Page 32 - Demo

30Chapter 2Wagenmakers, 2007) inform us about the credibility of the data given a hypothesis, Bayesian methods inform us about the credibility of our parametervalues given the data that we observed. This is reflected in the different interpretation of frequentist and Bayesian confidence intervals: the first is arange of values that contains the estimate in the long run, while the lattertells which parameter values are most credible based on the data (Kruschkeet al., 2012; McElreath, 2018). Furthermore, Bayesian methods allow forthe inclusion of prior expectations in the model, are less prone to Type Ierrors, and are more robust in small and noisy samples (Makowski et al.,2019). Altogether, these reasons make Bayesian methods a useful tool fordata analysis.First, we investigated whether the attractiveness ratings of the stimuligiven by our subjects matched with the categories that we used. To examinethis question, we fitted a Bayesian mixed model with an ordinal dependentvariable (attractiveness rating, 7 levels), and the interaction between Sexand Attractiveness Category as independent variables. Furthermore, weadded random intercepts per subject and stimulus, and allowed the effect ofattractiveness category to vary by subject by adding random slopes. We usedregularizing Gaussian priors with M = 0 and SD = 1 for the fixed effects,default Student’s t priors with 3 degrees of freedom for the thresholds, anddefault half Student’s t priors with 3 degrees of freedom for the randomeffects and residual standard deviation.To test our main hypothesis, we created a model that used by-subjectmean-centered RT as dependent variable and the interaction between Condition (attractive vs. intermediate or unattractive vs. intermediate) andProbe Location (behind intermediate or behind (un)attractive stimulus).Furthermore, to explore the effect of Sex and Age, we created two morecomplex models that included the three-way interaction between Condition,Probe location, and Sex and Age, respectively. All categorical fixed effectswere sum-to-zero coded, and Age was z-transformed. In all models, weadded random intercepts per subject and trial number (to control for ordereffects), and allowed slopes of the interaction between Condition and ProbeLocation to vary by subject. We used regularizing Gaussian priors with M= 0 and SD = 5 for all fixed effects, a Gaussian prior with M = 0 and SD= 10 for the intercept, and default half Student’s t priors with 3 degrees offreedom for the random effects and residual standard deviation, which wereweakly informative.We used multiple measures to summarize the posterior distributions foreach variable: (1) the median estimate and the median absolute deviation ofthis estimate, (2) the 89% credible interval (89% CI; McElreath, 2018), and(3) the probability of direction (pd). The 89% CI indicates the range withinwhich the effect falls with 89% probability, while the pd indicates the proportion of the posterior distribution that is of the median’s sign (Makowskiet al., 2019). We have chosen an 89% CI instead of the conventional 95% toIliana Samara 17x24.indd 30 08-04-2024 16:35