RMscoreSE: Raw-Score to Logit Score Transformation Table

In easyRasch2: Psychometric Analysis with Rasch Measurement Theory

Raw-Score to Logit Score Transformation Table

Description

For a given set of items, returns the score-to-theta lookup that maps each possible raw sum score to a person-location estimate (in logits) and its standard error. Useful when reporting a scale's measurement properties or converting raw totals to interval-scaled scores for downstream analysis.

Usage

RMscoreSE(
  data,
  method = "WLE",
  output = "kable",
  ci_multiplier = 1.96,
  point_size = 3,
  error_width = 0.5,
  theta_range = c(-10, 10)
)

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; the underlying model fit handles them.
method	Character string. Either "WLE" (default) for Warm's Weighted Likelihood Estimator computed from a CML-fitted Rasch / Partial Credit Model via psychotools, or "EAP" for Expected A Posteriori sum-score estimates from an MML-fitted model via mirt.
output	Character string controlling the return value: "kable" (default) for a formatted knitr::kable() table, "dataframe" for the underlying data.frame, or "ggplot" for a ggplot2 figure showing each raw score's logit estimate with ci_multiplier-scaled error bars.
ci_multiplier	Numeric. Multiplier applied to the standard error to draw error bars on the figure. Default 1.96 (\approx95% CI under a Gaussian approximation). Ignored when output != "ggplot".
point_size	Numeric. Point size for the figure. Default 3.
error_width	Numeric. Cap width for error bars on the figure. Default 0.5.
theta_range	Numeric length 2. Theta search range used for boundary raw scores under WLE estimation. Default c(-10, 10). Ignored when method = "EAP".

Details

The function automatically detects whether the data is dichotomous (max score 1) or polytomous (max score > 1) and selects the appropriate Rasch / Partial Credit model.

method = "WLE" fits the model by CML with psychotools::pcmodel(), centres the item thresholds to grand-mean-zero, and solves Warm's weighted-likelihood equation for each raw score with the same engine used by RMpersonParameters(); the two functions therefore report identical locations and standard errors. Warm's bias correction yields finite locations even at the minimum and maximum scores (only a root outside theta_range is clamped to the boundary with NA SE). The reported logit_se is the information-based standard error 1 / sqrt(I(theta)), matching catR, TAM and most Rasch software.

method = "EAP" fits the model with mirt::mirt(..., itemtype = "Rasch") (MML) and obtains sum-score-based EAP estimates and posterior SDs via mirt::fscores(method = "EAPsum", full.scores = FALSE, full.scores.SE = TRUE). EAP estimates are finite at all score boundaries (the prior shrinks them inward), but they depend on the assumed normal prior on theta. Item parameters from MML differ slightly from the CML values used by the WLE path; for well-behaved data the difference is small.

Value

• If output = "kable": a knitr_kable object with columns "Ordinal sum score", "Logit score", and "Logit std.error", and a caption noting the estimation method.

• If output = "dataframe": a data.frame with columns raw_score, logit_score, and logit_se (one row per possible raw sum score from 0 to the theoretical maximum).

• If output = "ggplot": a ggplot object — points at each (logit_score, raw_score) with horizontal error bars at ± ⁠ci_multiplier × logit_se⁠.

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")}

Examples

set.seed(42)
sim_data <- as.data.frame(
  matrix(sample(0:3, 200 * 6, replace = TRUE), nrow = 200, ncol = 6)
)
colnames(sim_data) <- paste0("Item", 1:6)

# Default kable output, WLE
RMscoreSE(sim_data)

# Underlying data.frame
RMscoreSE(sim_data, output = "dataframe")

# ggplot figure
if (requireNamespace("ggplot2", quietly = TRUE)) {
  RMscoreSE(sim_data, output = "ggplot")
}

# EAP via mirt
RMscoreSE(sim_data, method = "EAP")

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