The R package equate provides methods for linking and equating measurements scales.

Install from CRAN with:

install.packages("equate")

Or install the latest development version from Github using the devtools package:

install.packages("devtools")
devtools::install_github("talbano/equate")

The general process of equating or linking is divided into three main steps:

1. Data prep, using the freqtab and presmoothing functions.
2. Linking and equating score scales, using the equate and composite functions.
3. Evaluating results, using summary methods, plot methods, and bootstrap standard errors.

Some basic instructions on using the package are included below. For a detailed intro, see the main package vignette with vignette("equatevignette", package = "equate").

Data prep starts with the freqtab function, which converts vectors and matrices of raw total scores into frequency tables of class freqtab. These are simply undimensional or multidimensional arrays with dimnames set to the full score scale of each variable.

Data can be structured according to the single-group, equivalent-groups, and nonequivalent-groups with anchor test(s) designs.

The presmoothing function fits polynomial loglinear models to frequency distributions, with support for automatic creation of polynomial terms, model fit comparisons, and plotting.

The equate function does all the work. Give it your data, the type of equating function to apply, and the method for handling nonequivalent groups if necessary. You'll get descriptive statistics, conversion tables, synthetic score distributions, standard errors, and other goodies.

Equating types include identity, mean, linear, general linear, equipercentile, circle-arc, and composites of these. Methods for nonequivalent groups include synthetic, nominal weights, Tucker, Levine observed score, Levine true score, Braun/Holland, frequency estimation, and chained equating.

A boostrap function facilitates estimation of empirical and parametric bootstrap standard errors.

summary and plot methods are available for equating and bootstrap output.