bayesqm

Bayesian Q methodology: probabilistic factor analysis for the study of subjective opinions.

bayesqm is the first fully Bayesian framework for Q-methodology factor analysis. Since Stephenson (1935), Q analysis has relied on frequentist factor extraction with the standard error rule of Brown (1980), which returns participant-to-factor assignments as binary flagged / unflagged decisions and offers no measure of uncertainty about them. bayesqm replaces that with posterior credible intervals for every loading, probabilistic factor membership P(dominant_i = k | Y) that makes cross-loading visible and quantifiable, and a principled K-selection protocol built on element-wise PSIS-LOO. The model uses a Student-t likelihood for robustness to idiosyncratic Q-sorts and resolves rotational, sign, and label-permutation ambiguity through the MatchAlign post-processing of Poworoznek et al. (2025). Posterior sampling is via Stan (cmdstanr or rstan).

What the package gives you

For each Q-sort dataset, bayesqm returns four things classical Q analysis cannot:

1. Posterior credible intervals for every participant loading, replacing the binary flagged / unflagged classification of Brown
   1980. with a continuous measure of assignment certainty.
2. Probabilistic factor membership, P(dominant_i = k | Y), making cross-loading visible and quantifiable rather than forcing each participant onto a single factor.
3. A peak-plus-Sivula protocol for choosing K, pairing the ELPD peak with the conservative parsimony diagnostic of Sivula et al.
   2025. and surfacing the gap between them as informative about how strongly the data discriminate adjacent models.
4. Posterior distinguishing and consensus statements, reporting P(D_j > delta | Y) and P(D_j < delta | Y) from the posterior of an explicit viewpoint-divergence measure rather than a classical significance verdict.

Installation

# install.packages("remotes")
remotes::install_github("rdazadda/bayesqm")

Stan backend

bayesqm fits models with Stan and needs a working backend: cmdstanr (recommended) or rstan.

cmdstanr is not on CRAN and is installed from the Stan R-universe. CmdStan itself must then be installed separately:

install.packages("cmdstanr", repos = c("https://stan-dev.r-universe.dev", getOption("repos")))
cmdstanr::check_cmdstan_toolchain(fix = TRUE)
cmdstanr::install_cmdstan()
cmdstanr::cmdstan_version()   # verify

On Windows you also need Rtools; on macOS, the Xcode command-line tools (xcode-select --install). See the Getting Started vignette for the full setup walkthrough and the rstan alternative.

Minimal workflow

library(bayesqm)
qdata <- read_qsort("mystudy.csv")
fit   <- fit_bayesian(qdata, K = 3)
fit

read_qsort() auto-detects CSV, Excel (including HTMLQ, FlashQ, and tablet-export variants), PQMethod .DAT, Ken-Q JSON or multi-sheet Excel, KADE ZIP, and Easy-HTMLQ Firebase JSON.

fit_bayesian() returns an object of class bayesqm_fit. Standard R accessors work as expected: coef(), fitted(), residuals(), sigma(), nobs(), family(), as.matrix(), summary(), plot(), plus posterior_interval() and prior_summary() from the rstantools API.

Choosing K

run <- run_bayes(qdata, K_max = 5)
plot_elpd(run)

run_bayes() fits the model for K = 1..K_max and reports two summaries:

• The ELPD peak: argmax of the expected log pointwise predictive density via element-wise PSIS-LOO (Vehtari, Gelman, & Gabry, 2017).
• The Sivula parsimony diagnostic (Sivula et al., 2025): a sequential rule that accepts a more complex K only when ΔELPD > 4 and |ΔELPD| / SE(Δ) > 2.

The $case field labels their relationship as agree, gap, or reversed. The ELPD peak is always the adopted K; the case label indicates how confidently the data discriminate between adjacent models, and a gap between the two is itself diagnostic information.

Probabilistic factor membership

Rather than dichotomizing each loading into flagged or unflagged, bayesqm reports the posterior probability that factor k is participant i’s dominant factor, P(dominant_i = k | Y). compute_dominant_sign() adds the posterior probability that the dominant loading is positive, so negative exemplars (a viewpoint held by opposition) stay distinct. classify_membership() turns the probabilities into a descriptive Strong / Moderate / Weak tier:

compute_dominant_prob(fit$Lambda_draws)
compute_dominant_sign(fit$Lambda_draws)
classify_membership(fit$Lambda_draws)
plot_membership(fit)

Distinguishing and consensus statements come from the posterior of an explicit viewpoint-divergence measure D_j, with the probabilities P(D_j > delta | Y) and P(D_j < delta | Y) it implies. By default delta is the reliability-adjusted critical difference from classical Q analysis (Brown, 1980; Zabala & Pascual, 2016), computed from the posterior dominant-factor counts (critical_delta()); suggest_delta() (one forced-distribution category) is an alternative:

d <- critical_delta(fit$Lambda_draws)   # default separation (computed)
compute_divergence(fit$F_draws, delta = d)
plot_dist_cons(fit)                 # uses the fit's stored divergence summary

Plotting

The package provides nine base-R plots and matching ggplot2::autoplot() methods (registered when ggplot2 and ggdist are installed). All read their palette through bayesqm_colors() and restore par() on exit:

plot(fit)                       # cross-panel z-score dotchart
plot_loading_posterior(fit)     # loadings with 50% / 95% intervals
plot_membership(fit)            # dominant-factor probability heatmap
plot_dist_cons(fit)             # distinguishing/consensus divergence forest
plot_ppc(fit)                   # posterior predictive check on by-person correlations
plot_tucker(fit)                # MatchAlign alignment quality
plot_hyper(fit)                 # hyperparameter posteriors
plot_elpd(run)                  # ELPD across K with peak / Sivula annotations

For figure export, save_bayesqm_plot() opens the appropriate device from the file extension and caption_bayesqm() returns a figure caption that reports K, N, J, chains, coverage probability, and convergence diagnostics.

Compatibility with qmethod

bayesqm_fit deliberately mirrors the slot names from the qmethod package (Zabala, 2015): $dataset, $loa, $zsc, $zsc_n, $f_char, $qdc, $flagged. $qdc is the Bayesian divergence table: per-viewpoint grid position and z-score with 95% CrI, then D_j with 95% CrI, pi_D, and pi_C, not the classical significance-label vocabulary. Intentional Bayesian divergences are documented in ?bayesqm-package:

• $flagged is defined probabilistically as P(argmax_k |λ_ik| = k) > 0.5, replacing Brown’s (1980) significance-based rule.
• $f_char$characteristics omits the classical test-theory columns; factor-score uncertainty is already in the posterior credible intervals on $ci_lower and $ci_upper.

When you have substantive factor labels, rename_factors(fit, c("a", "b", "c")) relabels every factor-indexed slot in one call.

Integration with posterior and bayesplot

as.matrix(fit), as.array(fit), and as.data.frame(fit) return draws in Stan-style parameter naming (Lambda[i,k], F[j,k], nu, sigma, tau). as_draws_df(), as_draws_matrix(), and as_draws_array() are registered for posterior::as_draws_* when posterior is installed, so bayesplot and tidybayes consume bayesqm_fit objects natively.

Citing the package

Run citation("bayesqm") for the canonical citation, or use:

Azadda, R. D., AK-ACE Team, Hueffer, K., Peter, T., & Rasmus, S. (2026). bayesqm: Bayesian Q-Methodology Factor Analysis. R package version 0.1.0. https://github.com/rdazadda/bayesqm

BibTeX is available via toBibtex(citation("bayesqm")).

Where to look next

• vignette("bayesqm-intro") walks the full workflow end to end on a synthetic Q-sort.
• ?fit_bayesian documents every prior and sampler option.
• ?run_bayes covers the peak-plus-Sivula thresholds and the three case labels.
• ?bayesqm-membership covers the probabilistic membership and distinguishing-statement summaries.
• Issues and feature requests: https://github.com/rdazadda/bayesqm/issues.

Funding

This research was, in part, funded by the National Institutes of Health (NIH) Agreement OT2HL158287 (Stacy Rasmus, Contact PI, smrasmus@alaska.edu; Karsten Hueffer and Taa’aii Peter, MPIs). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the NIH.

License

Released under the GNU General Public License version 3 (GPL-3); see https://www.gnu.org/licenses/gpl-3.0.html for the full text.