Statistical models for speech perception tests

Speech perception tests are applied to evaluate speech intelligibility of hearing-impaired subjects. Subjects in a sound laboratory listen to sentences, which they repeat back. The proportion of correctly identified test items for each sentence is the response of interest and lies between zero and one, with high frequencies at zero and one, corresponding to sentences completely misunderstood or correctly identified. Historically, these data have been analyzed in a two-step procedure. In the first step, responses in each block of sentences are aggregated to a single number, the speech perception threshold (SRT), which is the signal-to-noise ratio (SNR) at which the proportion correct is 0.5. In the second stage, SRTs are analyzed using analysis of variance techniques. We instead propose a zero-and-one inflated Beta regression model for proportion correct as the response. Several advantages are associated with the new approach: (1) complete data is employed; (2) the special distributional properties of proportion correct are accommodated in our inflated Beta distribution; (3) more inferences can be generated than that of a single threshold point; (4) random effects of subjects are considered. The proposed model is successfully applied to two sample data sets from studies, conducted by Cochlear, the company which manufactures the cochlear implants.