Relative Measurement Uncertainty Reliability for the Hurdle PCM

Computes posterior reliability via Relative Measurement Uncertainty (Bignardi, Kievit & Bürkner, 2025) separately for each of the two person traits in a hurdle partial credit model fitted with the hurdle_acat custom family: the presence / susceptibility trait \(\theta_{hurdle}\) and the severity trait \(\theta_{pcm}\). Internally extracts per-submodel person draws via person_parameters_hpcm and applies RMUreliability to each.

Usage

RMUreliability_hpcm(
  x,
  item_var = item,
  person_var = id,
  level = 0.95,
  verbose = FALSE,
  center = TRUE
)

Arguments

x

Either:

• a fitted brmsfit object using the hurdle_acat family, or

• the result of person_parameters_hpcm(model, draws = TRUE), i.e., a list with $hurdle$draws_matrix and $pcm$draws_matrix.

Passing a pre-computed person_parameters_hpcm() result avoids re-extracting the posterior draws from brms.

item_var

An unquoted variable name identifying the item grouping variable in the model data. Used only when x is a brmsfit; ignored otherwise. Default is item.

person_var

An unquoted variable name identifying the person grouping variable in the model data. Used only when x is a brmsfit; ignored otherwise. Default is id.

level

Numeric in \((0, 1)\). Credibility level for the highest density continuous interval on each reliability. Default is 0.95.

verbose

Logical. If TRUE, print the number of subjects and posterior draws used for each submodel. Default is FALSE.

center

Logical. If TRUE (the default), use centered person draws (mean item parameter = 0 in each submodel). The centering shift is a constant per draw and does not affect the correlation across draw halves, so reliability is invariant to this choice; the argument is exposed only for consistency with person_parameters_hpcm.

Value

A list with two elements:

hurdle

A data frame with one row containing rmu_estimate, hdci_lowerbound, and hdci_upperbound for reliability of \(\theta_{hurdle}\), as returned by RMUreliability.

pcm

Same format, for reliability of \(\theta_{pcm}\).

Details

Two reliabilities, two traits. The hurdle PCM gives every person a posterior on \(\theta_{hurdle}\) (presence / susceptibility) and on \(\theta_{pcm}\) (severity given presence). Each posterior has its own measurement uncertainty, and the RMU framework therefore yields one reliability per trait. The two values address different questions: \(\theta_{hurdle}\) reliability is about how well the items rank persons by overall endorsement (a function of how many zeros appear and how discriminating the items are at the gate), while \(\theta_{pcm}\) reliability is about how well the conditional severity is recovered (a function of how many positive responses each person provides and how spread out the PCM thresholds are). Reporting both is necessary, as emphasised in Magnus and Garnier-Villarreal (2022, p. 277).

What about all-zero responders? For persons with \(Y = 0\) on every item, no items provide information about \(\theta_{pcm}\) directly. Their posterior on \(\theta_{pcm}\) is shaped by the multivariate-normal prior linking it to \(\theta_{hurdle}\) (and is therefore wide but well-defined). These persons still contribute to the RMU calculation; their contribution is appropriately downweighted through their large posterior variance.

Computational note. When x is a brmsfit, this function calls person_parameters_hpcm(..., draws = TRUE) internally, which extracts the full posterior draws of the person random effects. For large models you may prefer to call person_parameters_hpcm once and pass its result to RMUreliability_hpcm, plot_targeting, etc.

References

Bignardi, G., Kievit, R., & Bürkner, P.-C. (2025). A general method for estimating reliability using Bayesian Measurement Uncertainty. PsyArXiv. doi:10.31234/osf.io/h54k8_v1

Magnus, B. E. & Garnier-Villarreal, M. (2022). A multidimensional zero-inflated graded response model for ordinal symptom data. Psychological Methods, 27(2), 261-279. doi:10.1037/met0000395

See also

RMUreliability for the single-trait version, person_parameters_hpcm for the underlying person draws extraction.

Examples

if (FALSE) { # \dontrun{
# Fit a hurdle PCM with the hurdle_acat() family
fit <- brms::brm(
  brms::bf(
    response | brms::thres(gr = item) ~ 1 + (1 |g| id),
    hu ~ 0 + factor(item) + (1 |g| id)
  ),
  data     = dat,
  family   = hurdle_acat(),
  stanvars = hurdle_acat_stanvars()
)

# Option 1: pass the brmsfit directly
rel <- RMUreliability_hpcm(fit)
rel$hurdle
rel$pcm

# Option 2: reuse a cached person_parameters_hpcm() result
pp  <- person_parameters_hpcm(fit, draws = TRUE)
rel <- RMUreliability_hpcm(pp)
} # }