Loudness is a measure of suprathreshold perception that provides insight into the status of the entire auditory pathway; cochlear damage manifests primarily as loudness recruitment, while central adaptations may affect the level at which listeners report discomfort. In addition to these broad effects, individuals with matched thresholds show significant individual variability in the details of their loudness perception. As a means to analyze and model listener variability, we introduce the multi-category psychometric function (MCPF), a novel representation for categorical data that fully describes the probabilistic relationship between stimulus level and categorical-loudness perception. We present results based on categorical loudness scaling (CLS) data for 15 normal-hearing (NH) adults and 22 adults with hearing loss (HL). A principle-component analysis of the parameterized listener data shows the major underlying factors that contribute to individual variability across listeners. We show how the MCPF can be used to improve CLS estimates, by combining listener models with maximum-likelihood estimation. The MCPF could be additionally used in an entropy-based stimulus-selection technique. These techniques utilize the probabilistic nature of categorical perception, a new dimension of loudness information, to improve the quality of loudness measurements.