This dissertation investigates nonparametric item response theory (IRT) true and observed score equating under the common-item nonequivalent groups design. Nonparametric IRT is a less restrictive version of traditional parametric IRT that does not use a specific parametric function to describe the item characteristic curves (ICCs). Nonparametric IRT equating methods are expected to provide more accurate equating results than parametric IRT equating methods when the parametric model assumptions are severely violated. The main purpose of this dissertation is to investigate the conditions under which nonparametric IRT equating methods provide more accurate equating results than parametric IRT equating methods.

Four parametric IRT equating methods were considered: true and observed score equating based on separate or concurrent item parameter estimation. In addition, four nonparametric IRT equating methods were considered: true and observed score equating based on kernel smoothing ICC estimation assuming a normal or a uniform ability distribution. To compare the performance of these eight equating methods, a simulation study was conducted focusing on five factors: (1) the number of items, (2) the percentage of items that violate the parametric model assumptions, (3) the number of examinees, (4) ability distributions of two examinee groups, and (5) whether or not items have a lower asymptote parameter. In addition, a real data example was conducted to investigate the behavior of the equating methods in a realistic situation.

The results of the simulation study and the real data example suggest that (1) when the parametric model assumptions are met, parametric methods are more accurate than nonparametric methods, (2) nonparametric methods become more accurate than parametric methods as more items violate the parametric model assumptions, (3) the lower asymptote parameter affects the equating results, (4) nonparametric methods are more accurate with observed score equating than with true score equating, (5) observed score equating based on concurrent estimation appeared to be robust to the violation of the parametric model assumptions, (6) although nonparametric IRT observed score equating methods provided reasonable results in the real data example, nonparametric IRT true score equating methods produced anomalous results at the very low and very high score regions.