the column names of object$design_matrix; random-effects parameters use names tau1, tau2, ....

level

Confidence level for profile-likelihood intervals. Default 0.95.

n_points

Number of grid points used per profiled parameter. Default 21.

span

Multiplicative span around the MLE for automatic grids. Default 3.

grid

Optional custom grid specification:

  • numeric vector: reused for each parameter

  • named list of numeric vectors keyed by parameter name

  • unnamed list of numeric vectors with one entry per profiled parameter.

optim_method

Optimization method passed to optim(). Default "L-BFGS-B".

control

Control list passed to optim() for each conditional fit.

parameter_pairs

Optional 2D parameter-pair specification. May be a character vector of length 2, a numeric vector of length 2, or a list of such pairs.

Value

A list containing per-parameter profile grids and profile-likelihood confidence intervals. The profiles component contains one data frame per one-dimensional profile. The surfaces component contains optional two-dimensional grids with x, y, objective, converged, and cutoff entries.

Details

The profiled objective is reported on a deviance-like scale. For standard mars models this is the fitted objective, equivalent to -2 log L up to constants that do not depend on the profiled parameters. For publication-bias models the same -2 log L scaling is used. Lower values therefore indicate better-supported parameter values.

For a one-dimensional profile, the x-axis is the fixed value of the selected parameter and the y-axis is the deviance-scale objective after all remaining parameters have been re-optimized. The profile-likelihood interval contains values whose objective is no more than qchisq(level, df = 1) above the fitted minimum.

For a two-dimensional profile surface, the x- and y-axes are the two fixed parameter values and the contours show the deviance-scale objective after all other parameters have been re-optimized. The cutoff contour uses qchisq(level, df = 2) above the fitted minimum and can be interpreted as an approximate joint confidence region for the parameter pair.

Examples

if (FALSE) { # \dontrun{
fit <- mars(
  data = teacher_expectancy,
  studyID = "study",
  effectID = NULL,
  sample_size = NULL,
  formula = yi ~ 1,
  variance = "vi",
  varcov_type = "univariate",
  structure = "univariate"
)
prof <- profile_likelihood(fit, parameters = "tau1", n_points = 7)
plot(prof)
} # }