  This paper is concerned with the nonparametric item response theory (NIRT)
for estimating item characteristic curves (ICCs) and latent abilities of
examinees on educational and psychological tests. In contrast to parametric
models, NIRT models can estimate various forms of ICCs under mild shape
restrictions, such as the constraints of monotone homogeneity and double
monotonicity. However, NIRT models frequently suffer from estimation
instability because of the great flexibility of nonparametric ICCs, especially
when there is only a small amount of item-response data. To improve the
estimation accuracy, we propose a novel NIRT model constrained by monotone
homogeneity and smoothness based on ordered latent classes. Our smoothness
constraints avoid overfitting of nonparametric ICCs by keeping them close to
logistic curves. We also implement a tailored expectation--maximization
algorithm to calibrate our smoothness-constrained NIRT model efficiently. We
conducted computational experiments to assess the effectiveness of our
smoothness-constrained model in comparison with the common two-parameter
logistic model and the monotone-homogeneity model. The computational results
demonstrate that our model obtained more accurate estimation results than did
the two-parameter logistic model when the latent abilities of examinees for
some test items followed bimodal distributions. Moreover, our model
outperformed the monotone-homogeneity model because of the effect of the
smoothness constraints.
