Confidence Intervals for TMB Model Parameters

Usage

# S3 method for class 'beezdemand_tmb'
confint(
  object,
  parm = NULL,
  level = 0.95,
  report_space = c("internal", "natural"),
  method = c("wald", "simulate"),
  R = 1000L,
  seed = NULL,
  ...
)

Arguments

object: A beezdemand_tmb object.
parm: Character vector of parameter names.
level: Confidence level (default 0.95).
report_space: Character. "internal" or "natural". When "natural", beta_q0, beta_alpha, and log_k are exponentiated to the natural scale. For the intercept, this gives Q0 or alpha at the reference level. For non-intercept terms, the exponentiated value represents a multiplicative fold-change (ratio) relative to the reference level, not the absolute parameter value for that group. Variance parameters (logsigma_*, rho_bc_raw) remain on their internal scales; use summary() or .tmb_format_variance_components() for transformed variance components.
method: Character. "wald" (default) returns Hessian-based Wald intervals (coef +/- z * se). "simulate" draws R parametric Monte Carlo samples from the asymptotic Gaussian sampling approximation \(N(\hat\beta, \hat\Sigma)\) (with \(\hat\Sigma = \)vcov(object)) and reports per-coefficient empirical quantiles.
R: Integer. Number of Monte Carlo draws for method = "simulate". Must be >= 100; >= 1000 is recommended for stable quantiles. Ignored for method = "wald".
seed: Optional integer seed for method = "simulate" reproducibility. When supplied, the caller's RNG state is restored on exit so the global stream is left unperturbed.
...: Additional arguments.

Value

A tibble with term, estimate, conf.low, conf.high, level.

Details

method = "simulate" is Monte Carlo simulation from the asymptotic Gaussian sampling approximation to the MLE (neither a Bayesian posterior, nor a data-resampling bootstrap, nor a profile-likelihood interval). Because the sampled distribution is the same Gaussian that Wald assumes, the simulated per-coefficient quantiles converge to the Wald intervals as R -> Inf; the method does not improve on Wald at boundary cases and offers no positivity guarantee on the internal scale (logsigma_* intervals can be negative). Its value is (a) a diagnostic side-by-side check on the Gaussian approximation, and (b) a shared draw primitive (.tmb_parametric_draws()) for derived-metric confidence intervals.

Examples

# \donttest{
data(apt)
fit <- fit_demand_tmb(apt, equation = "exponential", verbose = 0)
#>   equation='exponential': Dropped 14 zero-consumption observations (146 remaining).
confint(fit)
#> # A tibble: 6 × 5
#>   term              estimate conf.low conf.high level
#>   <chr>                <dbl>    <dbl>     <dbl> <dbl>
#> 1 Q0:(Intercept)       1.88      1.64     2.12   0.95
#> 2 alpha:(Intercept)   -5.57     -5.86    -5.28   0.95
#> 3 logsigma            -0.951    -1.40    -0.501  0.95
#> 4 logsigma            -0.777    -1.23    -0.326  0.95
#> 5 logsigma_e          -1.95     -2.07    -1.82   0.95
#> 6 rho_raw             -0.459    -1.10     0.186  0.95
confint(fit, report_space = "natural")
#> # A tibble: 6 × 5
#>   term              estimate conf.low conf.high level
#>   <chr>                <dbl>    <dbl>     <dbl> <dbl>
#> 1 Q0:(Intercept)     6.55     5.14      8.36     0.95
#> 2 alpha:(Intercept)  0.00380  0.00285   0.00508  0.95
#> 3 logsigma          -0.951   -1.40     -0.501    0.95
#> 4 logsigma          -0.777   -1.23     -0.326    0.95
#> 5 logsigma_e        -1.95    -2.07     -1.82     0.95
#> 6 rho_raw           -0.459   -1.10      0.186    0.95
# Diagnostic Monte Carlo intervals (asymptotically Wald-equivalent):
confint(fit, method = "simulate", R = 1000, seed = 42)
#> # A tibble: 6 × 5
#>   term              estimate conf.low conf.high level
#>   <chr>                <dbl>    <dbl>     <dbl> <dbl>
#> 1 Q0:(Intercept)       1.88      1.63     2.11   0.95
#> 2 alpha:(Intercept)   -5.57     -5.86    -5.30   0.95
#> 3 logsigma            -0.951    -1.42    -0.476  0.95
#> 4 logsigma            -0.777    -1.22    -0.320  0.95
#> 5 logsigma_e          -1.95     -2.07    -1.82   0.95
#> 6 rho_raw             -0.459    -1.10     0.202  0.95
# }