Bayesian Rasch Analysis Using 'brms'

Reproduces classic Rasch psychometric analysis features using Bayesian item response theory models fitted with 'brms' following Bürkner (2021) and Bürkner (2020) . Supports dichotomous and polytomous Rasch models, and a hurdle partial credit model. Features include posterior predictive item fit, including infit and item-restscore associations conditional on the total score, person fit, differential item functioning, local dependence assessment via Q3 residual correlations, dimensionality assessment with residual principal components analysis, person-item targeting plots, item category probability curves, and reliability using relative measurement uncertainty following Bignardi et al. (2025) .

easyRaschBayes

easyRaschBayes provides Rasch measurement theory analysis workflows for Bayesian item response theory models fitted with brms. It supports dichotomous Rasch models, partial credit and rating scale models, and a hurdle partial credit model for data with many zero responses. All output exposes the full posterior distribution.

The frequentist counterpart is easyRasch2, which uses conditional maximum likelihood and simulation-based critical values. Both packages include the same phq9 example data, and their vignettes analyse it side by side. For broader Rasch-analysis tutorials, see the vignette for the archived package easyRasch.

Statement of need

brms fits Rasch-family models flexibly, with full posterior uncertainty and with extensions such as person covariates, extra facets and custom families (Bürkner, 2021). It does not provide the diagnostics a Rasch analysis needs: item fit, local dependence, dimensionality, differential item functioning, response category functioning, targeting and reliability. easyRaschBayes provides these for brms models, with one consistent interface, and reports each diagnostic with its posterior uncertainty.

Installation

Install the stable version from CRAN:

install.packages("easyRaschBayes")

Or install the development version from GitHub:

# install.packages("remotes") # if needed
remotes::install_github("pgmj/easyRaschBayes")

The development version changes several defaults and outputs, among them conditional item fit given the total score and a new targeting plot. See the changelog.

The hurdle partial credit model needs a patched version of brms, since CRAN brms 2.23 cannot fit custom ordinal families with item-specific thresholds:

remotes::install_github("rpsychologist/brms@fix-custom-ordinal-grouped-thres")

Key design principles

• Estimation: models are fitted with brms and Stan. Item thresholds are read from the posterior draws in the same way by every function, for partial credit models (thres(gr = item)), rating scale models and dichotomous models with fixed or random item effects. Person locations are posterior means (EAP), with Warm's weighted likelihood estimates (WLE) as an alternative.
• Inference: posterior predictive checks. For Rasch-family models the total score is sufficient for the person location, and item fit and local dependence are computed conditional on it: item-restscore associations are compared with their expected values given the total scores (Kreiner, 2011), and infit follows the conditional infit of Christensen et al. (2013). Replicated data are drawn conditional on each person's total score. In null simulations the restscore and Q3 posterior predictive p-values were close to uniform, while infit stays conservative, so infit and restscore are meant to be used together. Posterior predictive p-values are not measures of the size of misfit.
• Output: tibbles for tables and ggplot2 figures. Infit, item-restscore and Q3 are computed per draw by *_statistic() functions and summarised and plotted by *_post() functions, so the draws stay available for further analysis.
• Naming: snake_case, with the suffix _hpcm for functions for the hurdle partial credit model.

Functions by domain

Item fit

• infit_statistic() + infit_post(): conditional infit (and outfit) mean squares with posterior predictive p-values; method = "theta" for infit given each draw's person locations
• item_restscore_statistic() + item_restscore_post(): item-restscore association (Goodman-Kruskal's gamma) against its expected value given the total scores, with a max-T adjustment for the number of items
• plot_icc(): conditional item characteristic curves in class intervals of the total score
• fit_statistic_pcm(), fit_statistic_rm(): general posterior predictive item and person fit with user-supplied criteria

Local dependence

• q3_statistic() + q3_post(): Yen's Q3 residual correlations given the total scores, against replicated data, with a max-T adjustment for the number of item pairs; method = "theta" for residuals given each draw's person locations

Dimensionality

• plot_residual_pca(): first residual contrast, observed against replicated eigenvalue, with item loadings and locations

Differential item functioning

• dif_statistic(): refits the model with item-specific group differences, estimates the difference in latent means (impact) separately, and summarises the posterior of each item's DIF
• plot_icc() with dif_var: conditional item characteristic curves by group, with partial gamma

Response categories

• plot_ipf(): item category probability curves with credible bands
• item_parameters(): thresholds, with the posterior probability that each item's thresholds are disordered

Targeting and reliability

• plot_targeting(): person-item targeting plot with the ranges where each response category is the most likely, threshold credible intervals, and the posterior probability of collapsed categories and disordered thresholds
• RMUreliability(): reliability from relative measurement uncertainty (Bignardi et al., 2026)

Item and person parameters

• item_parameters(): item locations and thresholds with credible intervals
• person_parameters(): EAP and WLE person locations, and a sum score to WLE table
• posterior_to_prior(): informative priors from a fitted model, for use in a new model

Hurdle partial credit model

• hurdle_acat() + hurdle_acat_stanvars(): custom brms family: a hurdle for any response above 0 and a partial credit model for the positive categories, each with its own person location
• infit_statistic_hpcm(), q3_statistic_hpcm(), item_parameters_hpcm(), person_parameters_hpcm(), RMUreliability_hpcm(), plot_icc_hpcm(), plot_targeting_hpcm(): the diagnostics above for each part of the model

Data visualization

• plot_tile(), plot_bars(), plot_stackedbars(): response distributions from wide data

Data

• phq9: PHQ-9 depression screener, 600 NHANES respondents selected to have few zero sum scores, with gender, age and education. The same data as in easyRasch2
• phq9_nhanes: PHQ-9, a random sample of 1000 NHANES respondents with the many zero responses of a general population sample, for the hurdle partial credit model

Vignettes

• Rasch partial credit model, a full analysis of phq9
• Hurdle partial credit model, phq9_nhanes analysed with an ordinary and a hurdle partial credit model

There is also a comparison with frequentist Rasch tools in R.

Example

library(brms)
library(dplyr)
library(tidyr)
library(tibble)
library(easyRaschBayes)

# Long format, one row per person and item. The acat family expects
# response categories starting at 1.
df <- phq9[, 1:9] %>%
  rownames_to_column("id") %>%
  pivot_longer(!id, names_to = "item", values_to = "response") %>%
  mutate(response = response + 1)

# Partial credit model
fit <- brm(
  response | thres(gr = item) ~ 1 + (1 | id),
  data   = df,
  family = acat,
  chains = 4, cores = 4
)

# Conditional item fit: item-restscore and infit
item_restscore_post(item_restscore_statistic(fit))
infit_post(infit_statistic(fit))

# Local dependence with Yen's Q3
q3_post(q3_statistic(fit))

# Response categories and targeting
plot_ipf(fit)
plot_targeting(fit)

References

• Bignardi, G., Kievit, R., & Bürkner, P.-C. (2026). A general method for estimating reliability using Bayesian measurement uncertainty. OSF. https://osf.io/preprints/psyarxiv/h54k8
• Bürkner, P.-C. (2020). Analysing Standard Progressive Matrices (SPM-LS) with Bayesian item response models. Journal of Intelligence, 8(1). https://doi.org/10.3390/jintelligence8010005
• Bürkner, P.-C. (2021). Bayesian item response modeling in R with brms and Stan. Journal of Statistical Software, 100, 1–54. https://doi.org/10.18637/jss.v100.i05
• Christensen, K. B., Kreiner, S., & Mesbah, M. (Eds.) (2013). Rasch models in health. ISTE and Wiley.
• Kreiner, S. (2011). A note on item-restscore association in Rasch models. Applied Psychological Measurement, 35(7), 557–561. https://doi.org/10.1177/0146621611410227
• Magnus, B. E., & Garnier-Villarreal, M. (2022). A multidimensional zero-inflated graded response model for ordinal symptom data. Psychological Methods, 27(2), 261–279. https://doi.org/10.1037/met0000395
• Müller, M. (2020). Item fit statistics for Rasch analysis: Can we trust them? Journal of Statistical Distributions and Applications, 7(1), 5. https://doi.org/10.1186/s40488-020-00108-7

Credits

This started as a small side project to update the code to assess item fit included in Bürkner (2020). With the help of Claude Opus things expanded to try to reproduce core Rasch analysis aspects with Bayesian methods. Most of the code in this package is produced by the LLM.

Magnus Johansson is a licensed psychologist with a PhD in behavior analysis. He works as a research specialist at Karolinska Institutet, Department of Clinical Neuroscience, Center for Psychiatry Research.

• ORCID: 0000-0003-1669-592X
• Bluesky: @pgmj.bsky.social

License

GPL (>= 3)