A joint modeling framework of responses and response times to assess learning outcomes.

A general modeling framework of response accuracy and response times is proposed to track skill acquisition and provide additional diagnostic information on the change of latent speed in a learning environment. This framework consists of two types of models: a dynamic response model that captures the response accuracy and the change of discrete latent attribute profile upon factors such as practice, intervention effects, and other latent and observable covariates, and a dynamic response time model that describes the change of the continuous response latency due to change of latent attribute profile. These two types of models are connected through a parameter, describing the change rate of the latent speed through the learning process, and a covariate defined as a function of the latent attribute profile. A Bayesian estimation procedure is developed to calibrate the model parameters and measure the latent variables. The estimation algorithm is evaluated through several simulation studies under various conditions. The proposed models are applied to a real data set collected through a spatial rotation diagnostic assessment paired with learning tools.