Overview

This document reports convergence diagnostics and reusable posterior-check code for the Bayesian LR/RL arrangement models reported in Appendix A.

Model Specifications

model_id study outcome family formula
sentence_picture_match_accuracy Garcia et al. (2023, 2025) Sentence-picture match accuracy bernoulli accuracy ~ arrangement_bias * (language_group) + (1 | experiment) + (1 + arrangement_bias || participant_id) + (1 + arrangement_bias || item)
picture_match_response_time Garcia et al. (2023, 2025) Picture-match response time shifted_lognormal match_rt_ms ~ arrangement_bias * (language_group) + (1 | experiment) + (1 + arrangement_bias || participant_id) + (1 + arrangement_bias || item); ndt ~ 1 + (1 || participant_id)
word_order_priming_patient_initial Garcia et al. (2023, 2025) Patient-initial production bernoulli patient_initial ~ arrangement_bias * (language_group) + (1 | experiment) + (1 + arrangement_bias || participant_id) + (1 + arrangement_bias || item)
garcia_2020_sentence_picture_choice_accuracy Garcia et al. (2020) Sentence-picture choice accuracy bernoulli accuracy ~ arrangement_bias * (age_group) + (1 + arrangement_bias || participant) + (1 | item)
garcia_2021_who_question_accuracy Garcia et al. (2021) Who-question accuracy bernoulli accuracy ~ arrangement_bias * (age_group) + (1 + arrangement_bias || participant) + (1 + arrangement_bias || item)
garcia_kidd_2020_patient_initial Garcia and Kidd (2020) Patient-initial production bernoulli produced_pi ~ target_bias * (age_group + prime_action_direction) + (1 + target_bias * prime_action_direction || participant) + (1 + target_bias * prime_action_direction || item)
garcia_2018_patient_initial Garcia et al. (2018) Patient-initial production bernoulli patient_initial ~ arrangement_bias * (age_group) + (1 + arrangement_bias || participant) + (1 + arrangement_bias || item)
garcia_2019_picture_verification_accuracy Garcia et al. (2019) Picture-verification accuracy bernoulli accuracy ~ arrangement_bias * (age_group) + (1 + arrangement_bias || participant) + (1 + arrangement_bias || item)
garcia_2020_first_target_fixation Garcia et al. (2020) First image fixation to target bernoulli first_target_fixation ~ arrangement_bias * age_group + (1 + arrangement_bias || participant_id) + (1 | item)
garcia_2020_target_looking_duration_lognormal Garcia et al. (2020) Target looking duration lognormal target_look_duration_ms ~ arrangement_bias * age_group + (1 + arrangement_bias || participant_id) + (1 | item)
garcia_2021_first_fixation_agent Garcia et al. (2021) First entity fixation to agent bernoulli first_look_agent ~ arrangement_bias * age_group + (1 + arrangement_bias || participant_id) + (1 + arrangement_bias || item)
garcia_2021_agent_looking_duration_lognormal Garcia et al. (2021) Agent looking duration lognormal look_duration_ms ~ arrangement_bias * age_group + (1 + arrangement_bias || participant_id) + (1 + arrangement_bias || item)

Convergence Diagnostics

The primary convergence checks are the number of divergent transitions, maximum \(\hat{R}\), and the minimum bulk effective-sample-size ratio across parameters. All but one fitted model had no divergent transitions; the picture-match response-time model had four divergent transitions. The largest \(\hat{R}\) was 1.010.

model_id study outcome n_divergent max_rhat min_ess_bulk n_draws
sentence_picture_match_accuracy Garcia et al. (2023, 2025) Sentence-picture match accuracy 0 1.004 0.190 8000
picture_match_response_time Garcia et al. (2023, 2025) Picture-match response time 4 1.006 0.156 8000
word_order_priming_patient_initial Garcia et al. (2023, 2025) Patient-initial production 0 1.003 0.236 8000
garcia_2020_sentence_picture_choice_accuracy Garcia et al. (2020) Sentence-picture choice accuracy 0 1.002 0.265 8000
garcia_2021_who_question_accuracy Garcia et al. (2021) Who-question accuracy 0 1.003 0.259 8000
garcia_kidd_2020_patient_initial Garcia and Kidd (2020) Patient-initial production 0 1.003 0.296 8000
garcia_2018_patient_initial Garcia et al. (2018) Patient-initial production 0 1.003 0.284 8000
garcia_2019_picture_verification_accuracy Garcia et al. (2019) Picture-verification accuracy 0 1.004 0.159 8000
garcia_2020_first_target_fixation Garcia et al. (2020) First image fixation to target 0 1.002 0.272 8000
garcia_2020_target_looking_duration_lognormal Garcia et al. (2020) Target looking duration 0 1.003 0.155 8000
garcia_2021_first_fixation_agent Garcia et al. (2021) First entity fixation to agent 0 1.005 0.026 16000
garcia_2021_agent_looking_duration_lognormal Garcia et al. (2021) Agent looking duration 0 1.010 0.034 8000

Prior Sensitivity

The manuscript Bayes factors depend on the directional prior used to represent the LR-bias hypothesis. As a prior-sensitivity check, the table recalculates Bayes factors for effects with reported Bayes factors of at least 3 under half-width, reported-width, and double-width versions of the directional prior. This check shows how strongly the Bayes-factor interpretation depends on the chosen prior scale; the manuscript does not interpret smaller Bayes factors.

Study Outcome Group Direction Half BF Reported BF Double BF
Garcia et al. (2021) Agent looking duration 5 years against LR bias 22.3 4.7 1.9
Garcia et al. (2021) Agent looking duration 7 and 9 years against LR bias 45.9 9.8 4.0
Garcia et al. (2021) Agent looking duration adults for LR bias 276.3 1299.1 3156.1
Garcia et al. (2021) First entity fixation to agent 5 years for LR bias 1.5 7.1 17.2
Garcia et al. (2021) First entity fixation to agent 7 and 9 years for LR bias 14.9 70.1 170.2
Garcia et al. (2021) First entity fixation to agent adults for LR bias 21.2 99.8 242.4
Garcia and Kidd (2020) Patient-initial production 3 years; prime LR against LR bias 6.3 3.2 1.6
Garcia and Kidd (2020) Patient-initial production 3 years; prime RL against LR bias 18.9 9.4 4.7
Garcia and Kidd (2020) Patient-initial production 5 years; prime LR against LR bias 7.9 3.9 2.0
Garcia and Kidd (2020) Patient-initial production 5 years; prime RL against LR bias 24.7 12.3 6.2
Garcia and Kidd (2020) Patient-initial production 7 and 9 years; prime RL against LR bias 7.0 3.5 1.7
Garcia and Kidd (2020) Patient-initial production adults; prime RL against LR bias 9.7 4.8 2.4
Garcia et al. (2023) Patient-initial production Tagalog against LR bias 62.9 31.5 15.7
Garcia et al. (2025) Patient-initial production English L2 against LR bias 67.3 33.7 16.8
Garcia et al. (2023, 2025) Picture-match response time English L2 against LR bias 12.2 6.1 3.1
Garcia et al. (2019) Sentence-picture verification accuracy 7 and 9 years against LR bias 6.9 3.5 1.7
Garcia et al. (2023, 2025) Sentence-picture verification accuracy English L2 against LR bias 6.2 3.1 1.5
Garcia et al. (2023, 2025) Sentence-picture verification accuracy Indonesian against LR bias 20.8 10.4 5.2
Garcia et al. (2023, 2025) Sentence-picture verification accuracy Tagalog against LR bias 38.6 19.3 9.6
Garcia et al. (2020) Target looking duration 7 and 9 years against LR bias 114.3 24.3 10.0
Garcia et al. (2020) Target looking duration adults against LR bias 35.1 7.5 3.1

The sensitivity check was generally stable in direction. The largest Bayes factors remained large across prior widths, whereas some borderline Bayes factors near 3 were more sensitive to the prior scale.

Fixation-Duration Family Check

The fixation-duration outcomes were also fitted with Gamma likelihoods and log links. We retained the lognormal likelihood because approximate leave-one-out cross-validation favoured it for both duration outcomes.

Outcome Family ELPD difference SE difference ELPD LOO LOOIC
Target looking duration lognormal 0.0 0.0 -4537.1 9074.2
Target looking duration gamma -41.8 5.7 -4578.9 9157.9
Agent looking duration lognormal 0.0 0.0 -27394.1 54788.1
Agent looking duration gamma -74.4 11.6 -27468.4 54936.8

Posterior Predictive Checks

The following plots overlay the observed data with data simulated from the posterior predictive distribution for every fitted model. Binary models are shown as observed-versus-posterior-predicted bar overlays; response-time and fixation-duration models are shown as observed-versus-posterior-predicted density overlays with log-scaled x-axes.

Posterior Predictive Overlay: sentence_picture_match_accuracy

Posterior Predictive Overlay: picture_match_response_time

Posterior Predictive Overlay: word_order_priming_patient_initial

Posterior Predictive Overlay: garcia_2020_sentence_picture_choice_accuracy

Posterior Predictive Overlay: garcia_2021_who_question_accuracy

Posterior Predictive Overlay: garcia_kidd_2020_patient_initial

Posterior Predictive Overlay: garcia_2018_patient_initial

Posterior Predictive Overlay: garcia_2019_picture_verification_accuracy

Posterior Predictive Overlay: garcia_2020_first_target_fixation

Posterior Predictive Overlay: garcia_2020_target_looking_duration_lognormal

Posterior Predictive Overlay: garcia_2021_first_fixation_agent

Posterior Predictive Overlay: garcia_2021_agent_looking_duration_lognormal

Parameter Trace Checks

The following plots show Markov-chain traces for the population-level parameters. For models with many population-level parameters, the plot is limited to the first eight b_ parameters to keep the supplementary document readable.

Trace Plot: sentence_picture_match_accuracy

Trace Plot: picture_match_response_time

Trace Plot: word_order_priming_patient_initial

Trace Plot: garcia_2020_sentence_picture_choice_accuracy

Trace Plot: garcia_2021_who_question_accuracy

Trace Plot: garcia_kidd_2020_patient_initial

Trace Plot: garcia_2018_patient_initial

Trace Plot: garcia_2019_picture_verification_accuracy

Trace Plot: garcia_2020_first_target_fixation

Trace Plot: garcia_2020_target_looking_duration_lognormal

Trace Plot: garcia_2021_first_fixation_agent

Trace Plot: garcia_2021_agent_looking_duration_lognormal