A Semiparametric Approach for Modeling Not-Reached Items

Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory model for NRIs by (1) including a semiparametric representation of the distribution of the onset of NRIs, (2) modeling the relationships of NRIs with proficiency via a flexible multinomial logit regression, and (3) including additional covariates to predict NRIs. We show that Glas and Pimentel's and our model have close connections to event history analysis, thereby making it possible to apply tools developed in this context to the analysis of NRIs. Our model was applied to a timed low-stakes test of mathematics achievement. Our model fitted the data better than Glas and Pimentel's model, and allowed for a more fine-grained assessment of the onset of NRIs. The results of a simulation study showed that our model accurately recovered the relationships of proficiency and covariates with the onset of NRIs, and reduced bias in the estimates of item parameters, proficiency distributions, and covariate effects on proficiency.