Study 2.3: Lexical decision

Prior predictive checks

Figures 53, 54 and 55 show the prior predictive checks for the Gaussian models (for background on these checks, see Study 2.1). The three plots—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
    '/lexicaldecision/bayesian_analysis/prior_predictive_checks/plots/lexicaldecision_priorpredictivecheck_informativepriors.pdf'
  ))

Figure 53: Prior predictive checks for the Gaussian, informative prior model from the lexical decision study. y = observed data; yrep = predicted data.

Code 

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

Figure 54: Prior predictive checks for the Gaussian, weakly-informative prior model from the lexical decision study. y = observed data; yrep = predicted data.

Code 

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

Figure 55: Prior predictive checks for the Gaussian, diffuse prior model from the lexical decision study. y = observed data; yrep = predicted data.

In contrast to the results from the Gaussian models, Figures 56, 57 and 58 demonstrate that, when an ex-Gaussian distribution was used, the priors fitted the data far better, which converged with the results found in Studies 2.1 and 2.2.

Code 

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

Figure 56: Prior predictive checks for the ex-Gaussian, informative prior model from the lexical decision study. y = observed data; yrep = predicted data.

Code 

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

Figure 57: Prior predictive checks for the ex-Gaussian, weakly-informative prior model from the lexical decision study. y = observed data; yrep = predicted data.

Code 

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

Figure 58: Prior predictive checks for the ex-Gaussian, diffuse prior model from the lexical decision 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 59 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
    '/lexicaldecision/bayesian_analysis/posterior_predictive_checks/plots/lexicaldecision_posteriorpredictivechecks_allpriors_exgaussian.pdf'
  ))

Figure 59: Posterior predictive checks for the (ex-Gaussian) models from the lexical decision study. y = observed data; yrep = predicted data.


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

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