Alternative biased choice models

Luce's Biased Choice Model has never had a serious competitor as a model of identification data. Even when it has provided a poor model of such data, other models have done even less well. Two alternative models are presented and the three are fit to a published data set. One alternative model is very much like the Biased Choice Model, differing only in the way it treats response bias. It uses an ordinal assumption about the biases and might be called the Triangular Bias (TB) model. The Guessing Mixture Model (GMM) is quite different, although it too uses the concepts of bias and similarity. It posits that the observed confusion matrix is a probability mixture of two latent matrices, the one involving only similarity, not bias, while the other involves bias, not similarity.Illustrative data, a confusion matrix based on four stimuli constructed by crossing two binary features, can be naturally described in three hierarchical ways. The most general description ignores the feature structure of the stimuli. The next description, the feature pattern model, assumes that similarity depends only on the pattern of feature differences, and the simplest special case assumes that similarity depends only on the product of similarities from each of the features.For the general description the three models are not strikingly different, with the Biased Choice Model fitting least well, followed by GMM, with TB the winner. For the independent feature form, however, the GMM model fits much better than either of the others. Indeed, the independent feature model cannot be rejected at the 10% level using GMM, even though the sample of data is large.