A Latent Class Extension of Signal Detection Theory, with Applications.

A latent class extension of signal detection theory is presented and applications are illustrated. The approach is useful for situations where observers attempt to detect latent categorical events or where the goal of the analysis is to select or classify cases. Signal detection theory is shown to offer a simple summary of the observers' performance in terms of detection and response criteria. Implications of the view via signal detection for the training of raters are noted, as are approaches to validating the parameters and classifications. An extension of the signal detection model to more than two latent classes, with a simple restriction on the detection parameters, is introduced. Sample programs to fit the models using software for latent class analysis or software for second generation structural equation modeling are provided.