Softmax choice weights

Transforms a word-by-object association matrix so that Luce choice over it (as in get_perf(), mafc_test() and choice_probabilities()) is a softmax choice rule with inverse temperature phi: a word's probability of choosing object o among a set of alternatives is exp(phi * m[w, o]) / sum(exp(phi * m[w, alternatives])). Unlike Luce choice, softmax is defined for negative associations (which error-driven models such as rescorla_wagner() and kalman_filter() can learn) and gives objects a word has never been paired with nonzero probability.

Usage

softmax_weights(m, phi)

Arguments

m

A word-by-object association matrix.

phi

Inverse temperature (choice sensitivity), phi >= 0: 0 is uniform guessing, and larger values choose the strongest association more deterministically.

Value

A matrix of positive choice weights with m's dimensions and names. Each row is shifted by its maximum before exponentiating, which leaves the choice probabilities unchanged and avoids overflow.

Details

xsl_run() applies it automatically to a model with a phi parameter (e.g. rescorla_wagner(..., phi = 5)), to the mean of the simulations' matrices.

Examples

m <- matrix(c(1, -.5, 0, .2), 2, dimnames = list(1:2, 1:2))
get_perf(softmax_weights(m, phi = 3))
#>         1         2 
#> 0.9525741 0.8909032