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. Author manuscript; available in PMC: 2023 Sep 27.
Published in final edited form as: Cortex. 2023 Jun 9;166:188–206. doi: 10.1016/j.cortex.2023.04.017

Table 2 –

Temperature effects on pain during the adaptive calibration.a

Estimates Confidence Intervals P-values/Probability of direction Bayesian estimates
Outcome measure Effect LMERb NLMEc BRMSd LMER NLME BRMS LMER NLME BRMS % in ROPE Rhat ESS
Intensity (Intercept) 8.475 8.428 8.49 7.17–9.78 [7.08, 9.78] [7.18, 9.90] .000 .000 100% 0% 1.001 2277
Group −1.113 −1.115 −.99 −2.75 – .52 [−2.90, .67] [−2.58, .72] .196 .208 88.15% 21.48% 1 3487
Temperature 1.165 1.242 1.16 1.02–1.32 [1.08, 1.40] [1.00, 1.33] .000 .000 100% 0% 1 5609
Group × Temperature .078 .067 .07 −.11 – .27 [−.14, .27] [−.14, .27] .437 .521 76.44% 99.98% 1.001 7078
Unpleasantness (Intercept) 5.507 5.447 5.53 4.45–6.57 [4.37, 6.52] [4.34, 6.62] .000 .000 100% 0% 1.002 2328
Group −.881 −.887 −.81 −2.21 – .45 [−2.31, .53] [−2.16, .57] .207 .210 88.19% 21.22% 1 3397
Temperature .842 .872 .84 .71–.97 [.74, 1.01] [.69, .98] .000 .000 100% 0% 1.001 5904
Group × Temperature .072 .080 .07 −.10 – .24 [−.09, .25] [−.12, .26] .412 .364 77.88% 99.85% 1 6656
a

This table presents results of linear mixed models predicting subjective pain as a function of mean-centered Temperature and Group (VMPFC versus Healthy Control) based on ratings during the Adaptive Staircase Calibration task prior to the main experiment. Separate models were conducted using Intensity ratings and Unpleasantness ratings. All predictors were dummy-coded and mean centered to facilitate interpretation of coefficients and interactions. In this and subsequent tables, we compared three types of linear mixed models: frequentist analysis using the “lmer” function of lme4 (Bates et al., 2015), frequentist analysis using the “lme” function of nlme (Pinheiro et al., 2021) accounting for autoregression, and Bayesian estimation using mildly informative conservative priors (i.e., centered on 0 for all effects) implemented in brms (Bürkner, 2017). Effects that are both statistically and practically significant are bolded, whereas effects that are statistically significant but not practically significant (i.e., >2.5% in the region of practical equivalence (ROPE) (Makowski, Ben-Shachar, Chen, & Lüdecke, 2019)) are italicized.

b

Estimates based on a linear mixed effects model implemented in the “lmer” function of lme4 (Bates et al., 2015) using the following code: lmer(Rating ~ Group*Temperature + (1 + Temperature|ubject)). Confidence intervals were obtained using the “tab_model” function from sjPlot (Lüdecke, 2021) and corresponds to the 95% confidence interval.

c

Estimates based on a linear mixed effects model implemented in the “lme” function of nlme (Pinheiro et al., 2021) including autoregression using the following code: lme(Rating ~ Group*Temperature, random = ~1 + Temperature |Subject, correlation = corAR1(*), na.action = na.exclude). Confidence intervals were obtained using the “intervals” function from nlme(Pinheiro et al., 2021) and corresponds to the 95% confidence interval.

d

Estimates based on Bayesian model linear mixed models using the “brms” function (Bürkner, 2017) using the following code: brm(Rating ~ Group*Temperature + (1 + Temperature | Subject, prior = set_prior(“normal(0,2.5)”, class = “b”), save_all_pars = TRUE, silent = TRUE, refresh = 0, iter = 4000, warmup = 1000). Posterior estimates, including the probable direction (which is roughly equivalent to [1− frequentist p-value), 95% confidence intervals, and the ROPE were obtained using the “describe_posterior” function from the package BayesTestR (Makowski, Ben-Shachar, & Lüdecke, 2019) and interpreted as in Makowski, Ben-Shachar, Chen, & Lüdecke, 2019) We report the median estimate for each parameter.