Separating Predicted Randomness from Residual Behavior

We propose a novel measure of goodness of fit for stochastic choice models: that is, the maximal fraction of data that can be reconciled with the model. The procedure is to separate the data into two parts: one generated by the best specification of the model and another representing residual behavior. We claim that the three elements involved in a separation are instrumental to understanding the data. We show how to apply our approach to any stochastic choice model and then study the case of four well-known models, each capturing a different notion of randomness. We illustrate our results with an experimental dataset.