Hierarchical Bayesian modeling of contrast sensitivity functions in a within-subject design

Recent development of the quick contrast sensitivity function (qCSF) method has made it possible to obtain accurate, precise, and efficient contrast sensitivity function (CSF) assessment. To improve statistical inference on CSF changes in a within-subject design, we developed a hierarchical Bayesian model (HBM) to compute the joint distribution of CSF parameters and hyperparameters at test, subject, and population levels, utilizing information within- and between-subjects and experimental conditions. We evaluated the performance of the HBM relative to a non-hierarchical Bayesian inference procedure (BIP) on an existing CSF dataset of 112 subjects obtained with the qCSF method in three luminance conditions (Hou, Lesmes, Kim, Gu, Pitt, Myung, & Lu, 2016). We found that the average d′s of the area under log CSF (AULCSF) and CSF parameters between pairs of luminance conditions at the test-level from the HBM were 33.5% and 103.3% greater than those from the BIP analysis of AULCSF. The increased d′ resulted in greater statistical differences between experimental conditions across subjects. In addition, simulations showed that the HBM generated accurate and precise CSF parameter estimates. These results have strong implications for the application of HBM in clinical trials and patient care.