Extensions of multinomial processing tree models for continuous variables: A simulation study comparing parametric and non-parametric approaches

Both parametric and non-parametric extensions of the multinomial processing tree (MPT) models have been proposed for jointly modeling discrete and continuous variables. Since the two approaches have not yet been compared systematically, we assess their power and robustness in three simulation studies focusing on the weapon identification task. In this context, two statistically equivalent MPT models have been proposed, namely, the preemptive-conflict-resolution model (PCRM) and the default-interventionist model (DIM), which differ only in their assumptions regarding the order of latent processes (i.e., response times, RTs). The first simulation evaluates the calibration and statistical power of the nonstandard goodness-of-fit test for the parametric approach (i.e., the Dzhaparidze-Nikulin statistic), as well as the ability of different distributional assumptions to fit simulated RT data. The second simulation compares nested models to study the power for testing hypotheses about RTs within each model. The third simulation focuses on model-recovery performance for the two non-nested models. In all three simulations, we manipulated the size and nature of discrepancies (location/scale or shape) between latent RT distributions, sample size, and parametric assumptions. Results show that the parametric approach has higher statistical power but is also sensitive to misspecifications of distributional assumptions. In contrast, the non-parametric approach is more robust but less powerful, especially with small samples. We provide recommendations on when to use each approach and highlight the importance of properly specifying and selecting extended MPT models.