Nonlinear Latent Effects in Diagnostic Classification Modeling Incorporating Response Times

The hierarchical modeling framework (van der Linden WJ, Psychometrika 72:287–308. https://doi.org/10.1007/s11336-006-1478-z, 2007) has been widely used in the analysis of item response and response time (RT) data. To utilize RT in the diagnostic classification modeling, Zhan et al. (Br J Math Statist Psychol 72:262–286. https://doi.org/10.1111/bmsp.12114, 2017) proposed the joint diagnostic classification model (DCM) of responses and RTs, where DCMs provide fine-grained diagnostic information on respondents’ latent attributes. Similar to the hierarchical modeling approach, a majority of studies assume linear relationship between RTs and the person ability (e.g., Thissen D, Timed testing: an approach using item response theory. In: DJ Weiss (ed) New horizons in testing: latent trait test theory and computerized adaptive testing. Academic, New York, pp 179–203, 1983). Recently, Molenaar et al. (Multivar Behav Res 50(1):56–74, 2015) accommodated nonlinear relationships in the joint modeling of responses and RTs to further improve the measurement precision of latent ability. In diagnostic assessments, however, such nonlinear latent effects have not been investigated yet. Therefore, the current study aims to propose joint DCMs where linear and nonlinear relationships between responses and RTs can be accommodated. As a result, the nonlinear latent effects were found in the real data analysis. In addition, ignoring nonlinear latent effects led to less accurate person parameter estimates and the decrease of attribute and pattern correct classification rates in the simulation study.