Table 3. Multilevel model evaluating effects of Group, Cue, and Trial on medium heat pain prior to reversal*.
| Predictors | Estimates | Confidence intervals | P-Value / probability of direction | Bayesian estimates† | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| LMER‡ | NLME§ | BRMS† | LMER‡ | NLME§ | BRMS† | LMER‡ | NLME§ | BRMS† | % in ROPE | Rhat | ESS | ||
| All participants (n=40) | (Intercept) | 3.89 | 3.875 | 3.883 | 3.55–4.23 | [3.53, 4.221] | [ 3.598, 4.181] | <0.001 | 0.000 | 100.00% | 0 | 1 | 4860.246 |
| Group | 0.18 | 0.167 | 0.178 | –0.16–0.51 | [–0.183, 0.518] | [–0.106, 0.480] | 0.305 | 0.339 | 83.67% | 45.258 | 1 | 5043.495 | |
| Cue | 1.27 | 1.254 | 1.261 | 0.89–1.66 | [0.857, 1.651] | [ 0.939, 1.568] | <0.001 | 0.000 | 100.00% | 0 | 1 | 11882.091 | |
| Trial | 0.11 | 0.107 | 0.11 | 0.02–0.21 | [0.011, 0.202] | [ 0.031, 0.190] | 0.023 | 0.029 | 98.39% | 88.483 | 1 | 13555.299 | |
| Group * Cue | 0.44 | 0.425 | 0.442 | 0.06–0.83 | [0.028, 0.823] | [ 0.116, 0.758] | 0.024 | 0.036 | 98.45% | 8.892 | 1 | 12094.57 | |
| Group * Trial | 0.14 | 0.133 | 0.135 | 0.04–0.23 | [0.035, 0.231] | [ 0.049, 0.213] | 0.007 | 0.008 | 99.52% | 75.492 | 1 | 13395.889 | |
| Cue * Trial | 0.14 | 0.132 | 0.142 | –0.01–0.30 | [–0.032, 0.296] | [ 0.005, 0.274] | 0.071 | 0.114 | 95.07% | 62.758 | 1 | 14333.687 | |
| (Group *Cue) *Trial | 0.2 | 0.186 | 0.201 | 0.04–0.37 | [0.016, 0.357] | [ 0.060, 0.343] | 0.016 | 0.033 | 98.70% | 35.45 | 1 | 16585.744 | |
| Instructed Group (n=20) | (Intercept) | 4.07 | 4.034 | 4.076 | 3.63–4.51 | [3.594, 4.475] | [3.691, 4.455] | <0.001 | 0 | 100.00% | 0 | 1 | 4421.861 |
| Cue | 1.73 | 1.694 | 1.724 | 1.14–2.32 | [1.088, 2.3] | [1.204, 2.218] | <0.001 | 0 | 100.00% | 0 | 1 | 7914.074 | |
| Trial | 0.26 | 0.252 | 0.26 | 0.08–0.44 | [0.073, 0.43] | [0.106, 0.422] | 0.005 | 0.0063 | 99.28% | 17.733 | 1 | 6993.832 | |
| Cue * Trial | 0.35 | 0.294 | 0.361 | 0.04–0.66 | [–0.031, 0.618] | [0.088, 0.631] | 0.027 | 0.0755 | 97.65% | 13.558 | 1 | 7952.078 | |
| Uninstructed Group (n=20) | (Intercept) | 3.74 | 3.737 | 3.741 | 3.22–4.25 | [3.215, 4.259] | [ 3.261, 4.185] | <0.001 | 0 | 100.00% | 0 | 1.001 | 3062.443 |
| Cue | 0.89 | 0.885 | 0.874 | 0.40–1.38 | [0.378, 1.392] | [ 0.450, 1.262] | <0.001 | 0.0008 | 99.88% | 0.55 | 1.001 | 9645.377 | |
| Trial | 0 | –0.005 | –0.005 | –0.11–0.10 | [–0.113, 0.103] | [–0.095, 0.087] | 0.928 | 0.9333 | 53.46% | 99.433 | 1 | 8985.322 | |
| Cue * Trial | –0.03 | –0.035 | –0.035 | –0.20–0.14 | [–0.211, 0.142] | [–0.184, 0.112] | 0.704 | 0.6975 | 65.33% | 90.7 | 1 | 12054.973 | |
This table presents results of a linear mixed model predicting subjective pain on medium heat trials as a function of Group (Instructed vs Uninstructed), Cue (Original High vs Original Low), and Trial prior to the first reversal, as well as post-hoc tests in each Group. See Table 1 for additional information about model specification and presentation.
Estimates based on Bayesian model linear mixed models using the ‘brms’ function (Bürkner, 2017) using the following code: brmPain~Group*Cue*Trial+(1+Cue*Trial|Subject,prior = set_prior("normal(0,2.5)", class="b"), save_all_pars = TRUE, silent = TRUE, refresh = 0, iter = 4000,, warmup = 1000). Posterior estimates and the Region of Partial Equivalence were obtained using the “describe_posterior” function from the package BayesTestR (Makowski et al., 2019a) and interpreted as in Makowski et al., 2019b. The Region of Partial Equivalence (ROPE) was defined as [–0.17, 0.17] across all participants, [–.172,.172] when restricted to the Instructed Group, and [–.168,.168] when restricted to the Uninstructed Group.
Estimates based on a linear mixed effects model implemented in the ‘lmer’ function of lme4 (Bates et al., 2015) using the following code: lmer(PainMedium~Group*Cue*Trial+(1+Cue*Trial||Subject)).
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(Pain~Group *Cue*Trial, random = ~1 + Cue*Trial|Subject, correlation = corAR1, na.action=na.exclude).