Supplementary Materials: Bayesian Model Checks

Overview

This document reports diagnostic checks and supplementary Bayesian summaries for the models reported in the manuscript and Appendix A. The main analyses were fitted with brms (Bürkner, 2017, 2018), which uses Stan’s Hamiltonian Monte Carlo sampler (Carpenter et al., 2017; Hoffman & Gelman, 2014). The checks below are intended to show whether the fitted models sampled well and whether simulated data from the fitted models resemble the observed data. LR refers to agent-left/patient-right picture arrangements; RL refers to patient-left/agent-right arrangements. The reanalysed datasets come from Garcia and colleagues (Garcia et al., 2018, 2019, 2020, 2021, 2023, 2025; Garcia & Kidd, 2020).

Model Overview

Table S1 lists the fitted Bayesian models checked in this supplement.

Table S1. Overview of the fitted Bayesian models checked in this supplement.

Study	Outcome	Probability model
Garcia and Kidd (2020)	Patient-initial production	Bernoulli
Garcia et al. (2018)	Patient-initial production	Bernoulli
Garcia et al. (2019)	Picture-verification accuracy	Bernoulli
Garcia et al. (2020)	First image fixation to target	Bernoulli
Garcia et al. (2020)	Sentence-picture choice accuracy	Bernoulli
Garcia et al. (2020)	Target looking duration	lognormal
Garcia et al. (2021)	Agent looking duration	lognormal
Garcia et al. (2021)	First entity fixation to agent	Bernoulli
Garcia et al. (2021)	Who-question accuracy	Bernoulli
Garcia et al. (2023, 2025)	Patient-initial production	Bernoulli
Garcia et al. (2023, 2025)	Picture-match response time	shifted lognormal
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Bernoulli

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 fitted main models had no divergent transitions. The largest \(\hat{R}\) was 1.010. Table S2 gives the convergence diagnostics for each fitted model.

Table S2. Convergence diagnostics for the main fitted models.

Study	Outcome	Divergent transitions	Maximum R-hat	Minimum bulk ESS ratio	Posterior draws
Garcia and Kidd (2020)	Patient-initial production	0	1.003	0.296	8000
Garcia et al. (2018)	Patient-initial production	0	1.003	0.284	8000
Garcia et al. (2019)	Picture-verification accuracy	0	1.004	0.159	8000
Garcia et al. (2020)	First image fixation to target	0	1.002	0.272	8000
Garcia et al. (2020)	Sentence-picture choice accuracy	0	1.002	0.265	8000
Garcia et al. (2020)	Target looking duration	0	1.003	0.155	8000
Garcia et al. (2021)	Agent looking duration	0	1.010	0.034	8000
Garcia et al. (2021)	First entity fixation to agent	0	1.005	0.026	16000
Garcia et al. (2021)	Who-question accuracy	0	1.003	0.259	8000
Garcia et al. (2023, 2025)	Patient-initial production	0	1.003	0.236	8000
Garcia et al. (2023, 2025)	Picture-match response time	0	1.003	0.217	8000
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	0	1.008	0.137	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 relevant models were refitted 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. Table S3 shows the Bayes factors from the refitted prior-sensitivity models.

Table S3. Prior-sensitivity checks for interpreted Bayes factors.

Study	Outcome	Group	Direction	Half BF	Reported BF	Double BF
Garcia et al. (2021)	Agent looking duration	adults	for LR bias	222.2	144.8	55.3
Garcia et al. (2021)	First entity fixation to agent	5 years	for LR bias	8.5	5.3	16.5
Garcia et al. (2021)	First entity fixation to agent	7 and 9 years	for LR bias	168.7	593.5	415.4
Garcia et al. (2021)	First entity fixation to agent	adults	for LR bias	323.1	8.8	409.2
Garcia and Kidd (2020)	Patient-initial production	3 years; prime LR	against LR bias	5.2	3.2	2.0
Garcia and Kidd (2020)	Patient-initial production	3 years; prime RL	against LR bias	17.7	9.4	5.7
Garcia and Kidd (2020)	Patient-initial production	5 years; prime LR	against LR bias	6.3	3.9	2.6
Garcia and Kidd (2020)	Patient-initial production	5 years; prime RL	against LR bias	21.0	12.3	7.7
Garcia and Kidd (2020)	Patient-initial production	7 years; prime RL	against LR bias	6.8	3.5	2.0
Garcia and Kidd (2020)	Patient-initial production	adults; prime RL	against LR bias	8.1	4.8	3.4
Garcia et al. (2023)	Patient-initial production	Tagalog	against LR bias	11.7	31.5	13.3
Garcia et al. (2025)	Patient-initial production	English L2	against LR bias	262.4	33.7	113.2
Garcia et al. (2023, 2025)	Picture-match response time	English L2	against LR bias	53.5	20.4	11.8
Garcia et al. (2023, 2025)	Picture-match response time	Indonesian	against LR bias	10.1	5.3	2.7
Garcia et al. (2019)	Sentence-picture verification accuracy	7 years	against LR bias	7.1	3.5	1.6
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	English L2	against LR bias	11.2	6.8	4.5
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Indonesian	against LR bias	15.2	8.0	4.0
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Tagalog	against LR bias	14.1	24.3	26.2

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.

Exploratory Indonesian and English-L2 Analyses

The main manuscript focuses on Tagalog outcomes. Garcia et al. (2025) also included Indonesian-L1 participants and English-L2 response conditions. These contrasts are reported here as exploratory analyses because they are relevant to broader questions about bilingualism and word-order flexibility, but they are not central to the Tagalog-focused argument in the manuscript. Table S4 summarises these exploratory contrasts.

Table S4. Exploratory Indonesian-L1 and English-L2 posterior contrasts.

Study	Outcome	Group	RL - LR	P(pred.)	BF against LR bias	BF for LR bias
Garcia et al. (2025)	Patient-initial production	English L2	-0.6 [-3.9, 2.6] pp	.35	33.7	< 0.1
Garcia et al. (2023, 2025)	Picture-match response time	English L2	-36.4 [-97.4, 23.8] ms	.12	91.4	< 0.1
Garcia et al. (2023, 2025)	Picture-match response time	Indonesian	-4.1 [-93.1, 85.0] ms	.46	2.7	0.4
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	English L2	0.3 [-0.5, 1.2] pp	.20	7.0	0.1
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Indonesian	0.8 [-0.6, 2.5] pp	.14	9.0	0.1

Main-Effect Meta-Analysis

We fitted an exploratory Bayesian meta-analysis to the model-derived contrasts reported in the main manuscript. The analysis kept behavioural/language-related outcomes separate from eye-tracking outcomes. As in the sentence-order meta-analysis below, the outcome was a directional standardised index, computed as the posterior RL - LR effect divided by its posterior standard error and coded so that positive values indicate the predicted LR-bias direction. The model accounted for the known standard error of each standardised contrast and included a random intercept for source/outcome combinations. Table S5 gives the posterior meta-analytic estimates.

Table S5. Exploratory meta-analysis of main model-derived contrasts.

Contrast	Scale	Number of effects	Estimate	Lower	Upper	P(LR bias)	P(against LR bias)
behavioural outcomes	directional posterior-SE units	34	0.35	-0.23	0.96	.88	.12
eye-tracking outcomes	directional posterior-SE units	34	0.89	0.10	1.63	.98	.02

The meta-analysis had no divergent transitions, a maximum \(\hat{R}\) of 1.001, and a minimum bulk effective-sample-size ratio of 0.225.

Sentence-Order Sensitivity Checks

The main manuscript analyses tested whether responses differed for RL versus LR pictures, with LR defined as agent-left/patient-right. We also fitted post-hoc sensitivity models for datasets in which participants encountered an agent-initial or patient-initial sentence immediately before the relevant picture response. These models asked whether the RL - LR effect depended on the thematic order of the preceding sentence. For Garcia et al. (2023, 2025), the models included picture arrangement, prime thematic order, and language group. The response-time sensitivity model used the same shifted-lognormal likelihood as the main response-time model, but excluded implausibly fast responses and very long responses (200 ms < RT <= 5,000 ms). The accuracy sensitivity model used a Bernoulli likelihood. Additional Bernoulli sensitivity models were fitted for Garcia et al. (2019), Garcia et al. (2020), and Garcia and Kidd (2020). For Garcia and Kidd (2020), the model retained prime-picture LR/RL arrangement because prime-picture arrangement was part of the main analysis logic. The settled response-time trimming criterion removed 7.8% of Tagalog trials: 0.02% were faster than or equal to 200 ms and 7.8% were longer than 5,000 ms. In the exploratory language-group analyses, the same criterion removed 4.7% of Indonesian-L1 trials and 5.0% of English-L2 trials.

The sentence-order sensitivity models had no divergent transitions. Table S6 summarises their diagnostics and Table S7 gives the posterior contrasts.

Table S6. Convergence diagnostics for sentence-order sensitivity models.

Study	Outcome	Observations	Divergences	Maximum R-hat	Minimum ESS ratio
Garcia and Kidd (2020)	Patient-initial production	790	0	1.003	0.232
Garcia et al. (2019)	Picture-verification accuracy	1341	0	1.005	0.127
Garcia et al. (2020)	Sentence-picture choice accuracy	672	0	1.004	0.277
Garcia et al. (2023, 2025)	Picture-match response time	8703	0	1.003	0.217
Garcia et al. (2023, 2025)	Picture-match response time	8703	0	1.005	0.188
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	9331	0	1.006	0.165

Table S7. Posterior contrasts from sentence-order sensitivity models.

Study	Outcome	Group	RL - LR	P(pred.)	BF against LR bias	BF for LR bias
Garcia and Kidd (2020)	Patient-initial production	3 years; prime image LR; agent-initial prime sentence	1.5 [-17.4, 19.2] pp	.58	2.0	0.5
Garcia and Kidd (2020)	Patient-initial production	3 years; prime image LR; patient-initial prime sentence	-14.6 [-43.3, 13.9] pp	.16	7.5	0.1
Garcia and Kidd (2020)	Patient-initial production	3 years; prime image RL; agent-initial prime sentence	-7.6 [-35.4, 20.6] pp	.30	4.5	0.2
Garcia and Kidd (2020)	Patient-initial production	3 years; prime image RL; patient-initial prime sentence	-23.3 [-50.9, 8.8] pp	.07	19.0	0.1
Garcia and Kidd (2020)	Patient-initial production	5 years; prime image LR; agent-initial prime sentence	1.3 [-13.3, 14.6] pp	.60	2.0	0.5
Garcia and Kidd (2020)	Patient-initial production	5 years; prime image LR; patient-initial prime sentence	-8.1 [-34.5, 17.8] pp	.27	5.0	0.2
Garcia and Kidd (2020)	Patient-initial production	5 years; prime image RL; agent-initial prime sentence	-15.6 [-42.3, 8.6] pp	.11	11.3	0.1
Garcia and Kidd (2020)	Patient-initial production	5 years; prime image RL; patient-initial prime sentence	-27.9 [-57.3, 2.4] pp	.04	32.5	< 0.1
Garcia and Kidd (2020)	Patient-initial production	7 years; prime image LR; agent-initial prime sentence	4.0 [-6.1, 15.0] pp	.80	2.0	0.5
Garcia and Kidd (2020)	Patient-initial production	7 years; prime image LR; patient-initial prime sentence	1.0 [-18.5, 19.9] pp	.55	3.3	0.3
Garcia and Kidd (2020)	Patient-initial production	7 years; prime image RL; agent-initial prime sentence	-0.6 [-18.7, 16.8] pp	.48	3.4	0.3
Garcia and Kidd (2020)	Patient-initial production	7 years; prime image RL; patient-initial prime sentence	-4.9 [-29.2, 15.1] pp	.33	4.7	0.2
Garcia and Kidd (2020)	Patient-initial production	adults; prime image LR; agent-initial prime sentence	2.9 [-4.3, 9.5] pp	.83	0.9	1.1
Garcia and Kidd (2020)	Patient-initial production	adults; prime image LR; patient-initial prime sentence	-2.9 [-20.5, 12.0] pp	.36	3.2	0.3
Garcia and Kidd (2020)	Patient-initial production	adults; prime image RL; agent-initial prime sentence	-2.3 [-20.2, 13.0] pp	.40	3.0	0.3
Garcia and Kidd (2020)	Patient-initial production	adults; prime image RL; patient-initial prime sentence	-8.7 [-32.0, 10.4] pp	.19	6.3	0.2
Garcia et al. (2019)	Picture-verification accuracy	5 years; agent-initial sentence	-3.8 [-11.4, 3.4] pp	.85	1.5	0.7
Garcia et al. (2019)	Picture-verification accuracy	5 years; patient-initial sentence	-6.3 [-22.4, 9.9] pp	.78	1.6	0.6
Garcia et al. (2019)	Picture-verification accuracy	7 years; agent-initial sentence	0.6 [-5.2, 7.1] pp	.43	2.3	0.4
Garcia et al. (2019)	Picture-verification accuracy	7 years; patient-initial sentence	4.2 [-7.2, 16.4] pp	.24	4.5	0.2
Garcia et al. (2019)	Picture-verification accuracy	adults; agent-initial sentence	-0.9 [-2.3, 0.1] pp	.96	0.9	1.1
Garcia et al. (2019)	Picture-verification accuracy	adults; patient-initial sentence	-2.0 [-5.4, 0.7] pp	.93	2.1	0.5
Garcia et al. (2020)	Sentence-picture choice accuracy	5 years; agent-initial sentence	-3.0 [-15.1, 7.8] pp	.72	1.9	0.5
Garcia et al. (2020)	Sentence-picture choice accuracy	5 years; patient-initial sentence	-7.7 [-35.3, 20.4] pp	.70	3.0	0.3
Garcia et al. (2020)	Sentence-picture choice accuracy	7 years; agent-initial sentence	-0.4 [-3.8, 2.6] pp	.61	2.3	0.4
Garcia et al. (2020)	Sentence-picture choice accuracy	7 years; patient-initial sentence	-5.6 [-31.8, 21.0] pp	.67	2.8	0.4
Garcia et al. (2020)	Sentence-picture choice accuracy	adults; agent-initial sentence	-0.6 [-2.1, 0.3] pp	.90	1.0	1.0
Garcia et al. (2020)	Sentence-picture choice accuracy	adults; patient-initial sentence	-2.3 [-8.8, 1.6] pp	.87	2.7	0.4
Garcia et al. (2023, 2025)	Picture-match response time	English L2; agent-initial prime sentence	27.4 [-51.0, 105.1] ms	.76	1.2	0.9
Garcia et al. (2023, 2025)	Picture-match response time	English L2; patient-initial prime sentence	-113.0 [-211.4, -16.1] ms	.01	41509.3	< 0.1
Garcia et al. (2023, 2025)	Picture-match response time	Indonesian; agent-initial prime sentence	13.4 [-98.6, 125.1] ms	.59	1.6	0.6
Garcia et al. (2023, 2025)	Picture-match response time	Indonesian; patient-initial prime sentence	-28.4 [-160.8, 101.9] ms	.34	3.4	0.3
Garcia et al. (2023, 2025)	Picture-match response time	Tagalog; agent-initial prime sentence	41.2 [-11.9, 92.9] ms	.94	1.0	1.0
Garcia et al. (2023, 2025)	Picture-match response time	Tagalog; patient-initial prime sentence	2.2 [-70.3, 76.2] ms	.52	5.3	0.2
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	English L2; agent-initial prime sentence	-0.1 [-0.9, 0.7] pp	.59	1.8	0.6
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	English L2; patient-initial prime sentence	0.6 [-0.3, 1.6] pp	.12	11.8	0.1
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Indonesian; agent-initial prime sentence	0.4 [-0.7, 1.7] pp	.26	3.8	0.3
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Indonesian; patient-initial prime sentence	0.9 [-0.6, 2.9] pp	.12	9.7	0.1
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Tagalog; agent-initial prime sentence	-0.6 [-1.9, 0.7] pp	.83	1.1	0.9
Garcia et al. (2023, 2025)	Sentence-picture verification accuracy	Tagalog; patient-initial prime sentence	0.5 [-1.6, 2.7] pp	.32	15.1	0.1

The order-conditioned sensitivity analyses did not reveal a hidden LR advantage. In the Garcia et al. (2023, 2025) Tagalog-prime trials reported in the main manuscript, agent-initial sentences were inconclusive for both response times and accuracy, whereas patient-initial sentences provided evidence against the LR-bias prior. The same qualitative pattern was visible in several exploratory Indonesian and English-L2 patient-initial conditions. The additional Garcia et al. (2019), Garcia et al. (2020), and Garcia and Kidd (2020) sensitivity checks also did not reveal conditions with evidence for the LR-bias prior. Several Garcia and Kidd (2020) conditions instead provided evidence against the LR-bias prior, especially after patient-initial prime sentences and RL prime images. The probability-scale accuracy effects were small because accuracy was close to ceiling.

As an additional aggregate check, we fitted a Bayesian meta-analysis to the model-derived order-conditioned contrasts from the Tagalog analyses. The outcome was a directional standardised index, computed as the posterior RL - LR effect divided by its posterior standard error and coded so that positive values indicate the predicted LR-bias direction. The model accounted for the known standard error of each standardised contrast and included a random intercept for source/outcome combinations. Table S8 reports this aggregate sentence-order check.

Table S8. Exploratory meta-analysis of sentence-order-conditioned contrasts.

Contrast	Scale	Number of effects	Estimate	Lower	Upper	P(LR bias)	P(against LR bias)
agent-initial sentence	directional posterior-SE units	32	0.67	-0.05	1.35	.97	.03
patient-initial sentence	directional posterior-SE units	32	0.10	-0.65	0.78	.62	.38
patient-initial minus agent-initial	directional posterior-SE units	32	-0.57	-1.26	0.12	.05	.95

The meta-analysis had no divergent transitions, a maximum \(\hat{R}\) of 1.002, and a minimum bulk effective-sample-size ratio of 0.335. The aggregate estimate was more compatible with an LR-bias direction after agent-initial than after patient-initial sentences, although the difference remained exploratory.

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 (Vehtari et al., 2017, 2024). Table S9 reports this model-family comparison.

Table S9. Leave-one-out comparison of lognormal and Gamma fixation-duration models.

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 Plots

Garcia and Kidd (2020)

Garcia et al. (2018)

Garcia et al. (2019)

Garcia et al. (2020)

Garcia et al. (2021)

Garcia et al. (2023, 2025)

Parameter Trace Checks

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

Trace Plots

Garcia and Kidd (2020)

Garcia et al. (2018)

Garcia et al. (2019)

Garcia et al. (2020)

Garcia et al. (2021)

Garcia et al. (2023, 2025)

References

Bürkner, P.-C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28. https://doi.org/10.18637/jss.v080.i01

Bürkner, P.-C. (2018). Advanced Bayesian multilevel modeling with the R package brms. The R Journal, 10(1), 395–411. https://doi.org/10.32614/RJ-2018-017

Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1), 1–32. https://doi.org/10.18637/jss.v076.i01

Garcia, R., Dery, J. E., Roeser, J., & Höhle, B. (2018). Word order preferences of Tagalog-speaking adults and children. First Language, 38(6), 617–640. https://doi.org/10.1177/0142723718790317

Garcia, R., Garrido Rodriguez, G., & Kidd, E. (2021). Developmental effects in the online use of morphosyntactic cues in sentence processing: Evidence from Tagalog. Cognition, 216, 104859. https://doi.org/10.1016/j.cognition.2021.104859

Garcia, R., & Kidd, E. (2020). The acquisition of the Tagalog symmetrical voice system: Evidence from structural priming. Language Learning and Development, 16(4), 399–425. https://doi.org/10.1080/15475441.2020.1814780

Garcia, R., Roeser, J., & Höhle, B. (2019). Thematic role assignment in the L1 acquisition of Tagalog: Use of word order and morphosyntactic markers. Language Acquisition, 26(3), 235–261. https://doi.org/10.1080/10489223.2018.1525613

Garcia, R., Roeser, J., & Höhle, B. (2020). Children’s online use of word order and morphosyntactic markers in Tagalog thematic role assignment: An eye-tracking study. Journal of Child Language, 47(3), 533–555. https://doi.org/10.1017/S0305000919000618

Garcia, R., Roeser, J., & Kidd, E. (2023). Finding your voice: Voice-specific effects in Tagalog reveal the limits of word order priming. Cognition, 236, 105424. https://doi.org/10.1016/j.cognition.2023.105424

Garcia, R., Roeser, J., Vargas, J. C. K., Fathin, S., & Kidd, E. (2025). Teasing apart the impact of different forms of overlap on cross-linguistic structural priming. Language, Cognition and Neuroscience, 40(10), 1446–1464. https://doi.org/10.1080/23273798.2025.2558640

Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(47), 1593–1623.

Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432. https://doi.org/10.1007/s11222-016-9696-4

Vehtari, A., Simpson, D., Gelman, A., Yao, Y., & Gabry, J. (2024). Pareto smoothed importance sampling. Journal of Machine Learning Research, 25(72), 1–58. https://jmlr.org/papers/v25/19-556.html

Session Information

sessionInfo()

R version 4.5.2 (2025-10-31)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.4 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.12.0 
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_GB.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_GB.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

time zone: Europe/London
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] posterior_1.6.1  bayesplot_1.15.0 brms_2.23.0      Rcpp_1.1.1      
 [5] kableExtra_1.4.0 stringr_1.6.0    purrr_1.2.1      tibble_3.3.1    
 [9] readr_2.1.6      ggplot2_4.0.2    dplyr_1.2.0     

loaded via a namespace (and not attached):
 [1] tidyselect_1.2.1      viridisLite_0.4.3     farver_2.1.2         
 [4] loo_2.9.0             S7_0.2.1              fastmap_1.2.0        
 [7] tensorA_0.36.2.1      digest_0.6.39         estimability_1.5.1   
[10] lifecycle_1.0.5       StanHeaders_2.32.10   processx_3.8.6       
[13] magrittr_2.0.4        compiler_4.5.2        rlang_1.1.7          
[16] sass_0.4.10           tools_4.5.2           yaml_2.3.12          
[19] knitr_1.51            labeling_0.4.3        bridgesampling_1.2-1 
[22] curl_7.0.0            bit_4.6.0             pkgbuild_1.4.8       
[25] plyr_1.8.9            xml2_1.5.1            RColorBrewer_1.1-3   
[28] cmdstanr_0.9.0        abind_1.4-8           withr_3.0.2          
[31] grid_4.5.2            stats4_4.5.2          xtable_1.8-4         
[34] inline_0.3.21         emmeans_2.0.1         scales_1.4.0         
[37] cli_3.6.5             mvtnorm_1.3-3         rmarkdown_2.30       
[40] crayon_1.5.3          generics_0.1.4        otel_0.2.0           
[43] RcppParallel_5.1.11-1 rstudioapi_0.18.0     reshape2_1.4.5       
[46] tzdb_0.5.0            cachem_1.1.0          rstan_2.32.7         
[49] parallel_4.5.2        matrixStats_1.5.0     vctrs_0.7.1          
[52] V8_8.0.1              Matrix_1.7-4          jsonlite_2.0.0       
[55] hms_1.1.4             bit64_4.6.0-1         systemfonts_1.3.1    
[58] jquerylib_0.1.4       tidyr_1.3.2           glue_1.8.0           
[61] codetools_0.2-20      ps_1.9.1              distributional_0.5.0 
[64] stringi_1.8.7         gtable_0.3.6          QuickJSR_1.8.1       
[67] pillar_1.11.1         htmltools_0.5.9       Brobdingnag_1.2-9    
[70] R6_2.6.1              textshaping_1.0.4     vroom_1.6.7          
[73] evaluate_1.0.5        lattice_0.22-7        backports_1.5.0      
[76] bslib_0.10.0          rstantools_2.5.0      gridExtra_2.3        
[79] svglite_2.2.2         coda_0.19-4.1         nlme_3.1-168         
[82] checkmate_2.3.3       xfun_0.56             pkgconfig_2.0.3