Item response theory based methods are used to compute linking constants and conduct chain linking of unidimensional or multidimensional tests for multiple groups under a common item design. The unidimensional methods include the Mean/Mean, Mean/Sigma, Haebara, and Stocking-Lord methods for dichotomous (1PL, 2PL and 3PL) and/or polytomous (graded response, partial credit/generalized partial credit, nominal, and multiple-choice model) items. The multidimensional methods include the least squares method and extensions of the Haebara and Stocking-Lord method using single or multiple dilation parameters for multidimensional extensions of all the unidimensional dichotomous and polytomous item response models. The package also includes functions for importing item and/or ability parameters from common IRT software, conducting IRT true score and observed score equating, and plotting item response curves/surfaces, vector plots, information plots, and comparison plots for examining parameter drift.