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Compute posterior density of the DP mixture

dpmirt_dp_density.Rd

Samples from the posterior Dirichlet Process mixing distribution using NIMBLE's getSamplesDPmeasure() and evaluates the resulting mixture density on a grid. The density is computed by summing weighted Normal components from the DP base measure.

Usage

dpmirt_dp_density(
  fit,
  grid = seq(-6, 6, length.out = 500),
  credible_interval = 0.95,
  apply_rescaling = TRUE,
  verbose = TRUE,
  ...
)

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

Arguments

fit

A dpmirt_fit object with prior = "dpm".

grid

Numeric vector. Grid points for density evaluation. Default: seq(-6, 6, length.out = 500).

credible_interval

Numeric. Width of the pointwise credible band. Default: 0.95 (i.e., 95 percent band).

apply_rescaling

Logical. If TRUE (default), shift the grid by the retained-draw-specific location shift from post-hoc rescaling. Only changes output for unconstrained Rasch/location-shift fits.

verbose

Logical. Print progress messages. Default TRUE.

...

Additional arguments (currently unused).

x

A dpmirt_dp_density object.

Value

A list of class dpmirt_dp_density containing:

grid

Numeric vector of evaluation points.

density_mean

Numeric vector of posterior mean densities.

density_lower

Numeric vector of lower credible band.

density_upper

Numeric vector of upper credible band.

density_samples

Matrix (n_retained_draws x length(grid)) of per-retained-draw densities (for custom summaries).

dp_samples

List from getSamplesDPmeasure() – each element is a matrix with columns (weights, means, variances).

ci_level

The credible interval level used.

Details

This function follows Paganin et al.'s (2023) workflow:

  1. Extract posterior samples for DP parameters (alpha, zi, muTilde, s2Tilde) from the fitted model.

  2. Reconstruct a NIMBLE model and MCMC with monitors set to only DP parameters.

  3. Populate the MCMC's sample storage with the posterior samples using NIMBLE modelValues accessors.

  4. Call getSamplesDPmeasure() to compute stick-breaking weights and atoms for each posterior draw.

  5. Evaluate the mixture density f(x|Gs) = sum_k w_k * phi(x; mu_k, s2_k) for each posterior sample s and grid point x.

For Rasch models with unconstrained identification, a location shift (mean(beta) per iteration) is applied so the density is on the rescaled theta scale. For 2PL/3PL IRT and SI parameterizations, full transformed-scale density reconstruction would also require scale and Jacobian adjustments. The current implementation applies the Rasch/location-shift contract, so DP densities for transformed-scale 2PL/3PL fits should be treated as diagnostic summaries rather than definitive latent-density estimates.

See also

dpmirt, dpmirt_plot_dp_density

Examples

if (FALSE) { # \dontrun{
sim <- dpmirt_simulate(200, 20, model = "rasch",
                       latent_shape = "bimodal", seed = 42)
fit <- dpmirt(sim$response, model = "rasch", prior = "dpm",
              niter = 10000, nburnin = 3000, seed = 123)

# Compute DP density on default grid
dpd <- dpmirt_dp_density(fit)
print(dpd)

# Custom grid
dpd2 <- dpmirt_dp_density(fit, grid = seq(-4, 4, length.out = 200))
} # }