RMitemParameters: Item Parameters for a Rasch / Partial Credit Model

In easyRasch2: Psychometric Analysis with Rasch Measurement Theory

Item Parameters for a Rasch / Partial Credit Model

Description

Estimates item difficulty (dichotomous) or item-category threshold (polytomous) parameters and returns them in long or wide format, with optional standard errors and Wald confidence intervals. Item parameters are estimated by conditional maximum likelihood (CML, via psychotools) by default, with marginal maximum likelihood (MML, via mirt) available for sparse data where CML can be unstable.

Usage

RMitemParameters(
  data,
  estimator = c("CML", "MML"),
  format = c("long", "wide"),
  se = TRUE,
  ci_level = 0.95,
  center = TRUE,
  output = c("kable", "dataframe", "file"),
  filename = NULL
)

Arguments

data	A data.frame or matrix of item responses. Items must be scored starting at 0 (non-negative integers). Missing values (NA) are allowed; both estimators handle them.
estimator	Character. "CML" (default) estimates item parameters with psychotools::pcmodel() (a dichotomous item is a 2-category PCM); "MML" uses mirt::mirt() with itemtype = "Rasch". CML is preferred for Rasch measurement; MML can be more robust when data are sparse. When estimator = "CML" and sparse response categories are detected, a warning suggests switching to MML.
format	Character. "long" (default) returns one row per item (dichotomous) or per item-threshold (polytomous); "wide" returns one row per item with threshold columns t1, t2, ... plus a mean location column.
se	Logical. If TRUE (default), standard-error and confidence-interval columns are added.
ci_level	Numeric in (0, 1). Confidence level for the Wald interval (⁠estimate +/- z * SE⁠). Default 0.95.
center	Logical. If TRUE (default), all thresholds are shifted so their grand mean is zero, the usual Rasch identification. CML estimates are already centred; the shift mainly affects the MML path, keeping the two estimators on a common scale.
output	Character. "kable" (default) for a formatted knitr::kable() table, "dataframe" for the underlying data.frame, or "file" to write that data.frame to a CSV at filename (the data.frame is also returned invisibly).
filename	Character. Path to the CSV file to write when output = "file". Required in that case; ignored otherwise.

Details

Items are detected as dichotomous (maximum score 1) or polytomous (maximum score > 1), and the Rasch or Partial Credit model is chosen accordingly. Thresholds are reported as Andrich thresholds (the person locations at which adjacent response categories are equally probable) on the logit difficulty scale, matching RMtargeting().

Standard errors. For the CML path, threshold SEs are the square roots of the diagonal of the threshold-parameter covariance from psychotools::threshpar(vcov = TRUE). For the MML path, SEs come from the mirt parameter covariance, propagated by the delta method through the linear threshold map. Confidence intervals are Wald intervals and are symmetric on the logit scale.

Value

For output = "dataframe", a data.frame. In long format the columns are item, threshold (integer; 1 for dichotomous items), location, and – when se = TRUE – se, ci_lower, ci_upper. In wide format the columns are item, the threshold locations (t1, t2, ... or location for dichotomous items), and a mean location; when se = TRUE, matching se_t1, se_t2, ... columns are appended. For output = "kable", the same content as a knitr_kable object.

References

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02293814")}

Mair, P., & Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v020.i09")}

See Also

RMpersonParameters(), RMscoreSE(), RMtargeting()

Examples

set.seed(1)
poly <- as.data.frame(
  matrix(sample(0:2, 250 * 5, replace = TRUE), nrow = 250, ncol = 5)
)
colnames(poly) <- paste0("Item", 1:5)

# Default: long-format kable with SE and 95% CI
RMitemParameters(poly)

# Wide format, point estimates only
RMitemParameters(poly, format = "wide", se = FALSE, output = "dataframe")

# Dichotomous data
dich <- as.data.frame(
  matrix(sample(0:1, 250 * 6, replace = TRUE), nrow = 250, ncol = 6)
)
colnames(dich) <- paste0("Item", 1:6)
RMitemParameters(dich, output = "dataframe")

# Write the parameter table to a CSV (also returned invisibly)
RMitemParameters(poly, output = "file",
                 filename = tempfile(fileext = ".csv"))

easyRasch2 documentation built on Sept. 13, 2026, 1:07 a.m.