Response-on-Process Regression: A Statistical Model Describing Temporal Effects of Actions in Response Processes

Music City Center 

Response process data from computer-based problem-solving items capture respondents' problem-solving processes as timestamped sequences of actions. These data provide a valuable source for understanding the dynamics of problem-solving behaviors and their relationships with other variables. Due to the nonstandard format of response processes, analyzing such relationships typically involves a two-step approach: first, behavioral features are extracted from response processes using experts' knowledge or data-driven methods; then statistical or machine learning tools, such as linear or logistic regression, are applied to describe the relationship between these features and the variable of interest. In this work, we propose the response-on-process regression model, which directly links the timing of taking an action in the response process to the response variable. Unlike traditional two-step approaches, this model offers a coherent framework to characterize the temporal effects of individual actions on the response variable, providing a more nuanced understanding of problem-solving behaviors. This model also facilitates rigorous statistical inference. We demonstrate the performance of the proposed model through simulation studies and empirical analysis of PISA process data.