csemGT: An R Package for Estimating Raw-Score Conditional Standard Errors of Measurement in Generalizability Theory

Description

More than a quarter of a century ago, Brennan (1998) presented a general framework for estimating conditional standard errors of measurement (CSEMs) within Generalizability Theory (GT). For the univariate, single-facet, persons-by-items (p × i) crossed design, this approach yields person-specific estimates of absolute error variance (suited to criterion-referenced interpretations) and three estimates of relative error variance (relevant to norm-referenced testing).

Compared with alternative methods (see Lee & Harris, 2025, for a recent review), GT-based CSEM estimation offers several advantages: it requires only a single test administration, uses information from all items, accommodates dichotomous, ordinal, and continuous item responses, does not require grouping examinees by observed score, and assumes neither a specific latent variable model nor a particular distributional form for item responses. For dichotomous items, two of Brennan’s estimators also coincide with the well-known Lord and Keats-Lord binomial CSEMs. Despite these strengths, GT-based CSEM procedures have seen limited use in applied measurement.

This limited adoption stems in part from the scarcity of accessible software. Among traditional GT programs, only mGENOVA (Brennan, 2001) computes CSEMs, yet it implements only the absolute estimator and one of the three relative estimators. A more complete implementation has recently become available as gtcsem (Gempp, 2026), a user-written Stata command (StataCorp, 2025). However, no current R package provides the full set of GT-based raw-score CSEM estimators. The package gtheoryr (Tyagi, 2026) fits basic generalizability designs but does not provide CSEMs, while emreliability (Liu et al., 2025) computes some per-person CSEMs outside the GT framework. The latest version of JASP (JASP Team, 2026) includes CSEM estimators that are not GT-based.

The csemGT package fills this gap. Its core function, csem_gt(), accepts a balanced persons-by-items data matrix and computes, for each person, the absolute error variance in closed form (Brennan, 1998, Equation 20) and the relative error variance using any of the full, large_a, or uncorrelated estimators. These computations follow the corresponding formulations presented in Brennan (1998), specifically Equation 20 for absolute error variance and Equations 35–36, 40, and 41 for the relative-error variance estimators. Standard errors of CSEMs estimates can be obtained via closed-form analytical variances or item-resampling bootstrap.

Additional features include quadratic smoothing of CSEMs across the observed-score distribution, D-study extrapolation of CSEMs to alternate test lengths, and basic plotting capabilities. Resulting csem objects support print(), summary(), plot(), and coef() methods. Beyond CSEMs, the package also reports standard G-study and D-study results under the p × i design, including estimated variance components, generalizability coefficients, phi and phi(λ) coefficients, and overall absolute and relative error variances. Two synthetic datasets are included: iowa_like, based on Brennan (1998) ITED example, and ipip_like, a Likert-type conscientiousness scale.