Study 2.1: Semantic priming

Prior predictive checks

Figures 39, 40 and 41 show the prior predictive checks for the Gaussian models. These plots show the maximum, mean and minimum values of the observed data (y) and those of the predicted distribution (\(y_{rep}\), which stands for replications of the outcome). The way of interpreting these plots is by comparing the observed data to the predicted distribution. The specifics of this comparison vary across the three plots. First, in the upper plot, which shows the maximum values, the ideal scenario would show the observed maximum value (\(y\)) overlapping with the maximum value of the predicted distribution (\(y_{rep}\)). Second, in the middle plot, showing the mean values, the ideal scenario would show the observed mean value (\(y\)) overlapping with the mean value of the predicted distribution (\(y_{rep}\)). Last, in the lower plot, which shows the minimum values, the ideal scenario would have the observed minimum value (\(y\)) overlapping with the minimum value of the predicted distribution (\(y_{rep}\)). While the overlap need not be absolute, the closer the observed and the predicted values are on the X axis, the better. As such, the three predictive checks below—corresponding to models that used the default Gaussian distribution—show that the priors fitted the data acceptably but not very well.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_informativepriors.pdf'
  ))

Figure 39: Prior predictive checks for the Gaussian, informative prior model from the semantic priming study. y = observed data; yrep = predicted data.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_weaklyinformativepriors.pdf'
  ))

Figure 40: Prior predictive checks for the Gaussian, weakly-informative prior model from the semantic priming study. y = observed data; yrep = predicted data.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_diffusepriors.pdf'
  ))

Figure 41: Prior predictive checks for the Gaussian, diffuse prior model from the semantic priming study. y = observed data; yrep = predicted data.

In contrast to the above results, Figures 42, 43 and 44 demonstrate that, when an ex-Gaussian distribution was used, the priors fitted the data far better, which converged with the results of a similar comparison performed by Rodríguez-Ferreiro et al. (2020) (see supplementary materials of the latter study).

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_informativepriors_exgaussian.pdf'
  ))

Figure 42: Prior predictive checks for the ex-Gaussian, informative prior model from the semantic priming study. y = observed data; yrep = predicted data.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_weaklyinformativepriors_exgaussian.pdf'
  ))

Figure 43: Prior predictive checks for the ex-Gaussian, weakly-informative prior model from the semantic priming study. y = observed data; yrep = predicted data.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/prior_predictive_checks/plots/semanticpriming_priorpredictivecheck_diffusepriors_exgaussian.pdf'
  ))

Figure 44: Prior predictive checks for the ex-Gaussian, diffuse prior model from the semantic priming study. y = observed data; yrep = predicted data.

Posterior predictive checks

Based on the above results, the ex-Gaussian distribution was used in the final models. Figure 45 presents the posterior predictive checks for the latter models. The interpretation of these plots is simple: the distributions of the observed (y) and the predicted data (\(y_{rep}\)) should be as similar as possible. As such, the plots below suggest that the results are trustworthy.

Code 

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticpriming/bayesian_analysis/posterior_predictive_checks/plots/semanticpriming_posteriorpredictivechecks_allpriors_exgaussian.pdf'
  ))

Figure 45: Posterior predictive checks for the (ex-Gaussian) models from the semantic priming study. The observed data (y) and the predicted data (yrep) almost entirely overlap with each other, demonstrating a very good fit.

References

Rodríguez-Ferreiro, J., Aguilera, M., & Davies, R. (2020). Semantic priming and schizotypal personality: Reassessing the link between thought disorder and enhanced spreading of semantic activation. PeerJ, 8, e9511. https://doi.org/10.7717/peerj.9511

Pablo Bernabeu, 2022. Licence: CC BY 4.0.
Thesis: https://doi.org/10.17635/lancaster/thesis/1795.

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