Correction

Abstract

An error was noted in R programming that caused a modest overestimation of variance component values associated with the oven and batch (block) random effects. This led to posterior predictive distributions for that were slightly too dispersed for the diameter and strength responses. This error came from inadvertently treating the posterior Stan scale parameter variables, SO_1, SO_2, SB_1, SBx2_1, SB_2, and SBx2_2 (shown in the Appendix), as variance (for normal) and variance-related (for student t) parameters, rather than as standard deviation (for normal) and standard-deviation-related (for student t) parameters. (Stan represents the scalevariation parameter for the normal distribution as standard deviation parameter, not a variance parameter. A similar result holds proportionately for the student t distribution in Stan.). The author has corrected this programing error and recomputed Figures 3, 4, 6, and 7 and Table 3. These are shown below. The other figures and tables were not affected. As a high-level validation, a separate, parallel calculation was done using Stan’s generated quantities feature to sample the posterior random effects directly from Stan. This produced results very similar to the original approach (but not the same due to Monte Carlo random variation).