Summarize and Plot Posterior Predictive Infit Statistics

Postprocesses the output of infit_statistic to produce summary tables of posterior predictive infit statistics and a combined slab + interval plot comparing observed infit values to the posterior predictive distribution.

Usage

infit_post(infit_draws, ci = 0.84)

Arguments

infit_draws

A data frame (or tibble) as returned by infit_statistic containing at minimum the columns item, infit (observed infit per draw), and infit_rep (replicated infit per draw).

ci

Numeric in \((0, 1)\). Width of the credible interval used for the posterior predictive HDI and the slab display. Default is 0.84.

Value

A list with three elements:

summary

A tibble with one row per item containing: item, infit_obs (posterior mean of observed infit), infit_rep (posterior mean of replicated infit), and infit_ppp (posterior predictive p-value: proportion of draws where the replicated infit exceeds the observed infit). Values near 0.5 indicate good fit; values near 0 suggest underfit; values near 1 suggest overfit.

hdi

A tibble with one row per item containing: item, underfit (posterior probability that the observed infit exceeds the upper HDI bound of the replicated distribution), and overfit (posterior probability that the observed infit falls below the lower HDI bound).

plot

A ggplot object showing the posterior predictive distribution of replicated infit (grey filled slab) overlaid with the observed infit distribution (coloured slab + interval), with a dashed reference line at 1 (perfect fit).

Details

Two complementary summary tables are provided:

summary

Reports the posterior mean observed and replicated infit values alongside the posterior predictive p-value (ppp). The ppp is the proportion of draws where the replicated infit exceeds the observed infit. Under good fit, the ppp should be near 0.5. A ppp near 0 indicates the observed infit is consistently larger than expected (underfit); a ppp near 1 indicates it is consistently smaller (overfit).

hdi

Reports the probability that the observed infit falls above (underfit) or below (overfit) the HDI of the replicated distribution. This provides a more distributional assessment than the ppp alone.

The plot uses two layers from the ggdist package:

stat_slab

Displays the posterior predictive (replicated) infit distribution as a filled density slab per item, shaded by credible interval level.

stat_slabinterval

Displays the observed infit distribution per item as a semi-transparent slab with point and interval summaries.

Under good model fit, the observed infit distribution should overlap substantially with the replicated distribution. Items where the observed distribution sits systematically above the replicated HDI indicate underfit (more variation than expected); items below indicate overfit (less variation than expected).

See also

infit_statistic, item_restscore_post.

Examples

if (FALSE) { # \dontrun{
library(brms)
library(ggplot2)

# Assuming fit_pcm is a fitted brmsfit object
infit_draws <- infit_statistic(fit_pcm)

result <- infit_post(infit_draws)
result$summary
result$hdi
result$plot
} # }