IRT test equating with the R package equateIRT
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**Keywords**: Equating, Item Response Theory, Multiple Forms, Scoring, Testing.

**Webpages**: https://CRAN.R-project.org/package=equateIRT

In many testing programs, security reasons require that test forms are composed of different items, making test scores not comparable across different administrations. The equating process aims to provide comparable test scores. This talk focuses on Item Response Theory (IRT) methods for dichotomous items. In IRT models, the probability of a correct response depends on the latent trait under investigation and on the item parameters. Due to indentifiability issues, the latent variable is usually assumed to have zero mean and variance equal to one. Hence, when the model is fitted separately for different groups of examinees, the item parameter estimates are expressed on different measurement scales. The scale conversion can be achieved by applying a linear transformation of the item parameters, and the coefficients of this equation are called equating coefficients. This talk explains the functionalities of the*R* package **equateIRT** (Battauz 2015), which implements the estimation of the equating coefficients and the computation of the equated scores. Direct equating coefficients between pairs of forms that share some common items can be estimated using the mean-mean, mean-geometric mean, mean-sigma, Haebara and Stocking-Lord methods. However, the linkage plans are often quite complex, and not all forms can be linked directly. As proposed in Battauz (2013), the package computes also the indirect equating coefficients for a chain of forms and the average equating coefficients when two forms can be linked through more than one path. Using the equating coefficients so obtained, the item parameter estimates are converted to a common metric and it is possible to compute comparable scores. For this task, the package implements the true score equating and the observed score equating methods. Standard errors of the equating coefficients and the equated scores are also provided.

References Battauz, Michela. 2013. “IRT Test Equating in Complex Linkage Plans.”*Psychometrika* 78 (3): 464–80. doi:10.1007/s11336-012-9316-y.

———. 2015. “EquateIRT: An R Package for Irt Test Equating.”*Journal of Statistical Software* 68 (1): 1–22. doi:10.18637/jss.v068.i07.

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In many testing programs, security reasons require that test forms are composed of different items, making test scores not comparable across different administrations. The equating process aims to provide comparable test scores. This talk focuses on Item Response Theory (IRT) methods for dichotomous items. In IRT models, the probability of a correct response depends on the latent trait under investigation and on the item parameters. Due to indentifiability issues, the latent variable is usually assumed to have zero mean and variance equal to one. Hence, when the model is fitted separately for different groups of examinees, the item parameter estimates are expressed on different measurement scales. The scale conversion can be achieved by applying a linear transformation of the item parameters, and the coefficients of this equation are called equating coefficients. This talk explains the functionalities of the

References Battauz, Michela. 2013. “IRT Test Equating in Complex Linkage Plans.”

———. 2015. “EquateIRT: An R Package for Irt Test Equating.”

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