Development of a multi-category psychometric function to model categorical loudness measurements

A multi-category psychometric function (MCPF) is introduced for modeling the stimulus-level dependence of perceptual categorical probability distributions. The MCPF is described in the context of individual-listener categorical loudness scaling (CLS) data. During a CLS task, listeners select the loudness category that best corresponds to their perception of the presented stimulus. In this study, CLS MCPF results are reported for 37 listeners (15 normal hearing, 22 with hearing loss). Individual-listener MCPFs were parameterized, and a principal component analysis (PCA) was used to identify sources of inter-subject variability and reduce the dimensionality of the data. A representative "catalog" of potential listener MCPFs was created from the PCA results. A method is introduced for using the MCPF catalog and maximum-likelihood estimation, together, to derive CLS functions for additional participants; this technique improved the accuracy of the CLS results and provided a MCPF model for each listener. Such a technique is particularly beneficial when a relatively low number of measurements are available (e.g., International Standards Organization adaptive-level CLS testing). In general, the MCPF is a flexible tool that can characterize any type of ordinal, level-dependent categorical data. For CLS, the MCPF quantifies the suprathreshold variability across listeners and provides a model for probability-based analyses and methods.