Accounting for Estimation Uncertainty and Shrinkage in Bayesian Within-Subject Intervals: A Comment on Nathoo, Kilshaw, and Masson (2018)
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Description: To facilitate the interpretation of systematic mean differences in within-subject designs, Nathoo, Kilshaw, and Masson (2018, Journal of Mathematical Psychology, 86, 1-9) proposed a Bayesian within-subject highest-density interval (HDI). However, their approach rests on independent maximum-likelihood estimates for the random effects which do not take estimation uncertainty and shrinkage into account. I propose an extension of Nathoo et al.'s method using a fully Bayesian, two-step approach. First, posterior samples are drawn for the linear mixed model. Second, the within-subject HDI is computed repeatedly based on the posterior samples, thereby accounting for estimation uncertainty and shrinkage. After marginalizing over the posterior distribution, the two-step approach results in a Bayesian within-subject HDI with a width similar to that of the classical within-subject confidence interval proposed by Loftus and Masson (1994, Psychonomic Bulletin & Review, 1, 476-490).