Say I have a confusion matrix of perceptual similarity data for stimuli drawn from an underlying continuous spectrum. Participants also learned to categorise these stimuli such that the spectrum is evenly divided into two categories. I want to test whether the observed confusion matrix shows a better fit to either a continuous or a categorical model. One approach I have considered is to create a hypothetical confusion matrix for linear and categorical models (see below) and correlate these with the observed confusion matrix.
Note: Similarity values, 1 = identical, 0 = dissimilar
However, I’m not sure how to compare the degree of fit for each model. One idea is to take the partial correlation to measure how well the confusion matrix correlates with the categorical model after the correlation between the linear model and the data has been accounted for. This approach seems to have good psychophysical validity (since any categorical process would function in addition to a linear sensory one), however I’m concerned that the linear and categorical models are highly correlated (here at 0.83) and so any partial correlation approach would not be valid. Including more stimuli near the category boundary would probably go some way to decorrelating these models, however I’m wondering if there is a more sensible approach to figuring this out (but not orthogonalising the models)? Any leads appreciated.