Summarize and print a tulpa fit

print() shows a fit in a few lines: how it was produced (backend and inference tier), the call, the observation count and the fixed-effect point estimates. summary() returns the full report as a summary.tulpa_fit object, which prints as a sectioned display and whose parts are read by name; coef() on it returns the fixed-effect table.

Usage

# S3 method for class 'tulpa_fit'
print(x, ...)

# S3 method for class 'tulpa_fit'
summary(object, level = 0.95, ...)

# S3 method for class 'summary.tulpa_fit'
coef(object, ...)

# S3 method for class 'summary.tulpa_fit'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x: A tulpa_fit object (print.tulpa_fit()) or a summary.tulpa_fit object (print.summary.tulpa_fit()).
...: Ignored.
object: A tulpa_fit object.
level: Credible-interval level of the fixed-effect table, a single number in (0, 1) (default 0.95).
digits: Significant digits in the printed tables.

Value

print.tulpa_fit() and print.summary.tulpa_fit() return their input invisibly.

summary.tulpa_fit() returns a list of class summary.tulpa_fit:

call, formula, family: as the fit records them, NULL where it records none.
inference: how the fit was produced: a list of backend, inference_tier, inference_mode and selection_reason (why mode = "auto" chose that backend).
n_obs, n_draws: the observation count and the number of posterior draws the fixed-effect summaries read (NULL without draws).
level: the interval level of coefficients.
coefficients: data frame, one row per fixed effect named by the term: estimate, std.error and the lower / upper credible bounds, labelled as confint.tulpa_fit() labels them. Carries the interval_source, interval_declined, retained_mass and skew_applied attributes described in Details. Also returned by coef() on the summary.
random: the random-effect standard deviations as VarCorr() reports them, with their estimated / sampled / conditioned label; NULL on a fit with no random-effect terms.
hyperparameters: data frame of the integrated hyperparameters, one row each: parameter, mean, sd, median and the 2.5% / 97.5% bounds ci_lo / ci_hi. On a nested-Laplace fit these are the outer-grid axes; on the random-effect covariance integrators the derived standard deviations and correlations. NULL where the fit integrated none.
sigma: the residual / dispersion scale a fit reports as one number, else NULL.
smooth_terms: the fit's s(...) term metadata, NULL without smoothers; smooth_effects() returns the fitted curves.
reliability: a list: kind ("chain", "iid" or "point", the draws provenance diagnostics() routes on); on a chain rhat_max, ess_bulk_min and ess_tail_min over the parameters; on i.i.d. draws band, the one-row headline diagnostics() attaches as its summary attribute (outer pareto_k and its band, grid quadrature ESS, inner-Laplace scores, reliability), and moment_source, which read the per-parameter moments came from; verdict, the whole-fit reading ("converged" / "not converged" on a chain that records its convergence check, the combined reliability verdict on i.i.d. draws, NA otherwise); convergence, the fit's own convergence record; and the backend-specific quality numbers mean_accept (Metropolis acceptance rate), n_divergent (divergent transitions) and elbo (the variational objective), each NULL where the backend has none.
axis_fields_dropped: the grid axes the fit's own resolved path could not read, one row per dropped field (block, type, field, path, integrates, reason); NULL whenever every supplied axis was used. diagnostic_summary() reads the same record in sentences.
prior: a list whose beta is the Gaussian fixed-effect prior the fit ran under, as list(mean, sd): the engine default prior_normal(0, 2.5) whenever the caller supplied none, and NULL on the paths that express no Gaussian prior on the fixed effects.

coef.summary.tulpa_fit() returns the coefficients data frame.

Details

The fixed-effect table reads the same posterior coef(), confint() and vcov() read. Sampler tiers report empirical quantiles; the Laplace tier reports the Gaussian approximation, and so does any fit whose reported posterior is a closed-form Gaussian (expectation propagation, the multinomial Laplace fit), whose draws are then samples from that Gaussian and are not what the summary reads.

On a nested-Laplace fit the estimate and standard error are the hyperparameter-grid-marginalized moments, and the bounds invert the Gaussian mixture sum_k w_k N(mu_kj, V_kjj) that grid defines, rather than reading mu +/- z sigma off the single Gaussian matching those moments. The table's interval_source attribute records which read produced them ("mixture_cdf", "gaussian_moment", "skew_map_cell", or "skew_map_cell/mixture_cdf" when the two are in play on different coefficients) and interval_declined says why, whenever the mixture read did not run. Its retained_mass attribute gives the share of the grid weight whose cells retained a fixed-effect block: 1 on a complete grid, and below 1 on one that dropped a positive-weight cell, whose report is then the posterior conditional on the cells that remain.

Where no per-cell block was retained the estimate falls back to the grid-weighted average of the per-cell modes, restricted to the cells whose inner solve reached a mode. A fit where none did reports NA with interval_declined = "not_converged", rather than the vector its Newton started from as an estimate.

With control$skew_correct = TRUE a coefficient whose inner-Laplace gamma_3 is in the band it is valid on reports Cornish-Fisher quantiles instead, and the table's skew_applied attribute names which coefficients took the correction. That correction is measured at the MAP cell, so it is reported on its own and is not composed with the mixture read; a coefficient it declines keeps the mixture read rather than falling back further.

The reliability headline is read from diagnostics(), so it answers the question that applies to how the draws were produced: Rhat and effective sample size for a chain, the approximation-reliability band (outer Pareto-k, grid quadrature, inner Laplace, combined verdict) for i.i.d. draws from a deterministic approximation, and nothing for a point summary.

Examples

set.seed(1)
df <- data.frame(x = rnorm(60))
df$y <- rpois(60, exp(0.5 + 0.3 * df$x))
fit <- tulpa(y ~ x, data = df, family = "poisson", mode = "laplace")
fit
s <- summary(fit)
s
coef(s)
s$inference$backend

Usage

Arguments

Value

Details

See also

Examples