On a signal detection approach to m-alternative forced choice with bias,with maximum likelihood and Bayesian approaches to estimation

The standard signal detection theory (SDT) approach to $m$-alternative forced choice uses the proportion correct as the outcome variable and assumes that there is no response bias. The assumption of no bias is not made for theoretical reasons, but rather because it simplifies the model and estimation of its parameters. The SDT model for $m$AFC with bias is presented, with the cases of two, three, and four alternatives considered in detail. Two approaches to fitting the model are noted: maximum likelihood estimation with Gaussian quadrature and Bayesian estimation with Markov chain Monte Carlo. Both approaches are examined in simulations. SAS and OpenBUGS programs to fit the models are provided, and an application to real-world data is presented.