A Comparison of Strategies for Smoothing Parameter Selection for Mixed-Format Tests Under the Random Groups Design

Smoothing techniques are designed to improve the accuracy of equating functions. The main purpose of this study is to compare seven model selection strategies for choosing the smoothing parameter (C) for polynomial loglinear presmoothing and one procedure for model selection in cubic spline postsmoothing for mixed-format pseudo tests under the random groups design. These model selection strategies were compared for four sample sizes (500, 1,000, 2,000, and 3,000) and two content areas (Advanced Placement [AP] Biology and AP Environmental Science). For polynomial loglinear presmoothing, the Akaike information criterion (AIC) was the only statistic that reduced both random equating error and total equating error in all investigated conditions. Cubic spline postsmoothing tended to produce more accurate results than any of the model selection strategies in polynomial loglinear smoothing.