knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(message = FALSE)
knitr::opts_chunk$set(warning = FALSE)

options(width = 400)

library(brms)
library(knitr)
library(papeR)
library(stringr)
library(knitr)
library(papeR)
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(cache=TRUE)
library(compute.es)


library(lme4)
library(ggplot2)
library(gridExtra)
library(dplyr)
library(doBy)
library(sn)
library(bootstrap)
library(lubridate)
library(ggplot2)
library(readr)
library(dplyr)
## for bootstrapping 95% confidence intervals -- from Mike Frank https://github.com/langcog/KTE/blob/master/mcf.useful.R
library(bootstrap)
theta <- function(x,xdata,na.rm=T) {mean(xdata[x],na.rm=na.rm)}
ci.low <- function(x,na.rm=T) {
  quantile(bootstrap(1:length(x),1000,theta,x,na.rm=na.rm)$thetastar,.025,na.rm=na.rm)} #  mean(x,na.rm=na.rm) -
ci.high <- function(x,na.rm=T) {
  quantile(bootstrap(1:length(x),1000,theta,x,na.rm=na.rm)$thetastar,.975,na.rm=na.rm) } #- mean(x,na.rm=na.rm)}

 convert_stan_to_dataframe <- function(stan_object){
   sum.df <- data.frame(summary(stan_object)$fixed)
   sum.df$Diff_from_zero <- ifelse((sum.df$l.95..CI * sum.df$u.95..CI) > 0, "*","-")
   return(sum.df)
 }

read_TD_data <- function(csv,type){
word <- bind_rows(lapply(csv, read.csv, 
                         colClasses = c("num_siblings"="character",
                                        "birth_order"="character",
                                        "subject_id"="character",
                                        "dev_info"="character")))
word$DOT <- parse_date_time(word$date_stamp, "%m/%d/%Y")
word$DOB <- parse_date_time(word$date_of_birth,c("%Y-%m-%d","%d/%m.%y"))
word$age_weeks <- difftime(word$DOT,word$DOB,units = "weeks")
word$age <- as.numeric(floor(word$age_weeks/26)/2)
word$prevalence <- as.factor(word$prevalence)
contrasts(word$prevalence)[1] <- -1
# Have to get rid of this subset by age, as 
# some RAs entered DoT as DoB
#word <- subset(word, age > 1 )
word$Experiment = type
word$trial_type <- as.factor(word$trial_type)
#word <- subset(word, trial_type == "critical" )
return(word)
}

1 Experimental Design

(Hugh: note that materials for this Expt are under Github/mooney-picture-live/design-stance)

In this study, participants were taught the name of a novel object (e.g., this is a mef), and were then told about its original function. Then, they were told about a second function for the object, which was either idiosyncratic or conventionalized. Finally, they were asked to choose whether a denominal verb (e.g., meffing) referred to the original function or the second function.

Introduce object Function 1 Function 2 Test

In the conventional condition, function 2 would be replaced as so: Conventional Function 2

2 Both Labs Data

a=0
design_expt1_csv_ed <- dir(path = "./DataBoth/",pattern='*.csv$', recursive = T,full.names = T)

des_expt1 <- read_TD_data(design_expt1_csv_ed,"DesignSt Expt1")
total_n <- length(unique(des_expt1$subject_id))
adult_names = c("Jzin4",    "vQ9kd",    "EacbK",    "GRXZC",    "TT7vD",    "Ji6i8",    "UEkPP",    "FFV4A",    
                "cC7P3",    "NMV7V",    "hHuPe",    "gbig8",    "IXYa2",    "gpUCL",    "AvFRg",    "45vel",
                "9XL8e","53Jrb","D4DH5","h9prq","jvNSr","lYpAu","tLgrH","wjb8H",
                "adgFQ","EpGTI","3cn6G","ic8aW","BmxJP","GpeNt","nbuPP","ZASe7",
                "WdCBA","nvaIy","Qaa7h","fCfxr","NByx8","kD1Ga","3eHoH","5zPfp",
                "SeCGm","EypNI","rcUSO","BzKid","6pdGr","Tez42","ukfz7","YxpCP",
                "8dcrB","zJTaT","1gEsD","e9eGy","ymHuR","027Ke","QSW4M","AYYlf",
                "QiOqC","8HFxj","6m0Fo","joshM",
                "szBqs","mVEWU","yMuLA","LXr8B","gXvqG","zbwht","dg4Et","CcLBL",
                "IBuM1","7MJhs","Gih6v","JFX36","sVNMn","6z8cg","o3PpO","mwJHr",
                "DyREn","wW91e","A27X6","u2URN","kpJHP","0zu8T","31soU","1SUQH",
                "QoIqI","QwXgL","eQQNS","bXTSI","tHStk","LdnD0","Hp72M","iCdH6",
                "oW2tT","iWtjn","Fj0kh","Jzin4","VQ9kd","EacbK","29AmA","GRXZC",
                "TT7vD","Ji6i8","2p8MJ","y61xN","cC7P3","NMV7V","hHuPe","v9Xa5",
                "l4x2M","gbig8","IXYa2","gpUCL","wFfMn","UEkPP","tLgrH","jvNSr",
                "fWVGz","KmSdy","FFV4A","IYpAu","h9prq","KRCL4","AvFRg","9XL8e",
                "D4DH5","bMpOb","45vel","53Jrb","wjb8H","rAfUQ","Mn3sK","BzKid",
                "6pdGr","Tez42","Kh4iJ","oK2A9","3cn6G","kD1Ga","3eHoH","Lc3Gs",
                "SeCGm","ukfz7","YxpCP","STr6P","ic8aW","5zPfp","EypNI","wjyLD",
                "Odzh7","BmxJP","nvaly","Qaa7h","4tsOw","adgFQ","EpGTI","ZASe7",
                "bVyUg","2DPvU","nbuPP","NByx8","rcUSO","dPQPw","VnlKz","GpeNt",
                "WdCBA","fCfxr","6xabB","8dcrB","e9eGy","QSW4M","8HFxj","zJTaT",
                "ymHuR","AYYlf","6m0Fo","1gEsD","027Kw","QiOqC","joshM","qomFR",
                "dW5EX","DK2rv","aSCIO","Xg2rm","7BIeX","szBqs","LXr8B","dg4Et",
                "7MJhs","mVEWU","gXvqG","CcLBL","Gih6v","yMuLA","zbwht","IBuM1",
                "JFX36","XJ8p7","M585l","8YaRm","sVNMn","ci6Ek","bxdbA","wQ6Nb",
                "ci6Ek","Zjfhe","RKPwE","DRKZ5","rA2ld","TMU9i","kiyC1","9fzQp",
                "WXnfW","WQWgx","7bVIW","D8ufy","eV8aL","p9V9G","iNXHp")
#"7AAKi","MkAlx","yIIAB")


# Note that before Feb 7, all participants tested in ME_Conventional were
# Actually in ME_Idio. That list is:
# Edinburgh Child:
# PKcJO
#
# Berk Adults:
# adgFQ
# EpGTI
#
# Berk Kids:
# zRiaH
# XPFnX
# 7AAKi
# yIIAB

# Edinburgh excluded participants
ed_excluded_ptpts = c("mNiKL","xa5MU","aLqsz","yoliT")
des_expt1 = des_expt1[!des_expt1$subject_id %in% ed_excluded_ptpts,]

wrong_cond_names = c("PKcJO","adgFQ","EpGTI","zRiaH","XPFnX","7AAKi","yIIAB")

des_expt1[des_expt1$subject_id %in% wrong_cond_names,]$prevalence = "ME_idiosyncratic"

# Wrong gender
des_expt1[des_expt1$subject_id %in% c("DzgE5"),]$gender = "female"

# Describe participants
part_expt1 <- des_expt1 %>%
  dplyr::mutate(Age_Group = ifelse(subject_id %in% adult_names, "Adult","Child")) %>%
  dplyr::select(subject_id,trial_type,accuracy,Age_Group) %>%
  dplyr::group_by(subject_id,trial_type,Age_Group) %>%
  dplyr::summarise(n = n(), mean_acc = mean(accuracy)) 

part_expt1[part_expt1$trial_type == "critical",]$mean_acc <- 1  

part_expt1 <- part_expt1 %>%
  dplyr::group_by(subject_id,Age_Group) %>%
  dplyr::summarise(mean_acc = mean(mean_acc), n = sum(n)) #%>%
  #dplyr::filter( !n<8,!mean_acc <1)

# Exclude participants 
des_expt1 <- inner_join(des_expt1,part_expt1,by="subject_id") #%>%
#  dplyr::filter((age %in% c("4","4.5")|Age_Group == "Adult")) 

excluded_n <- total_n -  length(unique(des_expt1$subject_id))
des_expt1$ChooseLeft <- ifelse(des_expt1$side_chosen == "left",1,0)


des_expt1$Label = as.factor(ifelse(des_expt1$prevalence %in% c("conventional","idiosyncratic"), "WE", 
                                   ifelse(des_expt1$prevalence %in% c("ME_conventional","ME_idiosyncratic"),"ME","-")))
des_expt1$Task = as.factor(ifelse(des_expt1$prevalence %in% c("conventional","idiosyncratic",
                                                              "ME_conventional","ME_idiosyncratic"), 
                                  "Label",
                                  "Function"))
des_expt1$Prev = ifelse(des_expt1$prevalence %in% c("conventional","ME_conventional"),
                        "conventional", 
                        ifelse(des_expt1$prevalence =="function",
                               "conventional",
                               "idiosyncratic"))

des_expt1[des_expt1$poly_order %in% c("first"),]$Prev = "first"
des_expt1[des_expt1$poly_order %in% c("second"),]$Prev = "second"
                                             
des_expt1$Prev = as.factor(des_expt1$Prev)
des_expt1$Age_Group = as.factor(des_expt1$Age_Group)
contrasts(des_expt1$Label)[1] = -1
contrasts(des_expt1$Prev)[1] = 0
contrasts(des_expt1$Age_Group)[1] = 0
contrasts(des_expt1$Task)[1] = 0

# Process train trial 2 on function experiment to reverse code it.

des_expt1[des_expt1$trial_id == "train2" & des_expt1$Task == "Function",]$accuracy = ifelse(
  des_expt1[des_expt1$trial_id == "train2" & des_expt1$Task == "Function",]$accuracy == 1,0,
  1
)

kable(des_expt1 %>% 
 group_by(subject_id,Age_Group,Task,Label,Prev) %>%
 dplyr::summarise(acc = mean(accuracy)) %>%
 dplyr::select(subject_id,Age_Group,Task,Label,Prev,acc) %>%
 group_by(Age_Group,Task,Label,Prev) %>%
 dplyr::summarise(n = length(acc)),
 caption = "Number of participants per condition")

Number of participants per condition
Age_Group	Task	Label	Prev	n
Adult	Function	-	conventional	19
Adult	Function	-	first	18
Adult	Function	-	idiosyncratic	18
Adult	Function	-	second	18
Adult	Label	ME	conventional	18
Adult	Label	ME	idiosyncratic	18
Adult	Label	WE	conventional	18
Adult	Label	WE	idiosyncratic	18
Child	Function	-	conventional	59
Child	Function	-	first	40
Child	Function	-	idiosyncratic	40
Child	Function	-	second	41
Child	Label	ME	conventional	52
Child	Label	ME	idiosyncratic	41
Child	Label	WE	conventional	42
Child	Label	WE	idiosyncratic	40

2.1 Analysis

For Critical trials of all studies, we plot whether children are more likely to choose the original function.
For Training trials of labeling studies, we plot if they correctly chose the named function.
For Training trials of function studies, we plot if they correctly chose the original function.

a=0
des_expt1_summary <- des_expt1 %>%
  dplyr::group_by(trial_type,list,Task,Prev,prevalence,Label,subject_id,Age_Group) %>%
  dplyr::select(rt,accuracy,ChooseLeft,trial_type,list,prevalence,Task,Prev,Label,subject_id,Age_Group) %>%
  dplyr::summarise(ChooseLeft.m = mean(ChooseLeft), acc.m = mean(accuracy,na.rm = T),rt.m = mean(rt,na.rm = T)) 


des_expt1_summary_graph_NoPrev <- des_expt1_summary%>% 
  dplyr::group_by(trial_type,Label,Age_Group,Task) %>%
  dplyr::select(ChooseLeft.m,acc.m,rt.m,trial_type,Label,Task,subject_id,Age_Group) %>%
  dplyr::summarise(ChooseLeft.mean = mean(ChooseLeft.m),
                   acc.mean = mean(acc.m,na.rm = T),
                   acc.sd = sd(acc.m,na.rm=T),
                   rt.mean = mean(rt.m, na.rm = T), 
                   rt.sd = sd(rt.m,na.rm = T),
                   acc.low = ci.low(acc.m),
                   acc.high = ci.high(acc.m),
                   rt.low = ci.low(rt.m),
                   rt.high = ci.high(rt.m)) 

des_expt1_summary_graph <- des_expt1_summary%>% 
  dplyr::group_by(trial_type,prevalence,Age_Group,Label,Task,Prev) %>%
  dplyr::select(ChooseLeft.m,acc.m,rt.m,trial_type,prevalence,Task,Label,Prev,subject_id,Age_Group) %>%
  dplyr::summarise(ChooseLeft.mean = mean(ChooseLeft.m),
                   acc.mean = mean(acc.m,na.rm = T),
                   acc.sd = sd(acc.m,na.rm=T),
                   rt.mean = mean(rt.m, na.rm = T), 
                   rt.sd = sd(rt.m,na.rm = T),
                   acc.low = ci.low(acc.m),
                   acc.high = ci.high(acc.m),
                   rt.low = ci.low(rt.m),
                   rt.high = ci.high(rt.m)) 

des_expt1_summary_graph_list <- des_expt1_summary%>% 
    dplyr::group_by(trial_type,list,prevalence,Age_Group,Task,Prev,Label) %>%
    dplyr::select(acc.m,rt.m,trial_type,list,prevalence,Task,Prev,Label,subject_id,Age_Group) %>%
    dplyr::summarise(acc.mean = mean(acc.m,na.rm = T),
                     acc.sd = sd(acc.m,na.rm=T),
                     rt.mean = mean(rt.m, na.rm = T), 
                     rt.sd = sd(rt.m,na.rm = T),
                     acc.low = ci.low(acc.m),
                     acc.high = ci.high(acc.m),
                     rt.low = ci.low(rt.m),
                     rt.high = ci.high(rt.m)) 

dodge <- position_dodge(width=0.9)

labeling = ggplot(subset(des_expt1_summary_graph, Task == "Label"), aes(Label,acc.mean, fill = Prev)) +
  geom_bar(stat = "identity",  position = dodge) +
  facet_wrap(Age_Group~trial_type)+
  geom_errorbar(data = subset(des_expt1_summary_graph, Task == "Label"), aes(ymax = acc.high, ymin = acc.low), width=0.25, position = dodge) +
  labs(fill = "Prevalence") + 
  theme(axis.text.x = element_text(colour = "black", size = 12)) +
  ylab("Proportion of extensions to original function") +
  xlab("") + 
  ylim(c(0,1)) +
   geom_hline(yintercept = 0.5, size =1, linetype = 2)

function_prev = ggplot(subset(des_expt1_summary_graph, Task == "Function" & Prev 
                              %in% c("conventional","idiosyncratic")), 
                       aes(Prev,acc.mean, fill = Prev)) +
  geom_bar(stat = "identity",  position = dodge) +
  facet_wrap(Age_Group~trial_type)+
  geom_errorbar(data = subset(des_expt1_summary_graph, Task == "Function" & Prev 
                              %in% c("conventional","idiosyncratic")), aes(ymax = acc.high, ymin = acc.low), width=0.25, position = dodge) +
  labs(fill = "Prevalence") + 
  theme(axis.text.x = element_text(colour = "black", size = 12)) +
  ylab("Proportion of extensions to original function") +
  xlab("") + 
  ylim(c(0,1)) +
   geom_hline(yintercept = 0.5, size =1, linetype = 2)



function_label = ggplot(subset(des_expt1_summary_graph, Task == "Function" & !Prev 
                              %in% c("conventional","idiosyncratic")), 
                       aes(Prev,acc.mean, fill = Prev)) +
  geom_bar(stat = "identity",  position = dodge) +
  facet_wrap(Age_Group~trial_type)+
  geom_errorbar(data = subset(des_expt1_summary_graph, Task == "Function" & !Prev 
                              %in% c("conventional","idiosyncratic")), aes(ymax = acc.high, ymin = acc.low), width=0.25, position = dodge) +
  labs(fill = "Prevalence") + 
  theme(axis.text.x = element_text(colour = "black", size = 12)) +
  ylab("Proportion of extensions to original function") +
  xlab("") + 
  ylim(c(0,1)) +
   geom_hline(yintercept = 0.5, size =1, linetype = 2)

2.1.1 Labeling study

labeling_model = brm(accuracy ~ Prev*Label*Age_Group + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Task == "Label" & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

labeling_children = brm(accuracy ~ Prev*Label + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Label" & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

labeling_children_WE = brm(accuracy ~ Prev + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Label == "WE" & Age_Group == "Child" & Task == "Label" & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

labeling_children_ME = brm(accuracy ~ Prev + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Label == "ME" & Age_Group == "Child" & Task == "Label" & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

labeling

kable(convert_stan_to_dataframe(labeling_model),
       caption = "Labeling logistic regression")

Labeling logistic regression
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	-1.0849866	0.3310658	-1.7514482	-0.4665858	1337.529	1.003394	*
Previdiosyncratic	-1.3362685	0.4808109	-2.3055034	-0.4443511	1494.935	1.001924	*
LabelWE	2.7678612	0.4468512	1.9354536	3.6806839	1324.080	1.002244	*
Age_GroupChild	0.8966512	0.3372263	0.2523800	1.5635471	1552.101	1.000889	*
Previdiosyncratic:LabelWE	4.3398513	0.9811238	2.5446110	6.3892744	1470.642	1.004073	*
Previdiosyncratic:Age_GroupChild	1.3920055	0.5276435	0.4085851	2.4829471	1486.001	1.001447	*
LabelWE:Age_GroupChild	-2.1183407	0.4990415	-3.1112807	-1.1384267	1386.736	1.001908	*
Previdiosyncratic:LabelWE:Age_GroupChild	-4.3756917	1.0226094	-6.4916968	-2.4792923	1401.764	1.004056	*

kable(convert_stan_to_dataframe(labeling_children),
       caption = "Labeling logistic regression for children")

Labeling logistic regression for children
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	-0.1909612	0.1707636	-0.5258022	0.1333332	2075.865	1.000881	-
Previdiosyncratic	0.0969991	0.2131310	-0.3165154	0.5061316	2898.847	1.001646	-
LabelWE	0.6327583	0.2111274	0.2174868	1.0338828	2880.675	1.000376	*
Previdiosyncratic:LabelWE	-0.1129170	0.3079817	-0.7013668	0.5173954	2510.185	1.001281	-

kable(convert_stan_to_dataframe(labeling_children_WE),
       caption = "Labeling logistic regression for child WE")

Labeling logistic regression for child WE
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	0.4598106	0.2040438	0.0625166	0.8771937	2592.064	1.000557	*
Previdiosyncratic	-0.0286317	0.2484386	-0.5223661	0.4716816	4000.000	1.000080	-

kable(convert_stan_to_dataframe(labeling_children_ME),
       caption = "Labeling logistic regression for child ME")

Labeling logistic regression for child ME
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	-0.1789382	0.2361430	-0.5850651	0.2864920	190.0637	1.025671	-
Previdiosyncratic	0.0983333	0.2112191	-0.3116458	0.5241802	4000.0000	1.005602	-

There is a significant 3 way interaction between age, label type (WE/ME), and prevalence. Prevalence and label type interact for adults, but only label type has an effect for children.

2.1.2 Function – prevalence

func_prev_model = brm(accuracy ~ Prev*Age_Group + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Task == "Function" &   Prev 
                              %in% c("conventional","idiosyncratic") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

func_prev_children = brm(accuracy ~ Prev + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Function" &   Prev 
                              %in% c("conventional","idiosyncratic") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

func_prev_children_Conventional = brm(accuracy ~ 1 + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Function" &  Prev 
                              %in% c("conventional") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd)))

func_prev_children_Idio = brm(accuracy ~ 1 + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,   Age_Group == "Child" & Task == "Function" &   Prev 
                              %in% c("idiosyncratic") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd)))

a=0
function_prev

kable(convert_stan_to_dataframe(func_prev_model),
       caption = "Function Prevalence logistic regression")

Function Prevalence logistic regression
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	1.2353004	0.6264140	0.0250229	2.5184712	2230.567	1.002531	*
Previdiosyncratic	2.5045801	0.9150294	0.7809096	4.3740957	2364.229	1.001029	*
Age_GroupChild	-1.1934891	0.6684770	-2.5422028	0.0872245	2248.008	1.004081	-
Previdiosyncratic:Age_GroupChild	0.5816451	1.0293229	-1.4697554	2.6086211	2528.762	1.001420	-

kable(convert_stan_to_dataframe(func_prev_children),
       caption = "Function Prevalence logistic regression for children")

Function Prevalence logistic regression for children
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	0.0387044	0.3681217	-0.7028225	0.740034	1268.346	1.001893	-
Previdiosyncratic	2.8862707	0.5864400	1.8210975	4.130597	1458.678	1.000917	*

kable(convert_stan_to_dataframe(func_prev_children_Conventional),
       caption = "Function Prevalence logistic regression for child Conventional function")

Function Prevalence logistic regression for child Conventional function
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	-0.0045274	0.4365333	-0.8775804	0.8535145	934.1662	1.003941	-

kable(convert_stan_to_dataframe(func_prev_children_Idio),
       caption = "Function Prevalence logistic regression for child Idio function")

Function Prevalence logistic regression for child Idio function
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	3.010357	0.8248917	1.589812	4.849324	1120.819	1.003421	*

Prevalence affects function judgments for both children and adults.

2.1.3 Function – label first or second

func_label_model = brm(accuracy ~ Prev*Age_Group + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Task == "Function" &   Prev 
                              %in% c("first","second") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

func_label_children = brm(accuracy ~ Prev + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Function" &   Prev 
                              %in% c("first","second") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd),
                              prior(normal(0, 2.5), class = b)))

func_label_children_first = brm(accuracy ~ 1 + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Function" &  Prev 
                              %in% c("first") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd)))

func_label_children_second = brm(accuracy ~ 1 + (1|subject_id)+(1|trial_id), 
                     data = subset(des_expt1,  Age_Group == "Child" & Task == "Function" &   Prev 
                              %in% c("second") & trial_type == "critical"), 
                     family = "bernoulli", refresh = 0, 
                     prior= c(prior(normal(0, 2.5), class = sd)))

a=1
function_label

kable(convert_stan_to_dataframe(func_label_model),
       caption = "Function Label logistic regression")

Function Label logistic regression
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	2.2394556	0.6618053	0.9665637	3.5737913	1992.327	1.002336	*
Prevsecond	-0.2304119	0.8856856	-1.9569408	1.5667046	2156.848	1.001031	-
Age_GroupChild	-1.6161402	0.7419416	-3.1072027	-0.1619075	1928.534	1.001846	*
Prevsecond:Age_GroupChild	-0.3776143	1.0304924	-2.4847854	1.6389768	1913.877	1.001201	-

kable(convert_stan_to_dataframe(func_label_children),
       caption = "Function Label logistic regression for children")

Function Label logistic regression for children
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	0.4880208	0.4209073	-0.2813237	1.2419417	175.3606	1.025150	-
Prevsecond	-0.4797266	0.4676262	-1.3812218	0.5268622	563.1732	1.006677	-

kable(convert_stan_to_dataframe(func_label_children_first),
       caption = "Function Label logistic regression for child label first")

Function Label logistic regression for child label first
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	0.5471596	0.4285902	-0.2668054	1.403815	1151.176	1.000546	-

kable(convert_stan_to_dataframe(func_label_children_second),
       caption = "Function Label logistic regression for child label second")

Function Label logistic regression for child label second
	Estimate	Est.Error	l.95..CI	u.95..CI	Eff.Sample	Rhat	Diff_from_zero
Intercept	0.0241513	0.3759905	-0.7477375	0.7814655	1491.577	1.000231	-

nb. Small samples here!!

Whether the label affects the first or second function does not appear to affect function judgments for adults. Some trending evidence that it affects judgments for children, making the first function appear more likely to be the true function.

Design Stance