Give-Letter
13 November, 2026
Children Data
Number of participants
df.response <- read.csv("../../data/PROCESSED_DATA/response.csv")df.response %>%
summarise(n_participants = n_distinct(PID))## n_participants
## 1 48df.demog_age <- df.response %>%
group_by(PID) %>%
slice(1) %>%
ungroup()
df.demog_age_summary <- df.demog_age %>%
summarise(mean_age = mean(age_years_cont, na.rm = T),
sd_age = sd(age_years_cont, na.rm = T),
min_age = min(age_years_cont, na.rm = T),
max_age = max(age_years_cont, na.rm = T))
df.demog_age_summary## # A tibble: 1 × 4
## mean_age sd_age min_age max_age
## <dbl> <dbl> <dbl> <dbl>
## 1 4.99 0.506 4.02 5.99df.demog_gender <- df.response %>%
group_by(PID) %>%
slice(1) %>%
ungroup()
df.demog_gender_summary <- df.demog_gender %>%
group_by(Gender) %>%
count()
df.demog_gender_summary## # A tibble: 2 × 2
## # Groups: Gender [2]
## Gender n
## <chr> <int>
## 1 Female 32
## 2 Male 16Plots
Give-Letter Task
ggplot(df.response %>%
filter(Task == "Letter_Training") %>%
group_by(PID, LT.Letter_Requested),
aes(x = LT.Letter_Requested, y = LT.Correct, fill = LT.Phase)) +
stat_summary(fun.data = "mean_cl_boot",
geom = "bar") +
stat_summary(fun.data = "mean_cl_boot",
geom = "pointrange") +
ylim(0, 1) +
labs(y = "Proportion Correct",
x = "Letter Requested") +
theme(text=element_text(size=15)) +
scale_fill_manual(values = cbPalette)
Later-Greater Tasks
ggplot(df.response %>%
filter(Task %in% c("Number_LG", "Letter_LG")) %>%
mutate(LG.Is_Correct = coalesce(LLG.Is_Correct, NLG.Is_Correct)) %>%
group_by(PID, Task) %>%
summarize(LG.Mean_Correct = mean(LG.Is_Correct, na.rm = T)),
aes(x = Task, y = LG.Mean_Correct)) +
stat_summary(fun.data = "mean_cl_boot",
geom = "pointrange") +
geom_dotplot(binaxis = "y", stackdir = "center",
alpha = 0.5,
dotsize = 0.5,
aes(group = Task,
fill = Task)) +
geom_hline(yintercept = 0.5, linetype = "dashed")## `summarise()` has regrouped the output.
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## ℹ Summaries were computed grouped by PID and Task.
## ℹ Output is grouped by PID.
## ℹ Use `summarise(.groups = "drop_last")` to silence this message.
## ℹ Use `summarise(.by = c(PID, Task))` for per-operation grouping
## (`?dplyr::dplyr_by`) instead.
ggplot(df.response %>%
filter(Task %in% c("Number_LG", "Letter_LG")) %>%
mutate(LG.Is_Correct = coalesce(LLG.Is_Correct, NLG.Is_Correct)) %>%
group_by(PID, Task) %>%
summarize(LG.Mean_Correct = mean(LG.Is_Correct, na.rm = T)),
aes(x = Task, y = LG.Mean_Correct, group = PID)) +
geom_line() +
geom_dotplot(binaxis = "y", stackdir = "center",
alpha = 0.5,
dotsize = 0.5,
aes(group = Task,
fill = Task)) ## `summarise()` has regrouped the output.
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## ℹ Summaries were computed grouped by PID and Task.
## ℹ Output is grouped by PID.
## ℹ Use `summarise(.groups = "drop_last")` to silence this message.
## ℹ Use `summarise(.by = c(PID, Task))` for per-operation grouping
## (`?dplyr::dplyr_by`) instead.
Regression
Random structure: by-participant intercept
priors <- c(
prior("normal(0,2.5)", class = "b") # weakly informative prior
)Response in Give-Letter task with Expected Success Probability
we will calculate an Expected Success Probability, which is the probability of generating that set response based on the overall response distribution
TODO: redo this analysis with MN response distribution.
Correct set response (0/1) ~ 1 + offset(logit(Expected Success Probability) + Age + (1|subj) Result: 95% CI of Intercept > 0 –> performance above chance
gl_response_dist <- df.response %>%
filter(Task == "Letter_Training") %>%
count(LT.Final_Number_Given, name = "LT.N_Response") %>%
mutate(
LT.Prop_Response = LT.N_Response / sum(LT.N_Response)
)
ggplot(gl_response_dist,
aes(x = LT.Final_Number_Given, y = LT.Prop_Response)) +
geom_col()
fit.lt_esp <- brm(formula = LT.Correct ~ 1 + offset(logit(LT.Prop_Response)) + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Letter_Training") %>%
left_join(gl_response_dist, by = "LT.Final_Number_Given"),
prior = priors,
file = "./cache/lt_esp",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.lt_esp)## Family: bernoulli
## Links: mu = logit
## Formula: LT.Correct ~ 1 + offset(logit(LT.Prop_Response)) + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "Letter_Training") (Number of observations: 336)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.14 0.28 0.64 1.75 1.00 21363 31246
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.34 0.25 2.89 3.86 1.00 43826 41320
## age_zscored 0.64 0.24 0.19 1.13 1.00 44858 42367
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in Give-Letter task
Correct set response (0/1) ~ Trial Type (Trained / Untrained) * Number + Age + (1|subj)
Result: Performance is greater than chance, but worse at Untrained numbers compared to Trained numbers. Better at smaller numbers. Interaction between Trial Type x Number (probably that there is a difference by Number magnitude for Trained numbers but not for Untrained numbers).
fit.lt <- brm(formula = LT.Correct ~ LT.Phase * LT.Number_Requested + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Letter_Training"),
prior = priors,
file = "./cache/lt",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
# Calculate BF to do Bayesian stopping if necessary.
fit.lt_comparison <- brm(formula = LT.Correct ~ LT.Number_Requested + LT.Phase:LT.Number_Requested + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Letter_Training"),
prior = priors,
file = "./cache/lt_comparison",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.lt)## Family: bernoulli
## Links: mu = logit
## Formula: LT.Correct ~ LT.Phase * LT.Number_Requested + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "Letter_Training") (Number of observations: 336)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.81 0.37 1.18 2.63 1.00 18798 28249
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 5.79 0.91 4.15 7.68 1.00
## LT.PhaseUntrained -3.66 1.14 -5.92 -1.48 1.00
## LT.Number_Requested -0.61 0.12 -0.86 -0.38 1.00
## age_zscored 0.80 0.33 0.18 1.49 1.00
## LT.PhaseUntrained:LT.Number_Requested 0.38 0.19 0.01 0.75 1.00
## Bulk_ESS Tail_ESS
## Intercept 32943 36355
## LT.PhaseUntrained 37247 38645
## LT.Number_Requested 42217 39820
## age_zscored 23816 29353
## LT.PhaseUntrained:LT.Number_Requested 39818 40767
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).bayes_factor(fit.lt, fit.lt_comparison)## Iteration: 1
## Iteration: 2
## Iteration: 3
## Iteration: 4
## Iteration: 5
## Iteration: 1
## Iteration: 2
## Iteration: 3
## Iteration: 4
## Iteration: 5## Estimated Bayes factor in favor of fit.lt over fit.lt_comparison: 110.37835bf <- bayesfactor_parameters(fit.lt)## Sampling priors, please wait...bf <- bf %>%
select(-Effects, -Component) %>%
mutate(BF = exp(log_BF))Response magnitude in Give-Letter task
Set response ~ Trial Type (Trained / Untrained-Tested) * Number + Age + (1|subj)
Result: 95% CI of Number > 0 –> they do use larger numbers for larger requests. No interaction with Trial Type suggesting this is the case for both Trained and Untrained numbers.
fit.lt_size <- brm(formula = LT.Final_Number_Given ~ LT.Phase * LT.Number_Requested + age_zscored + (1|PID),
family = "gaussian",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Letter_Training"),
prior = priors,
file = "./cache/lt_size",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.lt_size)## Family: gaussian
## Links: mu = identity
## Formula: LT.Final_Number_Given ~ LT.Phase * LT.Number_Requested + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "Letter_Training") (Number of observations: 336)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.12 0.17 0.83 1.48 1.00 19637 29869
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.37 0.33 -0.27 1.01 1.00
## LT.PhaseUntrained 1.30 0.67 -0.02 2.64 1.00
## LT.Number_Requested 0.87 0.06 0.77 0.98 1.00
## age_zscored -0.19 0.19 -0.56 0.19 1.00
## LT.PhaseUntrained:LT.Number_Requested -0.16 0.12 -0.41 0.07 1.00
## Bulk_ESS Tail_ESS
## Intercept 44567 44878
## LT.PhaseUntrained 48914 42178
## LT.Number_Requested 70059 47003
## age_zscored 29274 33869
## LT.PhaseUntrained:LT.Number_Requested 47899 40665
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.76 0.07 1.62 1.92 1.00 58698 43889
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in Letter LG task
Correct comparison (0/1) ~ Letter Distance (Consecutive / Non-consecutive) + Age + (1|subj)
Result: Performance better than chance.
fit.llg <- brm(formula = LLG.Is_Correct ~ LLG.Distance + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Letter_LG"),
prior = priors,
file = "./cache/llg",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.llg)## Family: bernoulli
## Links: mu = logit
## Formula: LLG.Is_Correct ~ LLG.Distance + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "Letter_LG") (Number of observations: 192)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.58 0.33 0.04 1.26 1.00 12948 21106
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.53 0.24 0.06 1.02 1.00 58696
## LLG.DistanceNonMconsecutive 0.41 0.32 -0.22 1.04 1.00 74608
## age_zscored 0.32 0.19 -0.05 0.71 1.00 51457
## Tail_ESS
## Intercept 39399
## LLG.DistanceNonMconsecutive 45314
## age_zscored 39942
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in How Many task with Expected Success Probability
Correct How Many response (0/1) ~ 1 + offset(logit(Expected Success Probability) + Age + (1|subj)
Result: Performance better than chance
hm_response_dist <- df.response %>%
filter(Task == "How_Many") %>%
count(HM.Final_Response, name = "HM.N_Response") %>%
mutate(
HM.Prop_Response = HM.N_Response / sum(HM.N_Response)
)fit.hm_esp <- brm(formula = HM.Is_Correct ~ 1 + offset(logit(HM.Prop_Response)) + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "How_Many") %>%
left_join(hm_response_dist, by = "HM.Final_Response"),
prior = priors,
file = "./cache/hm_esp",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.hm_esp)## Family: bernoulli
## Links: mu = logit
## Formula: HM.Is_Correct ~ 1 + offset(logit(HM.Prop_Response)) + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "How_Many") %>% lef (Number of observations: 96)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.42 0.35 0.01 1.28 1.00 26147 26776
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.49 0.32 1.91 3.15 1.00 66090 35835
## age_zscored 0.44 0.33 -0.19 1.12 1.00 71615 39273
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in How Many task
NOTE: NOT SURE ABOUT THIS SECTION. I think the spontaneous letter use analysis is more informative
Result: Better than chance(?)
fit.hm <- brm(formula = HM.Is_Correct ~ 1 + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "How_Many"),
prior = priors,
file = "./cache/hm",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.hm)## Family: bernoulli
## Links: mu = logit
## Formula: HM.Is_Correct ~ 1 + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "How_Many") (Number of observations: 96)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.76 1.04 1.10 5.17 1.00 15114 24595
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.02 0.72 0.88 3.72 1.00 21798 26185
## age_zscored 1.16 0.64 0.06 2.60 1.00 27070 27382
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in How Many task - Spontaneous Letter Use
Spontaneous use = use a letter before the explicit prompt to use the alphabet, doesn’t matter if it’s the correct letter or not.
How Many letter use (0/1) ~ 1 + Age + (1|subj)
Result: They do not spontaneously use letters. (note that it’s unclear what “chance” here is)
fit.hm_spontaneous <- brm(formula = HM.Spontaneous_Letter_Use ~ 1 + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "How_Many"),
prior = priors,
file = "./cache/hm_spontaneous",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.hm_spontaneous)## Family: bernoulli
## Links: mu = logit
## Formula: HM.Spontaneous_Letter_Use ~ 1 + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "How_Many") (Number of observations: 96)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.62 0.46 0.03 1.72 1.00 15679 24493
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.40 0.33 -2.11 -0.83 1.00 38212 26439
## age_zscored -0.46 0.30 -1.07 0.09 1.00 50335 31921
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Response in Number LG task
Correct comparison (0/1) ~ Number Distance (Consecutive / Non-consecutive) + Age + (1|subj)
Result: Performance better than chance.
fit.nlg <- brm(formula = NLG.Is_Correct ~ NLG.Distance + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.response %>%
filter(Task == "Number_LG"),
prior = priors,
file = "./cache/nlg",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(fit.nlg)## Family: bernoulli
## Links: mu = logit
## Formula: NLG.Is_Correct ~ NLG.Distance + age_zscored + (1 | PID)
## Data: df.response %>% filter(Task == "Number_LG") (Number of observations: 192)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.54 0.39 0.02 1.45 1.00 21514 30671
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 1.98 0.37 1.34 2.78 1.00 55204
## NLG.DistanceNonMconsecutive 1.40 0.55 0.37 2.53 1.00 89132
## age_zscored 0.87 0.30 0.31 1.49 1.00 65572
## Tail_ESS
## Intercept 38176
## NLG.DistanceNonMconsecutive 44858
## age_zscored 39370
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Compare Number- and Letter-LG Responses
Correct comparison in Letter Later-Greater (0/1) ~ Correct comparison in Number Later-Greater + Age + (1|subj)
Result: Performance in Number-LG is not a significant predictor for the same trial in Letter-LG.
df.lg <- df.response %>%
filter(Task %in% c("Letter_LG", "Number_LG")) %>%
mutate(LG.Is_Correct = coalesce(LLG.Is_Correct, NLG.Is_Correct)) %>%
select(PID, age_zscored, Task, Trial, LG.Is_Correct, NLG.Pair) %>%
pivot_wider(
names_from = Task,
values_from = c(LG.Is_Correct, NLG.Pair),
) %>%
rename(
LG.Pair = NLG.Pair_Number_LG
) %>%
select(-NLG.Pair_Letter_LG)
table(df.lg$LG.Is_Correct_Letter_LG - df.lg$LG.Is_Correct_Number_LG) %>%
barplot(
xlab = "Difference in Accuracy (Letter - Number)",
ylab = "Frequency",
main = "Distribution of Accuracy Differences"
)
df.lg_comparison <- brm(formula = LG.Is_Correct_Letter_LG ~ LG.Is_Correct_Number_LG + age_zscored + (1|PID),
family = "bernoulli",
save_pars = save_pars(all = T),
data = df.lg,
prior = priors,
file = "./cache/lg_comparison",
chains = 4,
iter = 20000,
warmup = 5000,
control = list(adapt_delta = 0.9),
refresh = 0,
seed = 1)
summary(df.lg_comparison)## Family: bernoulli
## Links: mu = logit
## Formula: LG.Is_Correct_Letter_LG ~ LG.Is_Correct_Number_LG + age_zscored + (1 | PID)
## Data: df.lg (Number of observations: 192)
## Draws: 4 chains, each with iter = 20000; warmup = 5000; thin = 1;
## total post-warmup draws = 60000
##
## Multilevel Hyperparameters:
## ~PID (Number of levels: 48)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.54 0.32 0.03 1.20 1.00 15075 26489
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.14 0.49 -0.83 1.10 1.00 59141
## LG.Is_Correct_Number_LG 0.65 0.51 -0.34 1.66 1.00 67020
## age_zscored 0.27 0.19 -0.10 0.65 1.00 47374
## Tail_ESS
## Intercept 41939
## LG.Is_Correct_Number_LG 45296
## age_zscored 38072
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Session Info
session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.6.1 (2026-06-24)
## os macOS Golden Gate 27.2
## system aarch64, darwin23
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz America/Los_Angeles
## date 2026-11-13
## pandoc 3.10 @ /Applications/RStudio.app/Contents/Resources/app/quarto/bin/tools/aarch64/ (via rmarkdown)
## quarto 1.5.57 @ /usr/local/bin/quarto
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date (UTC) lib source
## abind 1.4-8 2024-09-12 [1] CRAN (R 4.6.0)
## backports 1.5.1 2026-04-03 [1] CRAN (R 4.6.0)
## base64enc 0.1-6 2026-02-02 [1] CRAN (R 4.6.0)
## BayesFactor * 0.9.12-4.8 2026-03-07 [1] CRAN (R 4.6.0)
## bayesplot 1.15.0 2025-12-12 [1] CRAN (R 4.6.0)
## bayestestR * 0.18.1 2026-05-24 [1] CRAN (R 4.6.0)
## boot * 1.3-32 2025-08-29 [1] CRAN (R 4.6.1)
## bridgesampling 1.2-1 2025-11-19 [1] CRAN (R 4.6.0)
## brms * 2.23.0 2025-09-09 [1] CRAN (R 4.6.0)
## Brobdingnag 1.2-9 2022-10-19 [1] CRAN (R 4.6.0)
## bslib 0.11.0 2026-05-16 [1] CRAN (R 4.6.0)
## cachem 1.1.0 2024-05-16 [1] CRAN (R 4.6.0)
## car * 3.1-5 2026-02-03 [1] CRAN (R 4.6.0)
## carData * 3.0-6 2026-01-30 [1] CRAN (R 4.6.0)
## checkmate 2.3.4 2026-02-03 [1] CRAN (R 4.6.0)
## cli 3.6.6 2026-04-09 [1] CRAN (R 4.6.0)
## cluster 2.1.8.2 2026-02-05 [1] CRAN (R 4.6.1)
## coda * 0.19-4.1 2024-01-31 [1] CRAN (R 4.6.0)
## codetools 0.2-20 2024-03-31 [1] CRAN (R 4.6.1)
## colorspace 2.1-3 2026-07-12 [1] CRAN (R 4.6.1)
## data.table 1.18.4 2026-05-06 [1] CRAN (R 4.6.0)
## datawizard 1.3.1 2026-04-26 [1] CRAN (R 4.6.0)
## digest 0.6.39 2025-11-19 [1] CRAN (R 4.6.0)
## distributional 0.8.1 2026-06-27 [1] CRAN (R 4.6.1)
## dplyr * 1.2.1 2026-04-03 [1] CRAN (R 4.6.0)
## emmeans * 2.0.4 2026-07-15 [1] CRAN (R 4.6.1)
## estimability 2.0.0 2026-06-26 [1] CRAN (R 4.6.1)
## evaluate 1.0.5 2025-08-27 [1] CRAN (R 4.6.0)
## farver 2.1.2 2024-05-13 [1] CRAN (R 4.6.0)
## fastmap 1.2.0 2024-05-15 [1] CRAN (R 4.6.0)
## forcats * 1.0.1 2025-09-25 [1] CRAN (R 4.6.0)
## foreign 0.8-91 2026-01-29 [1] CRAN (R 4.6.1)
## Formula 1.2-5 2023-02-24 [1] CRAN (R 4.6.0)
## generics 0.1.4 2025-05-09 [1] CRAN (R 4.6.0)
## ggplot2 * 4.0.3 2026-04-22 [1] CRAN (R 4.6.0)
## glue 1.8.1 2026-04-17 [1] CRAN (R 4.6.0)
## gridExtra 2.3.1 2026-06-25 [1] CRAN (R 4.6.1)
## gtable 0.3.6 2024-10-25 [1] CRAN (R 4.6.0)
## Hmisc 5.2-6 2026-06-19 [1] CRAN (R 4.6.0)
## hms 1.1.4 2025-10-17 [1] CRAN (R 4.6.0)
## htmlTable 2.5.0 2026-04-22 [1] CRAN (R 4.6.0)
## htmltools 0.5.9 2025-12-04 [1] CRAN (R 4.6.0)
## htmlwidgets 1.6.4 2023-12-06 [1] CRAN (R 4.6.0)
## inline 0.3.21 2025-01-09 [1] CRAN (R 4.6.0)
## insight 1.5.2 2026-06-28 [1] CRAN (R 4.6.1)
## jquerylib 0.1.4 2021-04-26 [1] CRAN (R 4.6.0)
## jsonlite 2.0.0 2025-03-27 [1] CRAN (R 4.6.0)
## knitr 1.51 2025-12-20 [1] CRAN (R 4.6.0)
## labeling 0.4.3 2023-08-29 [1] CRAN (R 4.6.0)
## lattice 0.22-9 2026-02-09 [1] CRAN (R 4.6.1)
## lifecycle 1.0.5 2026-01-08 [1] CRAN (R 4.6.0)
## lme4 * 2.0-1 2026-03-05 [1] CRAN (R 4.6.0)
## logspline 2.1.22 2024-05-10 [1] CRAN (R 4.6.0)
## loo 2.10.1 2026-07-24 [1] CRAN (R 4.6.1)
## lubridate * 1.9.5 2026-02-04 [1] CRAN (R 4.6.0)
## magrittr 2.0.5 2026-04-04 [1] CRAN (R 4.6.0)
## MASS 7.3-65 2025-02-28 [1] CRAN (R 4.6.1)
## Matrix * 1.7-5 2026-03-21 [1] CRAN (R 4.6.1)
## MatrixModels 0.5-4 2025-03-26 [1] CRAN (R 4.6.0)
## matrixStats 1.5.0 2025-01-07 [1] CRAN (R 4.6.0)
## minqa 1.2.8 2024-08-17 [1] CRAN (R 4.6.0)
## mvtnorm 1.4-2 2026-07-12 [1] CRAN (R 4.6.1)
## nlme 3.1-169 2026-03-27 [1] CRAN (R 4.6.1)
## nloptr 2.2.1 2025-03-17 [1] CRAN (R 4.6.0)
## nnet 7.3-20 2025-01-01 [1] CRAN (R 4.6.1)
## otel 0.2.0 2025-08-29 [1] CRAN (R 4.6.0)
## pbapply 1.7-4 2025-07-20 [1] CRAN (R 4.6.0)
## pillar 1.11.1 2025-09-17 [1] CRAN (R 4.6.0)
## pkgbuild 1.4.8 2025-05-26 [1] CRAN (R 4.6.0)
## pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.6.0)
## plyr 1.8.9 2023-10-02 [1] CRAN (R 4.6.0)
## posterior 1.7.0 2026-04-01 [1] CRAN (R 4.6.0)
## purrr * 1.2.2 2026-04-10 [1] CRAN (R 4.6.0)
## QuickJSR 1.10.0 2026-05-17 [1] CRAN (R 4.6.0)
## R6 2.6.1 2025-02-15 [1] CRAN (R 4.6.0)
## rbibutils 2.4.1 2026-01-21 [1] CRAN (R 4.6.0)
## RColorBrewer 1.1-3 2022-04-03 [1] CRAN (R 4.6.0)
## Rcpp * 1.1.2 2026-07-05 [1] CRAN (R 4.6.1)
## RcppParallel 5.1.11-2 2026-03-05 [1] CRAN (R 4.6.0)
## Rdpack 2.6.6 2026-02-08 [1] CRAN (R 4.6.0)
## readr * 2.2.0 2026-02-19 [1] CRAN (R 4.6.0)
## reformulas 0.4.4 2026-02-02 [1] CRAN (R 4.6.0)
## reshape2 1.4.5 2025-11-12 [1] CRAN (R 4.6.0)
## rlang 1.3.0 2026-07-05 [1] CRAN (R 4.6.1)
## rmarkdown 2.31 2026-03-26 [1] CRAN (R 4.6.0)
## rpart 4.1.27 2026-03-27 [1] CRAN (R 4.6.1)
## rstan 2.32.7 2025-03-10 [1] CRAN (R 4.6.0)
## rstantools 2.7.0 2026-07-26 [1] CRAN (R 4.6.1)
## rstudioapi 0.19.0 2026-06-11 [1] CRAN (R 4.6.0)
## S7 0.2.2 2026-04-22 [1] CRAN (R 4.6.0)
## sass 0.4.10 2025-04-11 [1] CRAN (R 4.6.0)
## scales 1.4.0 2025-04-24 [1] CRAN (R 4.6.0)
## sessioninfo * 1.2.4 2026-06-04 [1] CRAN (R 4.6.0)
## StanHeaders 2.32.10 2024-07-15 [1] CRAN (R 4.6.0)
## stringi 1.8.7 2025-03-27 [1] CRAN (R 4.6.0)
## stringr * 1.6.0 2025-11-04 [1] CRAN (R 4.6.0)
## tensorA 0.36.2.1 2023-12-13 [1] CRAN (R 4.6.0)
## tibble * 3.3.1 2026-01-11 [1] CRAN (R 4.6.0)
## tidyr * 1.3.2 2025-12-19 [1] CRAN (R 4.6.0)
## tidyselect 1.2.1 2024-03-11 [1] CRAN (R 4.6.0)
## tidyverse * 2.0.0 2023-02-22 [1] CRAN (R 4.6.0)
## timechange 0.4.0 2026-01-29 [1] CRAN (R 4.6.0)
## tzdb 0.5.0 2025-03-15 [1] CRAN (R 4.6.0)
## utf8 1.2.6 2025-06-08 [1] CRAN (R 4.6.0)
## vctrs 0.7.3 2026-04-11 [1] CRAN (R 4.6.0)
## withr 3.0.3 2026-06-19 [1] CRAN (R 4.6.0)
## xfun 0.60 2026-07-09 [1] CRAN (R 4.6.1)
## xtable 1.8-8 2026-02-22 [1] CRAN (R 4.6.0)
## yaml 2.3.12 2025-12-10 [1] CRAN (R 4.6.0)
##
## [1] /Library/Frameworks/R.framework/Versions/4.6/Resources/library
## * ── Packages attached to the search path.
##
## ──────────────────────────────────────────────────────────────────────────────