Polytomous Effectiveness Indicators in Complex Problem-Solving Tasks and Their Applications in Developing Measurement Model

Recent years have witnessed the emergence of measurement models for analyzing action sequences in computer-based problem-solving interactive tasks. The cutting-edge psychometrics process models require pre-specification of the effectiveness of state transitions often simplifying them into dichotomous indicators. However, the dichotomous effectiveness becomes impractical when dealing with complex tasks that involve multiple optimal paths and numerous state transitions. Building on the concept of problem-solving, we introduce polytomous indicators to assess the effectiveness of problem states \(d_{s}\) and state-to-state transitions \({\mathrm {\Delta }d}_{\mathrm {s\rightarrow s'}}\). The three-step evaluation method for these two types of indicators is proposed and illustrated across two real problem-solving tasks. We further present a novel psychometrics process model, the sequential response model with polytomous effectiveness indicators (SRM-PEI), which is tailored to encompass a broader range of problem-solving tasks. Monte Carlo simulations indicated that SRM-PEI performed well in the estimation of latent ability and transition tendency parameters across different conditions. Empirical studies conducted on two real tasks supported the better fit of SRM-PEI over previous models such as SRM and SRMM, providing rational and interpretable estimates of latent abilities and transition tendencies through effectiveness indicators. The paper concludes by outlining potential avenues for the further application and enhancement of polytomous effectiveness indicators and SRM-PEI.