A Nonparametric Approach to Estimate Classification Accuracy and Consistency

When cut scores for classifications occur on the total score scale, popular methods for estimating classification accuracy (CA) and classification consistency (CC) require assumptions about a parametric form of the test scores or about a parametric response model, such as item response theory (IRT). This article develops an approach to estimate CA and CC nonparametrically by replacing the role of the parametric IRT model in Lee's classification indices with a modified version of Ramsay's kernel-smoothed item response functions. The performance of the nonparametric CA and CC indices are tested in simulation studies in various conditions with different generating IRT models, test lengths, and ability distributions. The nonparametric approach to CA often outperforms Lee's method and Livingston and Lewis's method, showing robustness to nonnormality in the simulated ability. The nonparametric CC index performs similarly to Lee's method and outperforms Livingston and Lewis's method when the ability distributions are nonnormal.