The purpose of this study was to compare the relative performance of various smoothing methods under the common item nonequivalent groups (CINEG) design. In light of the previous literature on smoothing under the CINEG design, this study aimed to provide general guidelines and practical insights on the selection of smoothing procedures under specific testing conditions.
To investigate the smoothing procedures, 100 replications were simulated under various testing conditions by using an item response theory (IRT) framework. A total of 192 conditions (3 sample size × 4 group ability difference × 2 common-item proportion × 2 form difficulty difference × 1 test length × 2 common-item type × 2 common-item difficulty spread) were investigated. Two smoothing methods including log-linear presmoothing and cubic spline postsmoothing were considered with four equating methods including frequency estimation (FE), modified frequency estimation (MFE), chained equipercentile equating (CE), and kernel equating (KE). Bias, standard error, and root mean square error were computed to evaluate the performance of the smoothing methods.
Results showed that 1) there were always one or more smoothing methods that produced smaller total error than unsmoothed methods; 2) polynomial log-linear presmoothing tended to perform better than cubic spline postsmoothing in terms of systematic and total errors when FE or MFE were used; 3) cubic spline postsmoothing showed a strong tendency to produce the least amount of random error regardless of the equating method used; 4) KE produced more accurate equating relationships under a majority of testing conditions when paired with CE; and 5) log-linear presmoothing produced smaller total error under a majority testing conditions than did cubic spline postsmoothing. Tables are provided to show the best-performing method for all combinations of testing conditions considered.