A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

Continuous (reaction times) and binary (correct/ incorrect responses) measures of performance are routinely recorded to track the dynamics of a subject's cognitive state during a learning experiment. Current analyses of experimental data from learning studies do not consider the two performance measures together and do not use the concept of the cognitive state formally to design statistical methods. We develop a mixed filter algorithm to estimate the cognitive state modeled as a linear stochastic dynamical system from simultaneously recorded continuous and binary measures of performance. The mixed filter algorithm has the Kalman filter and the more recently developed recursive filtering algorithm for binary processes as special cases. In the analysis of a simulated learning experiment the mixed filter algorithm provided a more accurate and precise estimate of the cognitive state process than either the Kalman or binary filter alone. In the analysis of an actual learning experiment in which a monkey's performance was tracked by its series of reaction times, and correct and incorrect responses, the mixed filter gave a more complete description of the learning process than either the Kalman or binary filter. These results establish the feasibility of estimating cognitive state from simultaneously recorded continuous and binary performance measures and suggest a way to make practical use of concepts from learning theory in the design of statistical methods for the analysis of data from learning experiments.