RMpersonParameters: Person Locations for a Rasch / Partial Credit Model

In easyRasch2: Psychometric Analysis with Rasch Measurement Theory

Person Locations for a Rasch / Partial Credit Model

Description

Estimates a person location (theta) and its standard error of measurement (SEM) for every respondent. Estimation is performed directly on each person's observed response pattern, so partial missingness is handled correctly: two respondents with the same sum score on different subsets of items receive different estimates. This avoids the sum-score lookup used by RMscoreSE(), which assumes complete data.

Usage

RMpersonParameters(
  data,
  method = c("WLE", "EAP"),
  item_params = NULL,
  estimator = c("CML", "MML"),
  theta_range = c(-10, 10),
  prior_mean = 0,
  prior_sd = NULL,
  output = c("kable", "dataframe", "ggplot", "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.
method	Character. "WLE" (default) for Warm's Weighted Likelihood Estimate (lower bias than MLE; Warm, 1989), or "EAP" for the Expected A Posteriori estimate under a normal prior.
item_params	Optional pre-specified item parameters, e.g. for anchoring or equating. Either a named list of Andrich-threshold vectors (one per item) or the long-format data.frame returned by RMitemParameters(). When NULL (default) item parameters are estimated from data.
estimator	Character. How item parameters are estimated when item_params is NULL: "CML" (default, via psychotools) or "MML" (via mirt). Ignored when item_params is supplied.
theta_range	Numeric length 2. Search range for the WLE root and bounds for the EAP quadrature grid. Default c(-10, 10). Only if the WLE root falls outside this range is the boundary returned.
prior_mean	Numeric. Mean of the normal prior used by method = "EAP". Default 0, the natural choice when item parameters are centred at mean difficulty zero. Ignored for WLE.
prior_sd	Numeric or NULL. Standard deviation of the normal prior used by method = "EAP". When NULL (default) it is estimated from the data by marginal maximum likelihood, holding the item parameters fixed. Supply a number (e.g. 1 for a standard N(0, 1) prior, or a value carried over from a reference sample for equating) to fix it. Ignored for WLE.
output	Character. "kable" (default) for a formatted knitr::kable() table, "dataframe" for the underlying data.frame, "ggplot" for a histogram of the estimated person locations, or "file" to write the 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

Item parameters are obtained once (by CML or MML, or taken from item_params) and treated as fixed. Each person's theta is then estimated from the items they answered.

WLE solves Warm's weighted-likelihood score equation ⁠l'(theta) + J(theta) / (2 I(theta)) = 0⁠ by bracketed root finding, where the bias-correction term ⁠J / (2 I)⁠ keeps the equation solvable at the boundaries. The SEM is 1 / sqrt(I(theta)). Unlike the MLE, Warm's estimator therefore yields finite locations for the minimum and maximum possible scores (a sensible step beyond the next-most extreme score rather than +/-Inf; cf. Warm, 1989), matching established implementations such as catR and TAM. Such scores are still marked in the extreme column because they are extrapolated and carry large standard errors. Only if the root lies outside theta_range is the boundary returned with NA SEM.

EAP integrates the pattern likelihood against a normal prior over a quadrature grid; the estimate is the posterior mean and the SEM is the posterior standard deviation. Unlike WLE, EAP is finite at extreme scores because the prior shrinks them inward, at the cost of depending on the assumed prior. The prior actually used – including the marginal-ML estimate of prior_sd when it is left NULL – is reported in the kable caption and attached to the result as attr(result, "prior").

Value

For output = "dataframe", a data.frame with one row per respondent (in input order; respondents with no responses are dropped with a message) and columns theta (the person location), sem (standard error of measurement), sum_score, n_answered (number of non-missing responses), and extreme (logical: a minimum or maximum possible score given the items answered). For output = "kable", the same content as a knitr_kable object. For output = "ggplot", a histogram of theta.

References

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427-450. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02294627")}

Bock, R. D., & Mislevy, R. J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6(4), 431-444. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/014662168200600405")}

Magis, D. (2015). A note on weighted likelihood and Jeffreys modal estimation of proficiency levels in polytomous item response models. Psychometrika, 80(1), 200-204. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-013-9378-5")}

See Also

RMitemParameters(), RMscoreSE(), RMreliability()

Examples

set.seed(1)
dat <- as.data.frame(
  matrix(sample(0:2, 200 * 6, replace = TRUE), nrow = 200, ncol = 6)
)
colnames(dat) <- paste0("Item", 1:6)
# Introduce some missingness
dat[cbind(sample(200, 30), sample(6, 30, replace = TRUE))] <- NA

# Default: WLE person locations
RMpersonParameters(dat, output = "dataframe") |> head()

# EAP with a data-estimated prior SD
eap <- RMpersonParameters(dat, method = "EAP", output = "dataframe")
attr(eap, "prior")

# EAP with a fixed N(0, 1) prior
RMpersonParameters(dat, method = "EAP", prior_sd = 1, output = "dataframe") |>
  head()

# Write the person-location table to a CSV (also returned invisibly)
RMpersonParameters(dat, output = "file",
                   filename = tempfile(fileext = ".csv"))

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