Characterizing Learning by Simultaneous Analysis of Continuous and Binary Measures of Performance

1 Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, Massachusetts; 2 Department of Brain and Cognitive Sciences and 3 McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts; 4 Center for Neural Science, New York University, New York City, New York; 5 Division of Health Sciences and Technology, Harvard Medical School/Massachusetts Institute of Technology, Cambridge, Massachusetts; 6 Department of Mathematics and Statistics and 7 Program in Neuroscience, Boston University, Boston, Massachusetts Submitted 24 November 2008; accepted in final form 17 August 2009 ABSTRACT Continuous observations, such as reaction and run times, and binary observations, such as correct/incorrect responses, are recorded routinely in behavioral learning experiments. Although both types of performance measures are often recorded simultaneously, the two have not been used in combination to evaluate learning. We present a state-space model of learning in which the observation process has simultaneously recorded continuous and binary measures of performance. We use these performance measures simultaneously to estimate the model parameters and the unobserved cognitive state process by maximum likelihood using an approximate expectation maximization (EM) algorithm. We introduce the concept of a reaction-time curve and reformulate our previous definitions of the learning curve, the ideal observer curve, the learning trial and between-trial comparisons of performance in terms of the new model. We illustrate the properties of the new model in an analysis of a simulated learning experiment. In the simulated data analysis, simultaneous use of the two measures of performance provided more credible and accurate estimates of the learning than either measure analyzed separately. We also analyze two actual learning experiments in which the performance of rats and of monkeys was tracked across trials by simultaneously recorded reaction and run times and the correct and incorrect responses. In the analysis of the actual experiments, our algorithm gave a straightforward, efficient way to characterize learning by combining continuous and binary measures of performance. This analysis paradigm has implications for characterizing learning and for the more general problem of combining different data types to characterize the properties of a neural system. Address for reprint requests and other correspondence: E. N. Brown, Ne