Main Analysis CATegories

Load packages

library(tidyverse)
library(janitor)
library(cowplot)
library(here)
library(readxl)
library(Matrix)
library(lme4)
library(lmerTest)
library(TOSTER)
library(wesanderson)
library(gghalves)
library(car)
library(multilevelTools)
library(JWileymisc)
library(broom.mixed)
library(papaja)
library(effectsize)
library(ggimage)
library(sessioninfo)
library(broom)
library(performance)
#devtools::install_github("jmgirard/agreement")
source("compute_iccs.R")
source("common.R")

theme_set(theme_cowplot())

knitr::opts_chunk$set(cache = FALSE, warn = FALSE,warning=FALSE, message = FALSE)

Load data

#set paths
data_file_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_data_with_exclusion_info.csv")
useable_trial_summary_path <- here::here("..","..","data","processed_data","CATegories_exp2_useable_trial_summary.csv")
summarize_subj_trials_path <- here::here("..","..","data","processed_data","CATegories_exp2_trial_summary_data.csv")
participant_data_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_participant_data_anonymized.csv")
resampled_data_file_path <- here::here("..","..","data","processed_data","CATegories_exp2_processed_data_resampled.csv")
#load data
d <- read_csv(data_file_path) 
participant_total_useable_trials <- read_csv(useable_trial_summary_path)
summarize_subj_trials <- read_csv(summarize_subj_trials_path)
participant_data <- read_csv(participant_data_path)
d_resampled <- read_csv(resampled_data_file_path) #note that this file gets created in cluster_permutation_analysis.Rmd

Useable trial summary

In order for a trial to be included, participants must contribute at least 50% looking during the windows of interest when computing baseline-corrected proportion target looking: the critical window (300 ms - 2800 ms relative to target word onset) and the baseline window (-2000 ms - 0 ms relative to target word onset). See 2_process_exclusions.Rmd for detailed processing steps.

Overall, among the trials contributed by 141 participants (excluding 2 participants whose data was filtered out earlier in the process, because they either did not provide any useable trials or due to parent interference throughout the session), 81.1% of trials contained sufficient looking to meet our trial-level inclusion criteria (at least 50% looking during both the baseline window and the critical window). Overall, after additional trial-level exclusions (due technical errors or frame rate issues), 78.3% were retained. 84 of the 141 participants contributed valid data on at least half of the experimental trials (for all participants: M = 25.9; only for included participants: M = 36.7).

Summarize participant information

All participants contributing data

participant_data_summarized <- participant_data %>%
  summarize(
    N=length(unique(sub_num)),
    num_sessions = sum(session<3),
    session_1_N = sum(session==1),
    session_2_N = sum(session==2)
  )

participant_data_summarized %>%
  knitr::kable()

N	num_sessions	session_1_N	session_2_N
143	255	143	112

participant_data_summarized <- participant_data %>%
  distinct(sub_num,session_1_data,session_2_data) %>%
  left_join(participant_total_useable_trials)

#participants without session 2 data who were subsequently excluded
sum(filter(participant_data_summarized,session_2_data=="N")$exclude_participant)

## [1] 27

#participants with session 2 data who were subsequently excluded
sum(filter(participant_data_summarized,session_2_data=="Y")$exclude_participant)

## [1] 32

All participants providing coded looking data

#summarize subj info
subj_info_multisession <- d %>%
  distinct(sub_num, age,age_mo,child_gender,trial_order) %>%
  mutate(
    age_mo_c = age_mo - mean(age_mo),
    age_c = age - mean(age)
  )

subj_info <- d %>%
  distinct(sub_num,child_gender) %>%
  summarize(
    N = n(),
    N_female = sum(child_gender=="f")
  )

overall_subj_info <- subj_info_multisession %>%
  summarize(
    N = length(unique(sub_num)),
    sessions = n(),
    mean_age = mean(age_mo),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age_mo)
  ) %>%
  left_join(subj_info)
  
overall_subj_info %>%
  knitr::kable()

N	sessions	mean_age	min_age	max_age	sd_age	N_female
141	248	15.73065	410	718	1.613515	70

All included participants

# subjects with usable trial data only
subj_info_multisession_usable_trials <- d %>%
  filter(exclude_participant==0) %>%
  distinct(sub_num, age,age_mo,child_gender,trial_order) %>%
  mutate(
    age_mo_c = age_mo - mean(age_mo),
    age_c = age - mean(age)
  )

subj_info_usable_trials <- d %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  distinct(sub_num,child_gender) %>%
  summarize(
    N = n(),
    N_female = sum(child_gender=="f")
  )

overall_subj_info_usable_trials <- subj_info_multisession_usable_trials %>%
  summarize(
    N = length(unique(sub_num)),
    sessions = n(),
    mean_age = mean(age_mo),
    mean_age_days=mean(age),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age_mo)
  ) %>%
  left_join(subj_info_usable_trials)
  
overall_subj_info_usable_trials %>%
  knitr::kable()

N	sessions	mean_age	mean_age_days	min_age	max_age	sd_age	N_female
84	164	15.70122	477.8963	410	574	1.490131	51

Demographics of final useable sample

Next, we summarize demographic information for the final sample (removing participant exclusions).

demographics_summary <- d %>%
  filter(exclude_participant == 0) %>%
  distinct(sub_num,demographic_us_race_ethnicity_identification,demographic_education_level,demographic_annual_income,demographic_country,demographic_state,demographic_density)

Race/ Ethnicity

multiple_categories_list <- c("White, Middle Eastern or North African","White, Hispanic, Latino, or Spanish origin","White, Black or African American, Middle Eastern or North African","White, Black or African American","White, Asian, Middle Eastern or North African","White, Asian","Hispanic, Latino, or Spanish origin, Black or African American","Hispanic, Latino, or Spanish origin, Asian","Black or African American, Asian","Asian, Middle Eastern or North African")

race_ethnicity <- demographics_summary %>%
  group_by(demographic_us_race_ethnicity_identification)%>%
  summarize(
    N = n()
  ) %>%
  ungroup() %>%
  mutate(percent=N/sum(N),
         multiple_categories=ifelse(demographic_us_race_ethnicity_identification %in% multiple_categories_list,1,0))
#percent reporting multiple categories
sum(filter(race_ethnicity,multiple_categories==1)$N)/sum(race_ethnicity$N)

## [1] 0.2261905

#quick visualization
ggplot(demographics_summary,aes(y=demographic_us_race_ethnicity_identification)) +
  geom_bar()

Parent Income

income <- demographics_summary %>%
  group_by(demographic_annual_income)%>%
  summarize(
    N = n()
  )

income %>%
  knitr::kable()

demographic_annual_income	N
100000	6
110000	1
120000	5
130000	4
140000	1
15000	1
150000	11
160000	1
170000	1
180000	1
190000	1
20000	1
30000	1
40000	4
50000	7
60000	5
70000	4
80000	5
90000	3
>200000	19
NA	2

#quick visualiztion
ggplot(demographics_summary,aes(demographic_annual_income)) +
  geom_bar()+
  theme(axis.text.x = element_text(angle = 90))

Parent Education Level

education <- demographics_summary %>%
  group_by(demographic_education_level)%>%
  summarize(
    N = n()
  )

education %>%
  knitr::kable()

demographic_education_level	N
assoc	1
bach	31
col	2
grad	3
hs	1
prof	46

Geographic Information

states <- demographics_summary %>%
  group_by(demographic_state)%>%
  summarize(
    N = n()
  )

ggplot(demographics_summary,aes(demographic_state)) +
  geom_bar()+
  theme(axis.text.x = element_text(angle = 90))

population_density <- demographics_summary %>%
  group_by(demographic_density) %>%
  summarize(
    N = n()
  )
population_density %>%
  knitr::kable()

demographic_density	N
rural	4
suburban	57
urban	22
NA	1

Summarize Overall Target Looking by Participant

Here, we summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking.

# save key columns
key_cols_summarized_trial_data <- c(
  "sub_num","session", "age","age_mo","days_between_sessions", "child_gender", "trial_order","trial_number","condition","target_image","distractor_image","target_category","distractor_category","target_typicality_z","distractor_typicality_z","target_parent_typicality_rating","distractor_parent_typicality_rating","target_parent_typicality_rating_z","distractor_parent_typicality_rating_z","target_parent_typicality_by_category_z","distractor_parent_typicality_by_category_z","mean_target_looking_critical","mean_target_looking_baseline","corrected_target_looking","exclude_participant","age_exclusion","trial_exclusion","trial_exclusion_reason","exclude_technical_issue","exclude_frame_rate","useable_window","useable_critical_window","useable_baseline_window","useable_window_short","total_trials_short","exclude_participant_insufficient_data_short","mean_target_looking_critical_short","corrected_target_looking_short")

#extract summarized trial-level accuracy (see 2_process_exclusions.Rmd for details on how summarized columns are computed)
trial_corrected_accuracy_all <- d %>%
  select(all_of(key_cols_summarized_trial_data)) %>%
  distinct()

trial_corrected_accuracy <- trial_corrected_accuracy_all %>%
  filter(exclude_participant==0) %>%
  filter(trial_exclusion==0)

# summarize average accuracy
avg_corrected_target_looking <- trial_corrected_accuracy  %>%
  group_by(sub_num) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking <- avg_corrected_target_looking %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)
overall_corrected_target_looking %>%
  knitr::kable()

N	corrected_target_looking	ci	lower_ci	upper_ci
84	0.072012	0.0173402	0.0546718	0.0893522

By Typicality Condition

We summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking, split by typicality condition.

# summarize average accuracy within participant
avg_corrected_target_looking_by_typicality <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality <- avg_corrected_target_looking_by_typicality %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	84	0.0650543	0.0200254	0.0450288	0.0850797
typical	84	0.0804637	0.0221078	0.0583559	0.1025714

By Target Label

We summarize each participants’ average accuracy during the critical window and average baseline-corrected proportion target looking, split by typicality condition and target label.

# summarize average accuracy within participant
avg_corrected_target_looking_by_category <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

Main Analyses

1. Aim 1

1.1

1.1.1

To investigate whether there was an effect of typicality on infants’ word recognition, we fit a linear mixed-effects model predicting average baseline-corrected proportion target looking from typicality condition (centered), including a by-participant random intercept. No random slope was included because the number of observations in the model would otherwise be equal to the number of random effects - however, a model with (overriding the lmer error message) or without typicality condition as a random slope yields identical results.

avg_corrected_target_looking_by_typicality <- avg_corrected_target_looking_by_typicality %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

#Note that we ignore the warning here that number of observations is equal to the number of random effects, which lmer dislikes due to making it impossible to separate error at different hierarchical levels
#however, the model fit (at the fixed level) is for all intents and purposes identical for the model retaining the random slope for typicality and one removing the random slope for typicality
#(see commented-out model below)
#we therefore proceed with the (numerically identical) model with the random slope retained, for consistency with the Stage 1 plan.
#This same rationale applies to subsequent participant-level models we fit below.

#m_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1|sub_num),data=avg_corrected_target_looking_by_typicality)

summary(m_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -305
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.19855 -0.40450  0.06351  0.40240  1.93330 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.004316 0.06570      
##           typicality_condition_c 0.004443 0.06665  0.21
##  Residual                        0.004020 0.06340      
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.072759   0.008678 83.000021   8.384 1.11e-12 ***
## typicality_condition_c  0.015409   0.012190 82.999873   1.264     0.21    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.105 
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

confint(m_1_1,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.055750155 0.08976778
## typicality_condition_c -0.008482829 0.03930159

Infants successfully recognized the target words (Model Intercept: \(\hat{\beta} = 0.07\), 95% CI \([0.06, 0.09]\), \(t(83) = 8.38\), \(p < .001\)).

Overall Typicality Effect Plot

Next, we plot the overall average base-line corrected proportion target looking for each condition (in black). Individual points represent individual subjects, lines link subject responses between conditions. Error bars represent 95% CIs.

#Overall baseline-corrected proportion target looking by condition
pal <- wes_palette("Rushmore1", n=5)
set.seed(1)
jitterer <- position_jitter(width = .05,seed=1)
overall_typicality_plot <- ggplot(avg_corrected_target_looking_by_typicality,aes(x=condition,y=average_corrected_target_looking, fill=condition))+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality, condition=="atypical"),position = position_nudge(x = -.1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="l")+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality, condition=="typical"),position = position_nudge(x = .1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="r")+
  geom_path(aes(group=sub_num),color="black",fill=NA,alpha=0.15,size=0.75,position=jitterer)+
  geom_point(aes(color=condition,group=sub_num), size = 2.5, alpha=0.15,position=jitterer)+
  geom_point(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking),color="black",size=5)+
  geom_line(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking,group=1),color="black",size=3)+
  geom_errorbar(data=overall_corrected_target_looking_by_typicality,aes(y=corrected_target_looking,ymin=lower_ci,ymax=upper_ci),width=0,size=1.2,color="black")+
  #geom_boxplot(outlier.shape = NA, alpha = .5, width = .1, colour = "black")+
  #scale_colour_brewer(palette = "Dark2")+
  #scale_fill_brewer(palette = "Dark2")+
  geom_hline(yintercept=0,linetype="dashed")+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_fill_manual(values=pal[c(3,4)])+
  theme(legend.position="none")+
  xlab("Typicality Condition")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=14),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"))

overall_typicality_plot 

ggsave(here::here("..","figures","baseline_corrected_accuracy_overall.png"),width=7,height=6,bg = "white")

1.1.2

overall_condition_summary <- avg_corrected_target_looking_by_typicality %>%
  ungroup() %>%
  group_by(sub_num) %>%
  summarize(
    condition_diff = average_corrected_target_looking[condition=="typical"]-average_corrected_target_looking[condition=="atypical"]
  ) %>%
  ungroup() %>%
  summarize(
    N=n(),
    diff = mean(condition_diff),
    sd = sd(condition_diff)
  )

tost_results <- tsum_TOST(m1=overall_condition_summary$diff,sd1=overall_condition_summary$sd,n1=overall_condition_summary$N,eqb=0.25, eqbound_type = "SMD")

#quick sanity check
#t-test in tost is equivalent to regular old paired t-test
# AND equivalent to lmer estimate of typicality effect
t.test(
  avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"],
  avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"], 
  paired=T)
#effect size
typicality_effect_cohens_d <- cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"],
         avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"],
         paired=T)

There was no significant effect of typicality, \(\hat{\beta} = 0.02\), 95% CI \([-0.01, 0.04]\), \(t(83.00) = 1.26\), \(p = .210\), Cohen’s d=0.14, 95% CI [-0.08,0.35]. The equivalence test was non-significant, t(83) = -1.027, p = 1.54e-01. We therefore could not reject the null hypothesis that the absolute effect size was at least as large as d=0.25.

1.1.3

## Typical word recognition
# recentering the model on the typical condition to make the intercept interpretable
m_1_1_3_typ <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_1_1_3_typ)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -305
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.49953 -0.45988  0.07221  0.45749  2.19800 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.005182 0.07199      
##           typicality_condition_typ 0.002091 0.04573  0.60
##  Residual                          0.005196 0.07208      
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.08046    0.01112 82.99955   7.239 2.08e-10 ***
## typicality_condition_typ  0.01541    0.01219 83.00059   1.264     0.21    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.630 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_typ,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sig03                             NA         NA
## .sigma                             NA         NA
## (Intercept)               0.058678143 0.10224917
## typicality_condition_typ -0.008482714 0.03930147

#effect size
typical_cohens_d <- cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="typical"])

## Atypical word recognition
# recentering the model on the atypical condition to make the intercept interpretable
m_1_1_3_atyp <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_1_1_3_atyp)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -305
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.35170 -0.43268  0.06794  0.43044  2.06798 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.003916 0.06258       
##           typicality_condition_atyp 0.003284 0.05730  -0.20
##  Residual                           0.004599 0.06782       
## Number of obs: 168, groups:  sub_num, 84
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                0.06505    0.01007 83.00005   6.461 6.69e-09 ***
## typicality_condition_atyp  0.01541    0.01219 82.99930   1.264     0.21    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.515

confint(m_1_1_3_atyp,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.045320783 0.08478777
## typicality_condition_atyp -0.008482889 0.03930165

#effect size
atypical_cohens_d <-cohens_d(avg_corrected_target_looking_by_typicality$average_corrected_target_looking[avg_corrected_target_looking_by_typicality$condition=="atypical"])

Infants robustly recognized the target words for both typical (Model: \(\hat{\beta} = 0.08\), 95% CI \([0.06, 0.10]\), \(t(83.00) = 7.24\), \(p < .001\); Cohen’s d = 0.79, 95% CI [0.54,1.03]; Mean baseline-corrected looking: M=8%, 95% CI [5.8%, 10.3%]) and atypical exemplars (Model: \(\hat{\beta} = 0.07\), 95% CI \([0.05, 0.08]\), \(t(83) = 6.46\), \(p < .001\); Cohen’s d = 0.7, 95% CI [0.46,0.94]; Mean baseline-corrected looking: M=6.5%, 95% CI [4.5%, 8.5%]).

1.2

trial_corrected_accuracy <- trial_corrected_accuracy %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

#model with typicality condition yields a singular fit, so we removed the random slope
# however, the singular model still yields relatively identical results to the model
# without the typicality condition random slope
# m_1_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
#             (1 + typicality_condition_c|sub_num) +
#             (1|target_category),
#           data=trial_corrected_accuracy)

m_1_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
            (1 | sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2262.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.15492 -0.63130 -0.02562  0.65630  2.78234 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0031427 0.05606 
##  target_category (Intercept) 0.0002028 0.01424 
##  Residual                    0.1190987 0.34511 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)            7.366e-02  1.129e-02 5.932e+00   6.524 0.000648 ***
## typicality_condition_c 1.147e-02  1.244e-02 3.014e+03   0.922 0.356604    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.001

confint(m_1_2,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.05152909 0.09578319
## typicality_condition_c -0.01291181 0.03585025

#Centering on typical condition
m_1_2_typ <- lmer(corrected_target_looking ~ 1 + typicality_condition_typ + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2_typ)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_typ + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2262.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.15492 -0.63130 -0.02562  0.65630  2.78234 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0031427 0.05606 
##  target_category (Intercept) 0.0002028 0.01424 
##  Residual                    0.1190987 0.34511 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                           Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)              7.939e-02  1.290e-02 1.010e+01   6.156 0.000103 ***
## typicality_condition_typ 1.147e-02  1.244e-02 3.014e+03   0.922 0.356604    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.483

confint(m_1_2_typ,method="Wald")

##                                2.5 %     97.5 %
## .sig01                            NA         NA
## .sig02                            NA         NA
## .sigma                            NA         NA
## (Intercept)               0.05411442 0.10466709
## typicality_condition_typ -0.01291181 0.03585025

#Centering on atypical condition
m_1_2_atyp <- lmer(corrected_target_looking ~ 1 + typicality_condition_atyp + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_1_2_atyp)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_atyp + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2262.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.15492 -0.63130 -0.02562  0.65630  2.78234 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0031427 0.05606 
##  target_category (Intercept) 0.0002028 0.01424 
##  Residual                    0.1190987 0.34511 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                            Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)               6.792e-02  1.288e-02 1.006e+01   5.272 0.000355 ***
## typicality_condition_atyp 1.147e-02  1.244e-02 3.014e+03   0.922 0.356604    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.482

confint(m_1_2_atyp,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sigma                             NA         NA
## (Intercept)                0.04267204 0.09317103
## typicality_condition_atyp -0.01291181 0.03585025

The model with the maximal random effects structure yielded a singular fit that was only remedied by removing the by-participant random slope for typicality condition. However, the (singular) model including the typicality random slope yielded virtually identical results to the converging model including random intercepts for participant and target word only. As in the average participant-level analysis, infants’ overall recognition of target words was significant in the trial-level model (\(\hat{\beta} = 0.07\), 95% CI \([0.05, 0.10]\), \(t(5.93) = 6.52\), \(p < .001\)) and there was no significant effect of typicality (\(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.04]\), \(t(3014.08) = 0.92\), \(p = .357\)). Word recognition was robust both for typical (\(\hat{\beta} = 0.08\), 95% CI \([0.05, 0.10]\), \(t(10.10) = 6.16\), \(p < .001\)) and atypical exemplars (\(\hat{\beta} = 0.07\), 95% CI \([0.04, 0.09]\), \(t(10.06) = 5.27\), \(p < .001\)).

1.3

The cluster-based permutation analysis is executed in cluster_permutation_analysis.Rmd.

In the cluster-based permutation analyses, we found one cluster of adjacent time bins ranging from 0-200ms with |t|>2 (in the direction of higher accuracy for typical exemplars compared to atypical exemplars). However, this cluster did not reach significance in the permutation test, p=.41.

Timecourse Plots

Overall

Next, we plot the data. First we summarize the data in two steps: (1) summarize the data by subject for each time point, followed by (2) averaging looking for each time point across subjects.

#summarizing within subject for each time point
summarize_subj <- d_resampled %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  group_by(sub_num, child_gender, time_normalized_corrected) %>%
  summarize(N=n(),
            mean_age=mean(age),
            mean_age_mo=mean(age_mo),
            non_na_n = sum(!is.na(accuracy_transformed)), 
            mean_accuracy=mean(accuracy_transformed,na.rm=TRUE),
            ci=qt(0.975, non_na_n-1)*sd(accuracy_transformed,na.rm=T)/sqrt(non_na_n),
            lower_ci=mean_accuracy-ci,
            upper_ci=mean_accuracy+ci) %>%
  ungroup()

#summarizing across subjects for each time point
summarize_across_subj <- summarize_subj %>%
  group_by(time_normalized_corrected) %>%
  dplyr::summarize(n=n(),
            accuracy=mean(mean_accuracy,na.rm=TRUE),
            sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
            se_accuracy=sd_accuracy/sqrt(n))

ggplot(summarize_across_subj,aes(time_normalized_corrected,accuracy))+
  xlim(-2000,4000)+
  geom_smooth(method="gam")+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point()+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  ylim(0.35,0.65)+
  xlab("Time (normalized to target word onset) in ms")+
  ylab("Proportion Target Looking")

ggsave(here::here("..","figures","overall_accuracy.png"),bg = "white")

Timecourse by age

summarize_across_subj_by_age <- summarize_subj %>%
  mutate(age_group=cut_number(mean_age_mo,n=4)) %>%
  group_by(age_group,time_normalized_corrected) %>%
  dplyr::summarize(n=n(),
                   accuracy=mean(mean_accuracy,na.rm=TRUE),
                   sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
                   se_accuracy=sd_accuracy/sqrt(n))
ggplot(summarize_across_subj_by_age,aes(time_normalized_corrected,accuracy))+
  xlim(-2000,4000)+
  geom_smooth(method="gam")+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point()+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  facet_wrap(~age_group)+
  xlab("Time (normalized to target word onset) in ms")+
  ylab("Proportion Target Looking")

ggsave(here::here("..","figures","overall_accuracy_by_age.png"),width=12, height=9,bg = "white")

Timecourse by condition

summarize_subj_condition <- d_resampled %>%
  filter(exclude_participant==0) %>%
  filter(useable_window==1) %>%
  group_by(sub_num, child_gender, condition, time_normalized_corrected) %>%
  summarize(
    mean_age=mean(age),
    mean_age_mo=mean(age_mo),
    mean_accuracy=mean(accuracy_transformed,na.rm=TRUE))

summarize_across_subj_cond <- summarize_subj_condition %>%
  group_by(condition,time_normalized_corrected) %>%
  summarize(n=n(),
            accuracy=mean(mean_accuracy,na.rm=TRUE),
            sd_accuracy=sd(mean_accuracy,na.rm=TRUE),
            se_accuracy=sd_accuracy/sqrt(n))

#plot
#timecourse plot
pal <- wes_palette("Rushmore1", n=5)
timecourse_plot <- ggplot(summarize_across_subj_cond,aes(time_normalized_corrected,accuracy,color=condition))+
  geom_rect(data = data.frame(xmin = 300,
                              xmax = 2800,
                              ymin = -Inf,
                              ymax = Inf),
            aes(x=NULL, y=NULL,xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax,color=NULL),
            fill = "grey", alpha = 0.2)+
  geom_rect(data = data.frame(xmin = -2000,
                              xmax = 0,
                              ymin = -Inf,
                              ymax = Inf),
            aes(x=NULL, y=NULL,xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax,color=NULL),
            fill = "grey", alpha = 0.2)+
  geom_errorbar(aes(ymin=accuracy-se_accuracy,ymax=accuracy+se_accuracy),width=0)+
  geom_point(alpha=0.5)+
  geom_smooth(data=summarize_subj_condition,aes(y=mean_accuracy),method="gam")+
  geom_vline(xintercept=0,size=1.5)+
  geom_hline(yintercept=0.5,size=1.2,linetype="dashed")+
  geom_vline(xintercept=300,linetype="dotted")+
  geom_vline(xintercept=2800,linetype="dotted")+
  geom_vline(xintercept=-2000,linetype="dotted")+
  geom_vline(xintercept=0,linetype="dotted")+
  theme(legend.position = c(0.8,0.15))+
  annotate("text",label="Critical Window",x=1550,y=0.9,size=6)+
  annotate("text",label="Baseline Window",x=-1000,y=0.9,size=6)+
  ylim(0,1)+
  #xlim(-2000,4000)+
  scale_x_continuous(breaks=seq(-2000,4000,1000),limits=c(-2000,4000))+
  scale_colour_manual(values=pal[c(3,4)])+
  ylab("Proportion Target Looking")+
  xlab("Time (centered on target word onset, in ms)")+
  theme(
    strip.background = element_rect(size=1, colour = "black"),
    strip.text = element_text(size=16,face="bold"),
    axis.title=element_text(size=20,face="bold"),
    axis.text = element_text(size=14),
    legend.text=element_text(size=18),
    legend.title=element_text(size=18))
timecourse_plot

ggsave(here::here("..","figures","typicality_accuracy.png"),width=10,height=6,bg = "white")

2. Aim 2

Linear mixed-effects model

#join in average age-centered variables
trial_corrected_accuracy <- trial_corrected_accuracy %>%
  left_join(subj_info_multisession)
  
#fit main model
# the random slope of typicality causes a singular boundary fit
# all attempts to prune other random effects (including covariances) were not successful,
# so we removed the random slope for typicality.
# Note that the effects for the (singular fit) model including the random slope for typicality are 
# equivalent to the model with typicality condition as a random slope.
m_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c * age_mo_c + 
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)

summary(m_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c * age_mo_c +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2268.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1736 -0.6358 -0.0231  0.6607  2.8111 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0024581 0.04958 
##  target_category (Intercept) 0.0002099 0.01449 
##  Residual                    0.1191179 0.34513 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                     7.324e-02  1.100e-02 5.178e+00   6.657  0.00101
## typicality_condition_c          1.131e-02  1.245e-02 3.015e+03   0.909  0.36366
## age_mo_c                        1.852e-02  5.567e-03 8.856e+01   3.327  0.00128
## typicality_condition_c:age_mo_c 4.366e-03  8.439e-03 3.015e+03   0.517  0.60496
##                                   
## (Intercept)                     **
## typicality_condition_c            
## age_mo_c                        **
## typicality_condition_c:age_mo_c   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ ag_m_c
## typclty_cn_  0.001              
## age_mo_c    -0.017  0.003       
## typclt__:__  0.003 -0.035  0.002

confint(m_2,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                      0.051678144 0.09480310
## typicality_condition_c          -0.013086269 0.03570251
## age_mo_c                         0.007611899 0.02943539
## typicality_condition_c:age_mo_c -0.012174882 0.02090698

#save interim model object
m_2_tidy <- m_2 %>%
  summarize_mixed_effects_model()

In the trial-level linear mixed-effects model including age, typicality condition, and their interaction, we found a significant effect of age (\(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(88.56) = 3.33\), \(p = .001\)), suggesting that word recognition accuracy increased with age overall. There was no significant interaction between age and typicality (\(\hat{\beta} = 0.00\), 95% CI \([-0.01, 0.02]\), \(t(3014.86) = 0.52\), \(p = .605\)), meaning that we found no evidence that the effect of typicality changed with age.

Plot

Overall

ggplot(avg_corrected_target_looking,aes(mean_age_mo,average_corrected_target_looking))+
  geom_pointrange(aes(ymin=lower_ci,ymax=upper_ci),
                  position=position_jitter(width=0.1),
                  width=0,
                  size=1.5) +
  geom_hline(yintercept=0,linetype="dashed")+
  geom_smooth(method="lm")+
  xlab("Age (in months)")+
  ylab("Baseline-Corrected Proportion Target Looking")+
  ylim(-0.55,0.55)+
  scale_x_continuous(breaks=seq(12,18,1))

ggsave(here::here("..","figures","age_relationship_baseline_corrected_accuracy.png"),width=7,height=6,bg = "white")

By Condition

pal <- wes_palette("Rushmore1", n=5)
age_by_typicality_plot <- ggplot(avg_corrected_target_looking_by_typicality,aes(mean_age_mo,average_corrected_target_looking,color=condition,group=condition))+
  geom_pointrange(aes(ymin=lower_se,ymax=upper_se), 
                  position=position_jitter(width=0.2),
                  width=0,
                  size=1) +
  geom_hline(yintercept=0,linetype="dashed")+
  geom_smooth(method="lm",color="black",size=1.3)+
  xlab("Age (in months)")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  #ylim(-0.55,0.5)+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_x_continuous(breaks=seq(12,18,1))+
  facet_wrap(~condition)+
  theme(
    strip.background = element_rect(size=1, colour = "black"),
    strip.text = element_text(size=16,face="bold"),
    axis.title=element_text(size=20,face="bold"),
    axis.text = element_text(size=14))+
  theme(legend.position="none")
ggsave(here::here("..","figures","age_relationship_baseline_corrected_accuracy_typicality.png"),width=9,height=6,bg = "white")
age_by_typicality_plot

#combine key plots into one main figure
library(patchwork)

(overall_typicality_plot + age_by_typicality_plot) / timecourse_plot + 
  plot_annotation(tag_levels = 'A')+
  theme(plot.tag = element_text(size = 18))

ggsave(here::here("..","figures","main_figure.png"),width=12,height=12,bg = "white")

3. Aim 3

In Aim 3, we tested whether individual differences in word recognition or typicality effects are predicted by differences in experiences with each exemplar.

#subject details for aim 3 analysis (how many participants have survey data)
aim3_subject_info <- trial_corrected_accuracy %>%
  filter(!is.na(target_parent_typicality_rating_z)) %>%
  ungroup()%>%
  summarize(
    N = length(unique(sub_num)),
    mean_age = mean(age_c),
    sd_age = sd(age_c)
  )

aim3_subject_info%>%
  knitr::kable()

N	mean_age	sd_age
74	-0.7274035	45.04816

#fit main model
# as before, the random slope of typicality (this time parent-rated typicality) causes a singular boundary fit
# all attempts to prune other random effects (including covariances) were not successful,
# so we removed the random slope for target_parent_typicality_rating_z.
# Note that the effects for the (singular fit) model including the random slope for typicality are 
# equivalent to the model with typicality as a random slope.
# In other words, the decision to omit the random slope does not substantively impact the main estimates or change the pattern of results
# m_3 <- lmer(corrected_target_looking ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1+ target_parent_typicality_rating_z|sub_num) + (1|target_category), trial_corrected_accuracy)
m_3 <- lmer(corrected_target_looking ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1|sub_num) + (1|target_category), trial_corrected_accuracy)

summary(m_3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + target_parent_typicality_rating_z +  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2004.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.13146 -0.62555 -0.03277  0.65545  2.78542 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0026490 0.05147 
##  target_category (Intercept) 0.0003016 0.01737 
##  Residual                    0.1199959 0.34640 
## Number of obs: 2699, groups:  sub_num, 74; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error        df t value
## (Intercept)                       7.355e-02  1.253e-02 5.043e+00   5.869
## target_parent_typicality_rating_z 3.840e-03  6.883e-03 2.255e+03   0.558
## age_mo_c                          1.499e-02  6.070e-03 6.695e+01   2.469
##                                   Pr(>|t|)   
## (Intercept)                        0.00198 **
## target_parent_typicality_rating_z  0.57703   
## age_mo_c                           0.01611 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) tr____
## trgt_prn___ 0.008        
## age_mo_c    0.027  0.013

confint(m_3,method="Wald")

##                                          2.5 %     97.5 %
## .sig01                                      NA         NA
## .sig02                                      NA         NA
## .sigma                                      NA         NA
## (Intercept)                        0.048986101 0.09810614
## target_parent_typicality_rating_z -0.009651290 0.01733032
## age_mo_c                           0.003090034 0.02688578

m_3_tidy <- m_3 %>%
  summarize_mixed_effects_model()

Caregiver report of exemplar typicality did not significantly predict infants’ baseline-corrected word recognition accuracy (\(\hat{\beta} = 0.00\), 95% CI \([-0.01, 0.02]\), \(t(2254.94) = 0.56\), \(p = .577\)). Controlling for parent-reported typicality, age remained a significant predictor of infants’ word recognition (\(\hat{\beta} = 0.01\), 95% CI \([0.00, 0.03]\), \(t(66.95) = 2.47\), \(p = .016\)).

Visualization

#quick visualization of the (non-)effect for each category
#by category
ggplot(trial_corrected_accuracy,aes(target_parent_typicality_rating_z,corrected_target_looking))+
  geom_point(alpha=0.1)+
  geom_smooth(method = "lm")+
  facet_wrap(~target_category)

4. Robustness Analyses

We also conducted a series of robustness analyses to probe the degree to which any results hinged on key analytic decisions.

4.1. Window Choice

Summarize data

We conducted the same main analyses as those described above using an alternative, shorter critical window of 300-1800ms (e.g., Fernald et al., 2008) (with the exception of the cluster-based permutation analysis described in analysis section 1.3).

First, we summarize participants looking behavior as before, using the new critical window.

# apply exclusions based on the new critical window
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_all %>%
  filter(exclude_participant_insufficient_data_short==0) %>%
  #only include trials that are useable based on looking in the 300-1800ms window
  filter(useable_window_short==1) %>%
  #ignore trial exclusions due to "insufficient looking" based on 300-2800ms window
  filter(is.na(trial_exclusion_reason) | trial_exclusion_reason=="insufficient looking")

# summarize average accuracy within participant, split by typicality
avg_corrected_target_looking_by_typicality_short_window <- trial_corrected_accuracy_short_window  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking_short,na.rm=TRUE),
            se=sd(corrected_target_looking_short,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking_short,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_short_window %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	82	0.0607253	0.0222173	0.0385080	0.0829426
typical	82	0.0805892	0.0227677	0.0578215	0.1033570

Participant-level analysis

Aim 1.1

#1.1. Participant-level analysis of the typicality effect
avg_corrected_target_looking_by_typicality_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_4_1_1_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+ typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))

summary(m_4_1_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -274.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2088 -0.4208  0.1123  0.4960  1.5413 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.003886 0.06234      
##           typicality_condition_c 0.005990 0.07739  0.05
##  Residual                        0.005097 0.07139      
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.070657   0.008858 80.999530   7.976 8.37e-12 ***
## typicality_condition_c  0.019864   0.014048 81.000333   1.414    0.161    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.025 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_4_1_1_1,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.053294920 0.08801960
## typicality_condition_c -0.007670339 0.04739821

#effect size
typicality_effect_short_window_cohens_d <- cohens_d(
  filter(avg_corrected_target_looking_by_typicality_short_window,condition=="typical")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_short_window,condition=="atypical")$average_corrected_target_looking,
  paired=T)

There was no significant effect of typicality in the average participant-level analysis, \(\hat{\beta} = 0.02\), 95% CI \([-0.01, 0.05]\), \(t(81.00) = 1.41\), \(p = .161\), Cohen’s d=0.1561463, 95% CI [-0.0620985,0.3734399].

# run equivalence test
overall_condition_summary_short_window <- avg_corrected_target_looking_by_typicality_short_window %>%
  group_by(sub_num) %>%
  summarize(
    condition_diff_alternative = average_corrected_target_looking[condition=="typical"]-average_corrected_target_looking[condition=="atypical"]
  ) %>%
  ungroup() %>%
  summarize(
    N=n(),
    diff = mean(condition_diff_alternative),
    sd = sd(condition_diff_alternative)
  )

tost_results_short_window <- tsum_TOST(m1=overall_condition_summary_short_window$diff,sd1=overall_condition_summary_short_window$sd,n1=overall_condition_summary_short_window$N,eqb=0.25, eqbound_type = "SMD")

The equivalence test was non-significant, t(81) = -0.850, p = 1.99e-01, as in the main analysis.

#word recognition for typical items
m_1_1_3_typ_short_window <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_typ_short_window)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -274.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3156 -0.4411  0.1178  0.5200  1.6158 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.005136 0.07166      
##           typicality_condition_typ 0.004980 0.07057  0.54
##  Residual                          0.005601 0.07484      
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.08059    0.01144 81.00004   7.043 5.58e-10 ***
## typicality_condition_typ  0.01986    0.01405 81.00028   1.414    0.161    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.633 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_typ_short_window,method="Wald")

##                                 2.5 %     97.5 %
## .sig01                             NA         NA
## .sig02                             NA         NA
## .sig03                             NA         NA
## .sigma                             NA         NA
## (Intercept)               0.058161596 0.10301686
## typicality_condition_typ -0.007670371 0.04739824

#effect size
typical_cohens_d_short_window <- cohens_d(avg_corrected_target_looking_by_typicality_short_window$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_short_window$condition=="typical"])


#word recognition for atypical items
m_1_1_3_atyp_short_window <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality_short_window,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_atyp_short_window)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_short_window
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -274.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2792 -0.4342  0.1159  0.5118  1.5905 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.004797 0.06926       
##           typicality_condition_atyp 0.005329 0.07300  -0.48
##  Residual                           0.005427 0.07367       
## Number of obs: 164, groups:  sub_num, 82
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                0.06073    0.01117 80.99987   5.438 5.56e-07 ***
## typicality_condition_atyp  0.01986    0.01405 80.99968   1.414    0.161    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.609
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_atyp_short_window,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.038839907 0.08261068
## typicality_condition_atyp -0.007670419 0.04739829

#effect size
atypical_cohens_d_short_window <- cohens_d(avg_corrected_target_looking_by_typicality_short_window$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_short_window$condition=="atypical"])

Infants showed robust recognition of both typical (\(\hat{\beta} = 0.08\), 95% CI \([0.06, 0.10]\), \(t(81) = 7.04\), \(p < .001\); Cohen’s d = 0.7777403, 95% CI [0.5286035,1.0230632]) and atypical targets (\(\hat{\beta} = 0.06\), 95% CI \([0.04, 0.08]\), \(t(81.00) = 5.44\), \(p < .001\); Cohen’s d = 0.6005605, 95% CI [0.3636676,0.8342962]).

Trial-level analyses (Aims 1.2, 2, and 3)

Aim 1.2.

# 1.2.
# trial-level analysis of the typicality effect
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_short_window %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_4_1_1_2 <- lmer(corrected_target_looking_short ~ 1 + typicality_condition_c + 
            (1 |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_short_window)
summary(m_4_1_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking_short ~ 1 + typicality_condition_c +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 3174.5
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.72705 -0.69103  0.01208  0.74305  2.42063 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0022511 0.04745 
##  target_category (Intercept) 0.0004006 0.02002 
##  Residual                    0.1622463 0.40280 
## Number of obs: 3066, groups:  sub_num, 82; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)   
## (Intercept)            7.217e-02  1.346e-02 4.135e+00   5.362  0.00531 **
## typicality_condition_c 1.510e-02  1.456e-02 2.996e+03   1.037  0.29961   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.000

confint(m_4_1_1_2,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.04578524 0.09854802
## typicality_condition_c -0.01343104 0.04363985

We again found no significant effect of typicality (\(\hat{\beta} = 0.02\), 95% CI \([-0.01, 0.04]\), \(t(2996.23) = 1.04\), \(p = .300\)).

Aim 2

# Aim 2: Typicality by Age interaction
trial_corrected_accuracy_short_window <- trial_corrected_accuracy_short_window %>%
  left_join(subj_info_multisession)
  

m_4_1_2 <- lmer(corrected_target_looking_short ~ 1 + typicality_condition_c * age_mo_c + 
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_short_window)
summary(m_4_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking_short ~ 1 + typicality_condition_c *  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 3180.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.73503 -0.69424  0.00448  0.74206  2.45879 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0016077 0.04010 
##  target_category (Intercept) 0.0004124 0.02031 
##  Residual                    0.1622557 0.40281 
## Number of obs: 3066, groups:  sub_num, 82; target_category, 4
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                     7.172e-02  1.327e-02 3.775e+00   5.403  0.00669
## typicality_condition_c          1.492e-02  1.457e-02 2.997e+03   1.024  0.30577
## age_mo_c                        1.853e-02  5.831e-03 8.518e+01   3.178  0.00207
## typicality_condition_c:age_mo_c 6.154e-03  9.971e-03 2.995e+03   0.617  0.53716
##                                   
## (Intercept)                     **
## typicality_condition_c            
## age_mo_c                        **
## typicality_condition_c:age_mo_c   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ ag_m_c
## typclty_cn_  0.000              
## age_mo_c    -0.016  0.003       
## typclt__:__  0.003 -0.033  0.000

confint(m_4_1_2,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                      0.045700747 0.09772995
## typicality_condition_c          -0.013628291 0.04346818
## age_mo_c                         0.007100369 0.02995773
## typicality_condition_c:age_mo_c -0.013389289 0.02569764

Age remained a significant predictor of accuracy, \(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(85.18) = 3.18\), \(p = .002\). However, we found no evidence of a typicality by age interaction (\(t(2994.91) = 0.62\), \(p = .537\)).

Aim 3

#Aim 3
#parent typicality ratings as a predictor
m_4_1_3 <- lmer(corrected_target_looking_short ~ 1 + target_parent_typicality_rating_z + age_mo_c + (1|sub_num) + (1|target_category), trial_corrected_accuracy_short_window)

summary(m_4_1_3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## corrected_target_looking_short ~ 1 + target_parent_typicality_rating_z +  
##     age_mo_c + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_short_window
## 
## REML criterion at convergence: 2799.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.72410 -0.69864  0.01098  0.73981  2.48807 
## 
## Random effects:
##  Groups          Name        Variance Std.Dev.
##  sub_num         (Intercept) 0.001527 0.03907 
##  target_category (Intercept) 0.000610 0.02470 
##  Residual                    0.162857 0.40356 
## Number of obs: 2692, groups:  sub_num, 72; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error        df t value
## (Intercept)                       7.446e-02  1.533e-02 3.602e+00   4.858
## target_parent_typicality_rating_z 9.397e-03  8.048e-03 2.389e+03   1.168
## age_mo_c                          1.708e-02  6.147e-03 6.816e+01   2.778
##                                   Pr(>|t|)   
## (Intercept)                        0.01076 * 
## target_parent_typicality_rating_z  0.24307   
## age_mo_c                           0.00706 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) tr____
## trgt_prn___ 0.005        
## age_mo_c    0.011  0.010

m_4_1_3_tidy <- m_4_1_3 %>%
  summarize_mixed_effects_model()

Caregiver report of exemplar typicality did not significantly predict infants’ baseline-corrected word recognition accuracy (\(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.03]\), \(t(2388.88) = 1.17\), \(p = .243\)). After controlling for the effect of parental report of typicality, age remained a significant predictor of infants’ word recognition (\(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(68.16) = 2.78\), \(p = .007\)).

4.2 Excluding unknown words

We were unable to conduct a robustness analysis excluding words marked as unknown by caregivers due to the omission of the MCDI during data collection.

4.3 Using reaction times as the main dependent measure

To assess the consistency of typicality effects across multiple indices of word recognition, we fit the main two models in Aim 1 (section 1.1 and 1.2 in the Analysis Plan), testing for a typicality effect at the participant level and at the trial level, using a second dependent measure: reaction time.

Load RT

Reaction times are computed in 3_compute_rt.Rmd.

Here, we load in the trial-by-trial reaction time data and join it with other trial properties.

#load RT data
rt_path <- here::here("..","..","data","processed_data","CATegories_exp2_RT_by_trial.csv")
d_rt <- read_csv(rt_path)

#get some other useful metadata and combine with the RT data
d_trial_level <- d %>%
  distinct(sub_num,session, trial_number,condition, age, age_mo, target_image, child_gender,target_category,exclude_technical_issue,exclude_frame_rate)
d_rt<- d_rt %>%
  left_join(d_trial_level)

#participants must contribute 4 typical and 4 atypical trials to be included in analysis
d_rt_subj_summary <- d_rt %>%
  #we only care about distractor-to-target shifts (not e.g. T-D, target-distractor shifts)
  filter(shift_type == "D-T")%>%
  #only include RTs within the critical window
  filter(rt>=300) %>%
  filter(rt<=2800) %>%
  #only include participants from the final sample
  filter(exclude_participant==0) %>%
  #exclude any trials with technical issues or frame rate issues
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  group_by(sub_num, condition) %>%
  summarize(
    trials = n()
  ) %>%
  pivot_wider(names_from=condition,names_prefix="useable_rt_trials_",values_from=trials) %>%
  # only include participants with at least 4 reaction time trials of each type
  mutate(
    sufficient_rt_trials=case_when(
      is.na(useable_rt_trials_typical) ~ 0,
      is.na(useable_rt_trials_atypical) ~ 0,
      useable_rt_trials_typical>=4 & useable_rt_trials_atypical>=4 ~ 1,
      TRUE ~ 0)
  )

#add exclusionary criteria to DF
d_rt <- d_rt %>%
  left_join(d_rt_subj_summary)

#apply exclusions and store the final RT dataset to use in analyses
d_rt_final <- d_rt %>%
  filter(shift_type == "D-T")%>%
  #only include RTs within the critical window
  filter(rt>=300) %>%
  filter(rt<=2800) %>%
  #only include participants from the final sample
  filter(exclude_participant==0) %>%
  #exclude any trials with technical issues or frame rate issues
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  filter(sufficient_rt_trials==1)

Visualization of RTs

hist(filter(d_rt_final)$rt)

#log-transofrm rt
d_rt_final <- d_rt_final %>%
  mutate(
    log_rt = log(rt),
    log_shift_start_rt=log(shift_start_rt)
  )

The data are right skewed, which is common for RTs. We will use log transformations in the subsequent models to account for the distribution of the data.

4.3.1 Participant-level analysis with RT as DV

#summarize reaction time by participant and condition
avg_subj_rt <- d_rt_final %>%
  group_by(sub_num, child_gender,condition) %>%
  summarize(N=n(),
            average_rt=mean(rt,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(rt,na.rm=T)/sqrt(N),
            lower_ci=average_rt-ci,
            upper_ci=average_rt+ci,
            average_log_rt=mean(log_rt,na.rm=TRUE),
            log_rt_ci=qt(0.975, N-1)*sd(log_rt,na.rm=T)/sqrt(N),
            lower_log_rt_ci=average_log_rt-log_rt_ci,
            upper_log_rt_ci=average_log_rt+log_rt_ci) %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    )
  )

#overall reaction times
overall_rt <- avg_subj_rt %>%
  group_by(condition) %>%
  summarize(N=n(),
            avg_rt=mean(average_rt,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_rt,na.rm=T)/sqrt(N),
            lower_ci=avg_rt-ci,
            upper_ci=avg_rt+ci)

overall_rt %>%
  knitr::kable()

condition	N	avg_rt	ci	lower_ci	upper_ci
atypical	70	917.8128	64.37932	853.4335	982.1921
typical	70	881.3043	52.31590	828.9884	933.6202

# participant-level model testing the typicality effect
m_4_3_1 <- lmer(average_log_rt ~ 1 + typicality_condition_c + (1|sub_num),data=avg_subj_rt)

summary(m_4_3_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_log_rt ~ 1 + typicality_condition_c + (1 | sub_num)
##    Data: avg_subj_rt
## 
## REML criterion at convergence: -1.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.78625 -0.55526 -0.02807  0.50575  2.55587 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  sub_num  (Intercept) 0.02179  0.1476  
##  Residual             0.03696  0.1923  
## Number of obs: 140, groups:  sub_num, 70
## 
## Fixed effects:
##                        Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)             6.65438    0.02399 69.00000 277.428   <2e-16 ***
## typicality_condition_c -0.03571    0.03250 69.00000  -1.099    0.276    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.000

confint(m_4_3_1,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sigma                          NA         NA
## (Intercept)             6.60737115 6.70139438
## typicality_condition_c -0.09940132 0.02798935

There was no significant effect of typicality on infants’ log reaction time on the participant level (\(\hat{\beta} = -0.04\), 95% CI \([-0.10, 0.03]\), \(t(69) = -1.10\), \(p = .276\)).

4.3.2 Trial-level analysis with RT as DV

d_rt_final <- d_rt_final %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    )
  )

m_4_3_2 <- lmer(log_rt ~ 1 + typicality_condition_c + 
            (1|sub_num) +
            (1|target_category),
          data=d_rt_final)

summary(m_4_3_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## log_rt ~ 1 + typicality_condition_c + (1 | sub_num) + (1 | target_category)
##    Data: d_rt_final
## 
## REML criterion at convergence: 1617.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.16300 -0.68130 -0.07444  0.62074  2.52892 
## 
## Random effects:
##  Groups          Name        Variance Std.Dev.
##  sub_num         (Intercept) 0.018391 0.13561 
##  target_category (Intercept) 0.003048 0.05521 
##  Residual                    0.256901 0.50685 
## Number of obs: 1051, groups:  sub_num, 70; target_category, 4
## 
## Fixed effects:
##                          Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)               6.64363    0.03574    4.72533 185.881 2.58e-10 ***
## typicality_condition_c   -0.03107    0.03164 1010.47490  -0.982    0.326    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.004

confint(m_4_3_2,method="Wald")

##                             2.5 %     97.5 %
## .sig01                         NA         NA
## .sig02                         NA         NA
## .sigma                         NA         NA
## (Intercept)             6.5735742 6.71367708
## typicality_condition_c -0.0930796 0.03093668

There was no significant effect of typicality on infants’ log reaction time on the trial level (\(\hat{\beta} = -0.03\), 95% CI \([-0.09, 0.03]\), \(t(1010.47) = -0.98\), \(p = .326\)).

4.4 Testing whether effects interact with test session.

Given the multi-session structure of our data collection procedure, we also tested whether analyses held individually in each test session, by repeating the analyses above while including an interaction with test session (session 1 vs. session 2).

# summarize participants' overall average accuracy by session
avg_corrected_target_looking_by_session <- trial_corrected_accuracy  %>%
  group_by(sub_num,session,age,age_mo,days_between_sessions) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci)

# summarize average accuracy within participant, split by session and typicality
avg_corrected_target_looking_by_typicality_session <- trial_corrected_accuracy  %>%
  group_by(sub_num,session,age,age_mo,days_between_sessions, condition) %>%
  summarize(N=n(),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci)

4.4.1. Participant-level analysis with test session interaction

avg_corrected_target_looking_by_typicality_session <- avg_corrected_target_looking_by_typicality_session %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),    
    session_c = session - 1.5,
  )

m_4_4_1 <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c*session_c + (1+session_c|sub_num),data=avg_corrected_target_looking_by_typicality_session)

summary(m_4_4_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c *  
##     session_c + (1 + session_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_session
## 
## REML criterion at convergence: -377
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.3492 -0.6440  0.0004  0.5732  2.8515 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr 
##  sub_num  (Intercept) 0.004043 0.06359       
##           session_c   0.003318 0.05760  -0.67
##  Residual             0.013545 0.11638       
## Number of obs: 327, groups:  sub_num, 84
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                        0.070604   0.009479  78.851089   7.448
## typicality_condition_c             0.018873   0.012881 147.179841   1.465
## session_c                          0.010308   0.014368  77.047592   0.717
## typicality_condition_c:session_c  -0.045313   0.025762 147.179841  -1.759
##                                  Pr(>|t|)    
## (Intercept)                      1.04e-10 ***
## typicality_condition_c             0.1450    
## session_c                          0.4753    
## typicality_condition_c:session_c   0.0807 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ sssn_c
## typclty_cn_  0.003              
## session_c   -0.197 -0.003       
## typclty__:_ -0.003  0.020  0.003

confint(m_4_4_1,method="Wald")

##                                         2.5 %      97.5 %
## .sig01                                     NA          NA
## .sig02                                     NA          NA
## .sig03                                     NA          NA
## .sigma                                     NA          NA
## (Intercept)                       0.052024665 0.089183462
## typicality_condition_c           -0.006372639 0.044118988
## session_c                        -0.017852724 0.038468200
## typicality_condition_c:session_c -0.095805028 0.005178225

Focusing on the participant-level model, there was no significant interaction between typicality and test session (\(\hat{\beta} = -0.05\), 95% CI \([-0.10, 0.01]\), \(t(147.18) = -1.76\), \(p = .081\)) and the effect of typicality remained non-significant (\(\hat{\beta} = 0.02\), 95% CI \([-0.01, 0.04]\), \(t(147.18) = 1.47\), \(p = .145\)).

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_session <- avg_corrected_target_looking_by_typicality_session %>%
  group_by(session,condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_session %>%
  knitr::kable()

session	condition	N	corrected_target_looking	ci	lower_ci	upper_ci
1	atypical	84	0.0446853	0.0323194	0.0123658	0.0770047
1	typical	83	0.0894682	0.0302022	0.0592660	0.1196704
2	atypical	80	0.0772740	0.0274706	0.0498034	0.1047445
2	typical	80	0.0734904	0.0283799	0.0451105	0.1018703

4.4.2 Trial-level analysis with test session interaction

trial_corrected_accuracy <- trial_corrected_accuracy %>%
  mutate(
    session_c = session - 1.5
  )

m_4_4_2 <- lmer(corrected_target_looking ~ 1 + typicality_condition_c*session_c + 
            (1+session_c |sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_4_4_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c * session_c +  
##     (1 + session_c | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2273.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1781 -0.6264 -0.0213  0.6616  2.8020 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.  Corr 
##  sub_num         (Intercept) 3.143e-03 0.0560609      
##                  session_c   9.696e-07 0.0009847 -1.00
##  target_category (Intercept) 2.014e-04 0.0141929      
##  Residual                    1.191e-01 0.3451142      
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                       7.368e-02  1.128e-02  5.946e+00   6.535
## typicality_condition_c            1.183e-02  1.244e-02  3.012e+03   0.950
## session_c                         2.398e-03  1.258e-02  3.073e+03   0.191
## typicality_condition_c:session_c -3.383e-02  2.487e-02  3.006e+03  -1.360
##                                  Pr(>|t|)    
## (Intercept)                      0.000637 ***
## typicality_condition_c           0.341975    
## session_c                        0.848876    
## typicality_condition_c:session_c 0.173836    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ sssn_c
## typclty_cn_  0.001              
## session_c   -0.016 -0.007       
## typclty__:_ -0.004 -0.022  0.004
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

confint(m_4_4_2,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sig03                                    NA         NA
## .sig04                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                       0.05158176 0.09578048
## typicality_condition_c           -0.01256189 0.03621429
## session_c                        -0.02226126 0.02705646
## typicality_condition_c:session_c -0.08258366 0.01491515

Similarly, we found no evidence for an interaction between typicality and test session in the trial-level model (\(\hat{\beta} = -0.03\), 95% CI \([-0.08, 0.01]\), \(t(3005.87) = -1.36\), \(p = .174\)).

5. Exploratory analyses

5.1. Predicting average accuracy from continuous typicality ratings

Continuous typicality of target alone

Images were classified as typical vs. atypical based on an adult norming study. In this analysis, we investigated whether treating typicality as a continuous metric, using the norming ratings as a predictor, would provide us more power to detect a typicality effect.

#trial-level model
#we first considered a model with a by-participant random slope for typicality, but this model yielded a singular fit. The results were qualitatively similar when including the random slope (marginal p-value for typicality)
m_5_1_1 <- lmer(corrected_target_looking ~ 1 + target_typicality_z + 
            (1|sub_num)+
              (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_1_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + target_typicality_z + (1 | sub_num) +  
##     (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2261.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1717 -0.6353 -0.0247  0.6642  2.7780 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0031531 0.05615 
##  target_category (Intercept) 0.0002215 0.01488 
##  Residual                    0.1189918 0.34495 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                      Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)         7.375e-02  1.150e-02 5.781e+00   6.413 0.000785 ***
## target_typicality_z 1.157e-02  6.369e-03 2.842e+03   1.816 0.069477 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## trgt_typcl_ 0.005

confint(m_5_1_1,method="Wald")

##                             2.5 %     97.5 %
## .sig01                         NA         NA
## .sig02                         NA         NA
## .sigma                         NA         NA
## (Intercept)          0.0512077661 0.09628143
## target_typicality_z -0.0009169908 0.02404949

There was no significant effect of target typicality when analyzed continuously in a trial-level model (\(\hat{\beta} = 0.01\), 95% CI \([0.00, 0.02]\), \(t(2842.34) = 1.82\), \(p = .069\)).

We include a plot of the continuous typicality effect. Descriptively, it appears that perhaps there is a decrement in looking for items on the extreme end of typicality, and otherwise fairly similar target looking.

ggplot(trial_corrected_accuracy,aes(target_typicality_z,corrected_target_looking))+
  geom_point(aes(color=condition))+
  geom_hline(yintercept=0, linetype="dashed")+
  geom_smooth()

Continuous typicality of target AND distractor, including interaction

m_5_1_2 <- lmer(corrected_target_looking ~ 1 + target_typicality_z * distractor_typicality_z+
            (1+target_typicality_z : distractor_typicality_z|sub_num)+
              (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_1_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## corrected_target_looking ~ 1 + target_typicality_z * distractor_typicality_z +  
##     (1 + target_typicality_z:distractor_typicality_z | sub_num) +  
##     (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 2265.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.1987 -0.6346 -0.0279  0.6631  2.8227 
## 
## Random effects:
##  Groups          Name                                        Variance  Std.Dev.
##  sub_num         (Intercept)                                 0.0046687 0.06833 
##                  target_typicality_z:distractor_typicality_z 0.0019488 0.04415 
##  target_category (Intercept)                                 0.0002635 0.01623 
##  Residual                                                    0.1181687 0.34376 
##  Corr 
##       
##  -0.57
##       
##       
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                               Estimate Std. Error         df
## (Intercept)                                  1.025e-01  1.652e-02  1.634e+01
## target_typicality_z                          5.560e-03  1.284e-02  1.896e+03
## distractor_typicality_z                      2.204e-03  1.282e-02  1.910e+03
## target_typicality_z:distractor_typicality_z -3.427e-02  1.359e-02  6.659e+01
##                                             t value Pr(>|t|)    
## (Intercept)                                   6.203 1.15e-05 ***
## target_typicality_z                           0.433   0.6650    
## distractor_typicality_z                       0.172   0.8635    
## target_typicality_z:distractor_typicality_z  -2.521   0.0141 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trgt__ dstr__
## trgt_typcl_  0.003              
## dstrctr_ty_ -0.081 -0.862       
## trgt_ty_:__ -0.691  0.003  0.111

confint(m_5_1_2,method="Wald")

##                                                   2.5 %       97.5 %
## .sig01                                               NA           NA
## .sig02                                               NA           NA
## .sig03                                               NA           NA
## .sig04                                               NA           NA
## .sigma                                               NA           NA
## (Intercept)                                  0.07011322  0.134883634
## target_typicality_z                         -0.01960237  0.030722700
## distractor_typicality_z                     -0.02292264  0.027331222
## target_typicality_z:distractor_typicality_z -0.06091430 -0.007631645

We also explored including distractor typicality (z-scored) and its interaction with target typicality in the model. We found a significant interaction between distractor and target typicality, \(\hat{\beta} = -0.03\), 95% CI \([-0.06, -0.01]\), \(t(66.59) = -2.52\), \(p = .014\). The interaction seemed to be driven primarily by there being a stronger effect of target typicality when the distractor was more atypical compared to when the distractor was typical.

#figure explaining interaction
p1 <- ggplot(trial_corrected_accuracy,aes(target_typicality_z,corrected_target_looking))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  xlab("Target Typicality (z-scored adult ratings)")+
  scale_color_manual(values=pal[c(3,4)])+
  theme(legend.position="none")
p2 <- ggplot(trial_corrected_accuracy,aes(distractor_typicality_z,corrected_target_looking ))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  scale_color_manual(values=pal[c(3,4)])+
  xlab("Distractor Typicality (z-scored adult ratings)")+
  theme(legend.position="none")
p1+p2

Caregiver-reported typicality of target and distractor, including interaction

#more complex random effects structures yielded a singular fit
m_5_1_3 <- lmer(corrected_target_looking ~ target_parent_typicality_rating_z*distractor_parent_typicality_rating_z+ (1|sub_num) + (1|target_category), trial_corrected_accuracy)
summary(m_5_1_3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ target_parent_typicality_rating_z *  
##     distractor_parent_typicality_rating_z + (1 | sub_num) + (1 |  
##     target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 1991.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.14869 -0.62769 -0.02533  0.65859  2.77724 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0030465 0.05519 
##  target_category (Intercept) 0.0002714 0.01648 
##  Residual                    0.1193545 0.34548 
## Number of obs: 2687, groups:  sub_num, 73; target_category, 4
## 
## Fixed effects:
##                                                                           Estimate
## (Intercept)                                                              8.120e-02
## target_parent_typicality_rating_z                                       -1.303e-03
## distractor_parent_typicality_rating_z                                    8.234e-03
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z -1.491e-02
##                                                                         Std. Error
## (Intercept)                                                              1.294e-02
## target_parent_typicality_rating_z                                        7.764e-03
## distractor_parent_typicality_rating_z                                    7.660e-03
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z  8.121e-03
##                                                                                 df
## (Intercept)                                                              6.446e+00
## target_parent_typicality_rating_z                                        1.667e+03
## distractor_parent_typicality_rating_z                                    2.353e+03
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z  2.554e+03
##                                                                         t value
## (Intercept)                                                               6.275
## target_parent_typicality_rating_z                                        -0.168
## distractor_parent_typicality_rating_z                                     1.075
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z  -1.836
##                                                                         Pr(>|t|)
## (Intercept)                                                             0.000576
## target_parent_typicality_rating_z                                       0.866739
## distractor_parent_typicality_rating_z                                   0.282509
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z 0.066508
##                                                                            
## (Intercept)                                                             ***
## target_parent_typicality_rating_z                                          
## distractor_parent_typicality_rating_z                                      
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) tr____ ds____
## trgt_prn___ -0.005              
## dstrctr____ -0.009 -0.461       
## tr____:____ -0.271  0.046  0.028

confint(m_5_1_3,method="Wald")

##                                                                               2.5 %
## .sig01                                                                           NA
## .sig02                                                                           NA
## .sigma                                                                           NA
## (Intercept)                                                              0.05583514
## target_parent_typicality_rating_z                                       -0.01652050
## distractor_parent_typicality_rating_z                                   -0.00677946
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z -0.03082676
##                                                                              97.5 %
## .sig01                                                                           NA
## .sig02                                                                           NA
## .sigma                                                                           NA
## (Intercept)                                                             0.106559196
## target_parent_typicality_rating_z                                       0.013914418
## distractor_parent_typicality_rating_z                                   0.023248182
## target_parent_typicality_rating_z:distractor_parent_typicality_rating_z 0.001008613

We also investigated whether including caregiver-reported exemplar typicality for both target and distractor (as well as their interaction) predicted baseline-corrected proportion target looking, and found no interaction (\(\hat{\beta} = -0.01\), 95% CI \([-0.03, 0.00]\), \(t(2554.28) = -1.84\), \(p = .067\)) or evidence of significant main effects.

5.2. Category and item-level analysis

Next, we investigate category- (target word) and item-level (target image) variation in proportion target looking.

Summarize overall target looking

Target Word

# summarize average accuracy within participant (by word alone)
avg_corrected_target_looking_by_word <- trial_corrected_accuracy  %>%
  group_by(sub_num, target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            critical_window_ci = qt(0.975, N-1)*sd(mean_target_looking_critical,na.rm=T)/sqrt(N),
            critical_window_lower_ci=average_critical_window_looking-critical_window_ci,
            critical_window_upper_ci=average_critical_window_looking+critical_window_ci,
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE),
            baseline_window_ci = qt(0.975, N-1)*sd(mean_target_looking_baseline,na.rm=T)/sqrt(N),
            baseline_window_lower_ci=average_baseline_window_looking-baseline_window_ci,
            baseline_window_upper_ci=average_baseline_window_looking+baseline_window_ci)

# summarize average accuracy within participant (by word split by typicality)
avg_corrected_target_looking_by_typicality_word <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE))

#overall summarized looking
#by word alone
overall_target_looking_by_word <- avg_corrected_target_looking_by_word %>%
  group_by(target_category) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            )
#by word split by typicality
overall_target_looking_by_typicality_word <- avg_corrected_target_looking_by_typicality_word %>%
  group_by(condition,target_category) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            )

Overall, participants showed robust learning of all four words, in both typicality conditions.

overall_target_looking_by_word %>%
  select(target_category:upper_ci) %>%
  knitr::kable()

target_category	N	corrected_target_looking	ci	lower_ci	upper_ci
bird	84	0.0819635	0.0299145	0.0520490	0.1118781
cat	84	0.0862806	0.0288659	0.0574147	0.1151466
dog	84	0.0475030	0.0253042	0.0221988	0.0728072
fish	84	0.0662666	0.0308036	0.0354630	0.0970702

overall_target_looking_by_typicality_word %>%
  select(target_category:upper_ci) %>%
  knitr::kable()

condition	target_category	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	bird	84	0.0911260	0.0432014	0.0479245	0.1343274
atypical	cat	84	0.0751083	0.0384676	0.0366407	0.1135759
atypical	dog	84	0.0251985	0.0393336	-0.0141351	0.0645320
atypical	fish	84	0.0675099	0.0429791	0.0245308	0.1104890
typical	bird	84	0.0745592	0.0360839	0.0384753	0.1106431
typical	cat	84	0.1026123	0.0399858	0.0626265	0.1425981
typical	dog	84	0.0733940	0.0358556	0.0375384	0.1092495
typical	fish	84	0.0635989	0.0411800	0.0224190	0.1047789

#checking the typicality effect for bird
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="bird")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="bird")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "bird")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "bird")$average_corrected_target_looking
## t = -0.66186, df = 83, p-value = 0.5099
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.06635163  0.03321813
## sample estimates:
## mean difference 
##     -0.01656675

#checking the typicality effect for cat
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="cat")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="cat")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "cat")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "cat")$average_corrected_target_looking
## t = 1.0734, df = 83, p-value = 0.2862
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.02345916  0.07846713
## sample estimates:
## mean difference 
##      0.02750398

#checking the typicality effect for dog
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="dog")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="dog")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "dog")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "dog")$average_corrected_target_looking
## t = 1.7661, df = 83, p-value = 0.08106
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.006082161  0.102473211
## sample estimates:
## mean difference 
##      0.04819553

#checking the typicality effect for fish
t.test(
  filter(avg_corrected_target_looking_by_typicality_word,condition=="typical"&target_category=="fish")$average_corrected_target_looking,
  filter(avg_corrected_target_looking_by_typicality_word,condition=="atypical"&target_category=="fish")$average_corrected_target_looking,
  paired=TRUE
)

## 
##  Paired t-test
## 
## data:  filter(avg_corrected_target_looking_by_typicality_word, condition == "typical" & target_category == "fish")$average_corrected_target_looking and filter(avg_corrected_target_looking_by_typicality_word, condition == "atypical" & target_category == "fish")$average_corrected_target_looking
## t = -0.1334, df = 83, p-value = 0.8942
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.06222364  0.05440177
## sample estimates:
## mean difference 
##    -0.003910936

Plot

pal <- wes_palette("Rushmore1", n=5)
set.seed(1)
jitterer <- position_jitter(width = .05,seed=1)
p3 <- ggplot(avg_corrected_target_looking_by_typicality_word,aes(x=condition,y=average_corrected_target_looking, fill=condition))+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality_word, condition=="atypical"),position = position_nudge(x = -.1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="l")+
  geom_half_violin(data=filter(avg_corrected_target_looking_by_typicality_word, condition=="typical"),position = position_nudge(x = .1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="r")+
  geom_path(aes(group=sub_num),color="black",fill=NA,alpha=0.05,size=0.75,position=jitterer)+
  geom_point(aes(color=condition,group=sub_num), size = 2.5, alpha=0.05,position=jitterer)+
  geom_point(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking),color="black",size=1.8)+
  geom_line(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking,group=1),color="black",size=1.5)+
  geom_errorbar(data=overall_target_looking_by_typicality_word,aes(y=corrected_target_looking,ymin=lower_ci,ymax=upper_ci),width=0,color="black")+
  #geom_boxplot(outlier.shape = NA, alpha = .5, width = .1, colour = "black")+
  #scale_colour_brewer(palette = "Dark2")+
  #scale_fill_brewer(palette = "Dark2")+
  geom_hline(yintercept=0,linetype="dashed")+
  scale_colour_manual(values=pal[c(3,4)])+
  scale_fill_manual(values=pal[c(3,4)])+
  facet_wrap(.~target_category)+
  theme(legend.position="none")+
  xlab("Typicality Condition")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=16),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"))


ggsave(here::here("..","figures","baseline_corrected_accuracy_by_category.png"),width=7,height=6,bg = "white")

Target Image

# summarize average accuracy within participant
avg_corrected_target_looking_by_image <- trial_corrected_accuracy  %>%
  group_by(sub_num, condition,target_category,target_image,target_typicality_z) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            average_critical_window_looking=mean(mean_target_looking_critical,na.rm=TRUE),
            average_baseline_window_looking=mean(mean_target_looking_baseline,na.rm=TRUE))

#baseline-corrected target looking summarized overall
overall_target_looking_by_image <- avg_corrected_target_looking_by_image %>%
  group_by(condition,target_category,target_image,target_typicality_z) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci,
            target_looking_critical_window=mean(average_critical_window_looking,na.rm=TRUE),
            ci_critical_window=qt(0.975, N-1)*sd(average_critical_window_looking,na.rm=T)/sqrt(N),
            lower_ci_critical_window=target_looking_critical_window-ci_critical_window,
            upper_ci_critical_window=target_looking_critical_window+ci_critical_window,
            target_looking_baseline_window=mean(average_baseline_window_looking,na.rm=TRUE),
            ci_baseline_window=qt(0.975, N-1)*sd(average_baseline_window_looking,na.rm=T)/sqrt(N),
            lower_ci_baseline_window=target_looking_baseline_window-ci_baseline_window,
            upper_ci_baseline_window=target_looking_baseline_window+ci_baseline_window
            ) %>%
  rename(target_image_name=target_image) %>%
  mutate(target_image=str_replace(target_image_name,"_600x600",""),
         target_image_path=here("images",paste(target_image_name,".png",sep="")))
overall_target_looking_by_image %>%
  ungroup() %>%
  relocate(target_image) %>%
  select(-target_image_path,-target_image_name) %>%
  knitr::kable()

target_image	condition	target_category	target_typicality_z	N	corrected_target_looking	ci	lower_ci	upper_ci	target_looking_critical_window	ci_critical_window	lower_ci_critical_window	upper_ci_critical_window	target_looking_baseline_window	ci_baseline_window	lower_ci_baseline_window	upper_ci_baseline_window
heron	atypical	bird	-0.2912701	82	0.1336470	0.0687414	0.0649057	0.2023884	0.5533569	0.0556233	0.4977336	0.6089803	0.4197099	0.0407751	0.3789348	0.4604849
kingfisher	atypical	bird	-0.1281589	79	0.0411643	0.0715193	-0.0303550	0.1126836	0.4865531	0.0624677	0.4240854	0.5490208	0.4453888	0.0422521	0.4031367	0.4876409
kookaburra	atypical	bird	-1.0835249	78	0.1024738	0.0584785	0.0439954	0.1609523	0.5498303	0.0490565	0.5007739	0.5988868	0.4473565	0.0411067	0.4062499	0.4884632
cornishrex	atypical	cat	-1.1767313	80	0.0786173	0.0679227	0.0106946	0.1465400	0.5411904	0.0587587	0.4824317	0.5999491	0.4625731	0.0395486	0.4230245	0.5021217
oriental	atypical	cat	-1.1301281	80	0.1554697	0.0687158	0.0867539	0.2241855	0.6587850	0.0530770	0.6057080	0.7118620	0.5033153	0.0472142	0.4561011	0.5505296
sphynx	atypical	cat	-1.8058748	83	0.0042218	0.0681615	-0.0639397	0.0723833	0.6178601	0.0498591	0.5680010	0.6677192	0.6136383	0.0431810	0.5704573	0.6568193
afghanhound	atypical	dog	-1.0136201	79	0.0617888	0.0633279	-0.0015390	0.1251167	0.6046304	0.0519757	0.5526547	0.6566061	0.5428416	0.0419047	0.5009369	0.5847462
bassethound	atypical	dog	-0.5708895	81	0.0439038	0.0748536	-0.0309498	0.1187574	0.6521356	0.0541309	0.5980047	0.7062665	0.6082318	0.0481543	0.5600775	0.6563861
sheepdog	atypical	dog	-1.4563507	82	-0.0222387	0.0621909	-0.0844295	0.0399522	0.4799202	0.0506011	0.4293191	0.5305212	0.5021588	0.0420160	0.4601428	0.5441749
betafish	atypical	fish	-0.5475879	83	0.0891884	0.0647377	0.0244507	0.1539262	0.5334215	0.0581915	0.4752300	0.5916130	0.4442331	0.0395320	0.4047011	0.4837651
lionfish	atypical	fish	-0.9670168	80	0.0043154	0.0691845	-0.0648691	0.0734998	0.5216443	0.0574138	0.4642305	0.5790581	0.5173290	0.0403106	0.4770184	0.5576396
sturgeon	atypical	fish	-0.7573023	81	0.1330115	0.0743575	0.0586540	0.2073690	0.4875952	0.0614066	0.4261886	0.5490019	0.3545838	0.0477587	0.3068250	0.4023425
cardinal	typical	bird	0.6873975	82	0.0773277	0.0586860	0.0186416	0.1360137	0.5538145	0.0469000	0.5069145	0.6007144	0.4764868	0.0420795	0.4344073	0.5185663
robin	typical	bird	0.7340007	81	0.1104396	0.0719358	0.0385038	0.1823754	0.5652489	0.0533763	0.5118725	0.6186252	0.4548093	0.0435451	0.4112642	0.4983544
sparrow	typical	bird	1.0369217	83	0.0334298	0.0492813	-0.0158515	0.0827112	0.5101554	0.0434339	0.4667215	0.5535893	0.4767255	0.0383011	0.4384245	0.5150266
arabianmau	typical	cat	0.8272072	82	0.0651690	0.0524962	0.0126728	0.1176652	0.5950371	0.0509703	0.5440668	0.6460074	0.5298681	0.0350749	0.4947931	0.5649430
chartreux	typical	cat	0.6407943	81	0.1568510	0.0728699	0.0839812	0.2297209	0.5975451	0.0573779	0.5401672	0.6549230	0.4406941	0.0509444	0.3897496	0.4916385
tabby	typical	cat	1.3631442	81	0.0870967	0.0710616	0.0160351	0.1581583	0.6242526	0.0623083	0.5619443	0.6865608	0.5371559	0.0420838	0.4950721	0.5792397
beagle	typical	dog	1.1534297	79	0.1037907	0.0659255	0.0378653	0.1697162	0.6298141	0.0522568	0.5775574	0.6820709	0.5260234	0.0395162	0.4865072	0.5655396
germanshepherd	typical	dog	1.1767313	82	0.0859428	0.0648708	0.0210719	0.1508136	0.5713628	0.0480559	0.5233069	0.6194188	0.4854201	0.0407560	0.4446640	0.5261761
goldenretriever	typical	dog	0.9670168	83	0.0325998	0.0576596	-0.0250598	0.0902594	0.5494472	0.0464993	0.5029479	0.5959465	0.5168474	0.0412220	0.4756254	0.5580694
bass	typical	fish	0.7806040	80	0.0714446	0.0704467	0.0009979	0.1418913	0.5231518	0.0608834	0.4622683	0.5840352	0.4517072	0.0365771	0.4151300	0.4882843
bluegill	typical	fish	0.8039056	81	0.0705323	0.0644594	0.0060729	0.1349917	0.5662295	0.0534655	0.5127640	0.6196950	0.4956972	0.0432685	0.4524287	0.5389657
clownfish	typical	fish	0.7573023	80	0.0456986	0.0622121	-0.0165136	0.1079107	0.5340094	0.0495836	0.4844258	0.5835930	0.4883109	0.0448740	0.4434368	0.5331849

Plot

#clean names for individual images for plot
overall_target_looking_by_image <- overall_target_looking_by_image %>%
  mutate(
    target_image_clean = case_when(
      target_image == "oriental" ~ "Oriental cat",
      target_image == "chartreux" ~ "Chartreux cat",
      target_image == "betafish" ~ "Betta fish",
      target_image == "tabby" ~ "Tabby cat",
      target_image == "germanshepherd" ~ "German Shepherd",
      target_image == "cornishrex" ~ "Cornish Rex",
      target_image == "arabianmau" ~ "Arabian Mau",
      target_image == "bassethound" ~ "Basset Hound",
      target_image == "goldenretriever" ~ "Golden Retriever",
      target_image == "sphynx" ~ "Sphynx cat",
      TRUE ~ str_to_title(target_image)
    )
  )


ggplot(overall_target_looking_by_image,aes(reorder(target_image_clean,corrected_target_looking),corrected_target_looking))+
  geom_image(aes(y=corrected_target_looking+0.1,image=target_image_path),size=.1)+
  geom_hline(yintercept=0,linetype="dashed")+
  geom_errorbar(aes(ymin=lower_ci,ymax=upper_ci,color=condition),width=0)+
  geom_point(aes(color=condition),size=3)+
  xlab("Target Image")+
  ylab("Baseline-Corrected\nProportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=16,angle=90,vjust=0.5,hjust=1),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"),
        legend.position=c(0.8,0.15)
        )+
  scale_color_manual(values=pal[c(3,4)])

ggsave(here::here("..","figures","baseline_corrected_accuracy_by_word.png"),width=9,height=6,bg = "white")

5.3. Reliability

5.3.1. How correlated is accuracy within participants between session 1 and session 2

avg_corrected_target_looking_by_session_wide <- avg_corrected_target_looking_by_session %>%
  ungroup() %>%
  select(sub_num,session,average_corrected_target_looking) %>%
  pivot_wider(names_from=session,names_prefix="session_",values_from=average_corrected_target_looking)

#compute correlation
cor.test(
  avg_corrected_target_looking_by_session_wide$session_1,
  avg_corrected_target_looking_by_session_wide$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_corrected_target_looking_by_session_wide$session_1 and avg_corrected_target_looking_by_session_wide$session_2
## t = 2.6968, df = 78, p-value = 0.008575
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.07728388 0.48090090
## sample estimates:
##       cor 
## 0.2920417

ggplot(avg_corrected_target_looking_by_session_wide,aes(session_1,session_2)) +
  geom_point()+
  geom_smooth(method="lm")+
  annotate("text",label="r=.29, t(78)=2.70, p=.009",x=-0.3,y=0.25,size=5)+
  xlab("Session 1\nAverage Baseline-Corrected Proportion Target Looking")+
  ylab("Session 2\nAverage Baseline-Corrected Proportion Target Looking")

ggsave(here::here("..","figures","session_correlation.png"),width=9,height=6,bg = "white")

#correlation also holds when excluding the outlier
cor.test(
  filter(avg_corrected_target_looking_by_session_wide,session_1>-0.25)$session_1,
  filter(avg_corrected_target_looking_by_session_wide,session_1>-0.25)$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(avg_corrected_target_looking_by_session_wide, session_1 > -0.25)$session_1 and filter(avg_corrected_target_looking_by_session_wide, session_1 > -0.25)$session_2
## t = 2.5513, df = 77, p-value = 0.01272
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.06189355 0.47120595
## sample estimates:
##       cor 
## 0.2791832

avg_corrected_target_looking_by_typicality_session_wide <- avg_corrected_target_looking_by_typicality_session %>%
  ungroup() %>%
  select(sub_num,session,condition,average_corrected_target_looking) %>%
  pivot_wider(names_from=session,names_prefix="session_",values_from=average_corrected_target_looking)

#compute correlation
#typical
cor.test(
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="typical")$session_1,
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="typical")$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "typical")$session_1 and filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "typical")$session_2
## t = 1.4414, df = 77, p-value = 0.1535
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.06120993  0.36994557
## sample estimates:
##       cor 
## 0.1620943

#atypical
cor.test(
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="atypical")$session_1,
  filter(avg_corrected_target_looking_by_typicality_session_wide,condition=="atypical")$session_2)

## 
##  Pearson's product-moment correlation
## 
## data:  filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "atypical")$session_1 and filter(avg_corrected_target_looking_by_typicality_session_wide, condition == "atypical")$session_2
## t = 1.5738, df = 78, p-value = 0.1196
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.04605773  0.38048524
## sample estimates:
##       cor 
## 0.1754345

ggplot(avg_corrected_target_looking_by_typicality_session_wide,aes(session_1,session_2,color=condition)) +
  geom_point()+
  geom_smooth(method="lm")+
  xlab("Session 1\nAverage Baseline-Corrected Proportion Target Looking")+
  ylab("Session 2\nAverage Baseline-Corrected Proportion Target Looking")+
  facet_wrap(~condition)+
  scale_color_manual(values=pal[c(3,4)])+
  theme(legend.position="none")

ggsave(here::here("..","figures","session_correlation_by_typicality.png"),width=9,height=6,bg = "white")

5.3.2. ICCs

df_for_icc <- trial_corrected_accuracy %>%
  #some light renaming to use Peekbank icc function
  mutate(
    administration_id = sub_num
  ) %>%
  unite("trial_id", administration_id, trial_number,remove=F) %>%
  mutate(
    target_label=target_image
  )

#ICC for participants
icc_participants <- df_for_icc %>%
  get_icc(object = "administration",column="corrected_target_looking",type_icc="consistency")
icc_participants_baseline <- df_for_icc %>%
  get_icc(object = "administration",column="mean_target_looking_baseline",type_icc="consistency")
icc_participants_critical <- df_for_icc %>%
  get_icc(object = "administration",column="mean_target_looking_critical",type_icc="consistency")


#ICC for stimuli
icc_stimuli <- df_for_icc %>%
  get_icc(object = "stimulus",column="corrected_target_looking",type_icc="consistency")
icc_stimuli_baseline <- df_for_icc %>%
  get_icc(object = "stimulus",column="mean_target_looking_baseline",type_icc="consistency")
icc_stimuli_critical <-  df_for_icc %>%
  get_icc(object = "stimulus",column="mean_target_looking_critical",type_icc="consistency")

In S10.2.2., we further investigated the measurement reliability of infants’ word recognition (Byers-Heinlein et al., 2022) by estimating the intraclass correlation coefficient (ICC) of baseline-corrected proportion target looking across all trials, based on a mean-rating, consistency, 2-way random-effects model (model 2A). We estimated low-to-moderate ICC values for both by-participant (ICC = 0.39) and by-item (a given target image; ICC = 0.47) consistency.

5.4. Exploring alternative trial-based inclusion criteria

Participants were required to contribute at least 24 valid trials in order to be included in the final sample. Here, we explore the impact of this criterion on whether we observe a typicality effect, by estimating the typicality effect for a range of looser and stricter trial-based exclusion criteria

min_trials_required_list = c(4,8,12,16,20,24,28,32,36,40,44,48)

# set up summarized dataset to use
subj_typ_data <- trial_corrected_accuracy_all %>%
  #apply exclusion criteria to trials
  filter(exclude_frame_rate==0) %>%
  filter(exclude_technical_issue==0) %>%
  filter(useable_window==1) %>%
  filter(age_exclusion==0) %>%
  group_by(sub_num,condition) %>%
  summarize(
    N=n(),
    average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE)
    ) %>%
  ungroup() %>%
  group_by(sub_num) %>%
  mutate(total_trials=sum(N,na.rm=TRUE)) %>%
  pivot_wider(names_from=condition,values_from=c(N,average_corrected_target_looking)) %>%
  ungroup() 

#add and apply min trial exclusion criteria,
#creating nested dataframes for each minimum trial exclusion criterion
#then test the typicality effect within each dataset and store the results

typ_effect_min_valid_trials <- expand_grid(
  subj_typ_data,
  min_valid_trials_req = min_trials_required_list
) %>%
  #apply min trial exclusion criterion 
  group_by(min_valid_trials_req) %>%
  filter(total_trials>=min_valid_trials_req) %>%
  mutate(
    N=length(sub_num)
  ) %>%
  group_by(min_valid_trials_req,N) %>%
  #nest the data
  nest() %>%
  mutate(t_test = map(data, ~ t.test(.x$average_corrected_target_looking_typical, .x$average_corrected_target_looking_atypical,paired = T)),
         result = map(t_test, tidy)
         ) %>%
  unnest(result)

# typ_effect_min_valid_trials %>%
#   knitr::kable()

## plot the result
ggplot(typ_effect_min_valid_trials, aes(min_valid_trials_req,estimate))+
  geom_errorbar(aes(ymin=conf.low,ymax=conf.high),width=0)+
  geom_point(size=3)+
  geom_hline(yintercept=0,linetype="dashed")+
  geom_text(aes(label=N),nudge_y = 0.07)+
  ylab("Estimated Participant-Level Typicality Effect")+
  xlab("Minimum Number of Trials Required for Inclusion")+
  scale_x_continuous(breaks=min_trials_required_list)

ggsave(here::here("..","figures","typicality_effect_min_trials_for_inclusion.png"),width=9,height=6,bg = "white")

5.5. Testing the main results with a final sample of N=80

In our Stage 1 manuscript, we preregistered a sample of N=80. Our current results report data from all participants who contributed valid data, leading to a final N of 84 participants. Here, we remove the data from the final 4 participants who contributed data on Lookit and re-run the main analyses from Aim 1 (1.1 and 1.2), to ensure that the decision to include all participants did not change the outcome of the study.

Remove the final 4 participants

CAT_343, CAT_344, CAT_345, and CAT_346 were the final 4 participants contributing data on Lookit.

subj_to_remove <- c("CAT_343","CAT_344","CAT_345","CAT_346")
trial_corrected_accuracy_red <- trial_corrected_accuracy_all %>%
  filter(exclude_participant==0) %>%
  filter(trial_exclusion==0) %>%
  filter(!(sub_num %in% subj_to_remove))

# summarize by-participant and typicality
avg_corrected_target_looking_by_typicality_red <- trial_corrected_accuracy_red  %>%
  group_by(sub_num, condition) %>%
  summarize(N=n(),
            mean_age = mean(age),
            mean_age_mo = mean(age_mo),
            average_corrected_target_looking=mean(corrected_target_looking,na.rm=TRUE),
            se=sd(corrected_target_looking,na.rm=T)/sqrt(N),
            ci=qt(0.975, N-1)*sd(corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=average_corrected_target_looking-ci,
            upper_ci=average_corrected_target_looking+ci,
            lower_se=average_corrected_target_looking-se,
            upper_se=average_corrected_target_looking+se)

#baseline-corrected target looking summarized overall
overall_corrected_target_looking_by_typicality_red <- avg_corrected_target_looking_by_typicality_red %>%
  group_by(condition) %>%
  summarize(N=n(),
            corrected_target_looking=mean(average_corrected_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_corrected_target_looking,na.rm=T)/sqrt(N),
            lower_ci=corrected_target_looking-ci,
            upper_ci=corrected_target_looking+ci)

overall_corrected_target_looking_by_typicality_red %>%
  knitr::kable()

condition	N	corrected_target_looking	ci	lower_ci	upper_ci
atypical	80	0.0607143	0.0201484	0.0405660	0.0808627
typical	80	0.0775846	0.0218312	0.0557533	0.0994158

Participant-level analysis

avg_corrected_target_looking_by_typicality_red <- avg_corrected_target_looking_by_typicality_red %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

m_1_1_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_c + (1+ typicality_condition_c|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_c +  
##     (1 + typicality_condition_c | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -296
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.19796 -0.42206  0.06897  0.39230  1.95368 
## 
## Random effects:
##  Groups   Name                   Variance Std.Dev. Corr
##  sub_num  (Intercept)            0.003699 0.06082      
##           typicality_condition_c 0.004567 0.06758  0.17
##  Residual                        0.004070 0.06380      
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)             0.069149   0.008466 78.999851   8.168  4.1e-12 ***
## typicality_condition_c  0.016870   0.012603 79.000025   1.339    0.185    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.084 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_red,method="Wald")

##                               2.5 %     97.5 %
## .sig01                           NA         NA
## .sig02                           NA         NA
## .sig03                           NA         NA
## .sigma                           NA         NA
## (Intercept)             0.052556409 0.08574249
## typicality_condition_c -0.007830941 0.04157135

There remained no significant effect of typicality in the participant-level analysis, \(\hat{\beta} = 0.02\), 95% CI \([-0.01, 0.04]\), \(t(79) = 1.34\), \(p = .185\).

## Typical word recognition
# recentering the model on the typical condition to make the intercept interpretable
m_1_1_3_typ_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_typ + (1+ typicality_condition_typ|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_typ_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_typ +  
##     (1 + typicality_condition_typ | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -296
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.42058 -0.46480  0.07596  0.43204  2.15156 
## 
## Random effects:
##  Groups   Name                     Variance Std.Dev. Corr
##  sub_num  (Intercept)              0.004688 0.06847      
##           typicality_condition_typ 0.002834 0.05324  0.58
##  Residual                          0.004936 0.07026      
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                          Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)               0.07758    0.01097 78.99956   7.074  5.4e-10 ***
## typicality_condition_typ  0.01687    0.01260 78.99986   1.339    0.185    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.639 
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

confint(m_1_1_3_typ_red,method="Wald")

##                                2.5 %     97.5 %
## .sig01                            NA         NA
## .sig02                            NA         NA
## .sig03                            NA         NA
## .sigma                            NA         NA
## (Intercept)               0.05608766 0.09908144
## typicality_condition_typ -0.00783094 0.04157135

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_red$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_red$condition=="typical"])

## Cohen's d |       95% CI
## ------------------------
## 0.79      | [0.54, 1.04]

## Atypical word recognition
# recentering the model on the atypical condition to make the intercept interpretable
m_1_1_3_atyp_red <- lmer(average_corrected_target_looking ~ 1 + typicality_condition_atyp + (1+ typicality_condition_atyp|sub_num),data=avg_corrected_target_looking_by_typicality_red,control=lmerControl(check.nobs.vs.nlev= "ignore",check.nobs.vs.nRE= "ignore"))
summary(m_1_1_3_atyp_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: average_corrected_target_looking ~ 1 + typicality_condition_atyp +  
##     (1 + typicality_condition_atyp | sub_num)
##    Data: avg_corrected_target_looking_by_typicality_red
## Control: 
## lmerControl(check.nobs.vs.nlev = "ignore", check.nobs.vs.nRE = "ignore")
## 
## REML criterion at convergence: -296
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.35893 -0.45297  0.07402  0.42103  2.09674 
## 
## Random effects:
##  Groups   Name                      Variance Std.Dev. Corr 
##  sub_num  (Intercept)               0.003509 0.05924       
##           typicality_condition_atyp 0.003331 0.05771  -0.28
##  Residual                           0.004688 0.06847       
## Number of obs: 160, groups:  sub_num, 80
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                0.06071    0.01012 78.99713   5.998 5.69e-08 ***
## typicality_condition_atyp  0.01687    0.01260 78.99018   1.339    0.185    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ -0.553
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model is nearly unidentifiable: large eigenvalue ratio
##  - Rescale variables?

confint(m_1_1_3_atyp_red,method="Wald")

##                                  2.5 %     97.5 %
## .sig01                              NA         NA
## .sig02                              NA         NA
## .sig03                              NA         NA
## .sigma                              NA         NA
## (Intercept)                0.040874649 0.08055405
## typicality_condition_atyp -0.007830908 0.04157132

#effect size
cohens_d(avg_corrected_target_looking_by_typicality_red$average_corrected_target_looking[avg_corrected_target_looking_by_typicality_red$condition=="atypical"])

## Cohen's d |       95% CI
## ------------------------
## 0.67      | [0.43, 0.91]

Infants recognized both typical and atypical exemplars, with similar effect sizes.

Trial-level analysis

trial_corrected_accuracy_red <- trial_corrected_accuracy_red %>%
  mutate(
    typicality_condition_c = case_when(
      condition == "atypical" ~ -0.5,
      condition == "typical" ~ 0.5,
      TRUE ~ NA_real_
    ),
    typicality_condition_typ = case_when(
      condition == "atypical" ~ -1,
      condition == "typical" ~ 0,
      TRUE ~ NA_real_
    ),
    typicality_condition_atyp = case_when(
      condition == "atypical" ~ 0,
      condition == "typical" ~ 1,
      TRUE ~ NA_real_
    ),
  )

#model with typicality random intercept has singular fit but yields basically identical results
m_1_2_red <- lmer(corrected_target_looking ~ 1 + typicality_condition_c + 
            (1 | sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy_red)
summary(m_1_2_red)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: corrected_target_looking ~ 1 + typicality_condition_c + (1 |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy_red
## 
## REML criterion at convergence: 2165.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.12871 -0.62986 -0.03006  0.65800  2.76258 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0025466 0.05046 
##  target_category (Intercept) 0.0001313 0.01146 
##  Residual                    0.1202984 0.34684 
## Number of obs: 2924, groups:  sub_num, 80; target_category, 4
## 
## Fixed effects:
##                         Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)            7.024e-02  1.032e-02 5.969e+00   6.806 0.000504 ***
## typicality_condition_c 1.358e-02  1.284e-02 2.856e+03   1.058 0.290246    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## typclty_cn_ 0.000

confint(m_1_2_red,method="Wald")

##                              2.5 %     97.5 %
## .sig01                          NA         NA
## .sig02                          NA         NA
## .sigma                          NA         NA
## (Intercept)             0.05001304 0.09046888
## typicality_condition_c -0.01158511 0.03875135

The trial-level model also yields no significant typicality effect, \(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.04]\), \(t(2856.47) = 1.06\), \(p = .290\).

5.6. Alternative model specifications for baseline and critical window looking

We also considered alternative methods of specifying a regression model incorporating information about target looking during the baseline window and the critical window: predicting target looking during the critical window while controlling for baseline looking (5.6.1.) and predicting target looking from a model including the interaction between typicality and trial window (critical window vs. baseline window) (5.6.2.).

5.6.1. Controlling for baseline looking (instead of baseline correction)

Typicality Effect: Trial-level model

#model with a by-participant random slope for typicality condition yields a singular fit
#however, the model itself yields very similar results.
m_5_6_1 <- lmer(mean_target_looking_critical ~ 1 + typicality_condition_c + mean_target_looking_baseline +
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_6_1)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## mean_target_looking_critical ~ 1 + typicality_condition_c + mean_target_looking_baseline +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 914.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.40807 -0.62977  0.04601  0.70981  1.97695 
## 
## Random effects:
##  Groups          Name        Variance  Std.Dev.
##  sub_num         (Intercept) 0.0024950 0.04995 
##  target_category (Intercept) 0.0009999 0.03162 
##  Residual                    0.0764645 0.27652 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                               Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                  5.182e-01  2.052e-02 6.997e+00  25.253 3.92e-08
## typicality_condition_c       1.290e-02  9.969e-03 3.010e+03   1.294    0.196
## mean_target_looking_baseline 9.146e-02  2.201e-02 3.037e+03   4.155 3.34e-05
##                                 
## (Intercept)                  ***
## typicality_condition_c          
## mean_target_looking_baseline ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__
## typclty_cn_  0.002       
## mn_trgt_lk_ -0.525 -0.004

confint(m_5_6_1,method="Wald")

##                                     2.5 %     97.5 %
## .sig01                                 NA         NA
## .sig02                                 NA         NA
## .sigma                                 NA         NA
## (Intercept)                   0.477963914 0.55839772
## typicality_condition_c       -0.006643998 0.03243501
## mean_target_looking_baseline  0.048316434 0.13460452

We fit a linear mixed-effects model predicting proportion target looking during the critical window from typicality condition while controlling for proportion target looking during the baseline window. We included by-participant and by-word random intercepts. As in the main analyses, we found no significant typicality effect, \(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.03]\), \(t(3009.89) = 1.29\), \(p = .196\).

Typicality Effect: Trial-level model with continuous typicality ratings

#model with the by-participant random slope for target_typicality_z yields a singular fit (though qualitatively equivalent results)
m_5_6_1_continuous <- lmer(mean_target_looking_critical ~ 1 + target_typicality_z + mean_target_looking_baseline +
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_6_1_continuous)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## mean_target_looking_critical ~ 1 + target_typicality_z + mean_target_looking_baseline +  
##     (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 915.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.41858 -0.62784  0.04423  0.70344  1.98124 
## 
## Random effects:
##  Groups          Name        Variance Std.Dev.
##  sub_num         (Intercept) 0.002498 0.04998 
##  target_category (Intercept) 0.001071 0.03273 
##  Residual                    0.076429 0.27646 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                               Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                  5.180e-01  2.095e-02 6.693e+00  24.723 7.90e-08
## target_typicality_z          8.605e-03  5.124e-03 3.011e+03   1.679   0.0932
## mean_target_looking_baseline 9.204e-02  2.201e-02 3.039e+03   4.181 2.98e-05
##                                 
## (Intercept)                  ***
## target_typicality_z          .  
## mean_target_looking_baseline ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trgt__
## trgt_typcl_ -0.006       
## mn_trgt_lk_ -0.514  0.015

confint(m_5_6_1_continuous,method="Wald")

##                                     2.5 %     97.5 %
## .sig01                                 NA         NA
## .sig02                                 NA         NA
## .sigma                                 NA         NA
## (Intercept)                   0.476896001 0.55902100
## target_typicality_z          -0.001437492 0.01864668
## mean_target_looking_baseline  0.048892796 0.13517660

Similarly, there was no significant effect when treating typicality as a continuous predictor (based on z-scored adult ratings), \(\hat{\beta} = 0.01\), 95% CI \([0.00, 0.02]\), \(t(3010.79) = 1.68\), \(p = .093\).

Age * Typicality Interaction

m_5_6_1_age_int <- lmer(mean_target_looking_critical ~ 1 + typicality_condition_c*age_mo_c + mean_target_looking_baseline +
            (1|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy)
summary(m_5_6_1_age_int)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## mean_target_looking_critical ~ 1 + typicality_condition_c * age_mo_c +  
##     mean_target_looking_baseline + (1 | sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## 
## REML criterion at convergence: 918.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.43095 -0.62132  0.04606  0.69385  2.01864 
## 
## Random effects:
##  Groups          Name        Variance Std.Dev.
##  sub_num         (Intercept) 0.001887 0.04344 
##  target_category (Intercept) 0.001011 0.03179 
##  Residual                    0.076469 0.27653 
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                     5.180e-01  2.040e-02 6.713e+00  25.387 6.39e-08
## typicality_condition_c          1.275e-02  9.974e-03 3.011e+03   1.279 0.201154
## age_mo_c                        1.731e-02  4.640e-03 8.724e+01   3.731 0.000339
## mean_target_looking_baseline    9.119e-02  2.200e-02 3.041e+03   4.145 3.50e-05
## typicality_condition_c:age_mo_c 4.671e-03  6.763e-03 3.011e+03   0.691 0.489821
##                                    
## (Intercept)                     ***
## typicality_condition_c             
## age_mo_c                        ***
## mean_target_looking_baseline    ***
## typicality_condition_c:age_mo_c    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ ag_m_c mn_t__
## typclty_cn_  0.002                     
## age_mo_c    -0.010  0.003              
## mn_trgt_lk_ -0.528 -0.004  0.006       
## typclt__:__  0.002 -0.035  0.002 -0.001

confint(m_5_6_1_age_int,method="Wald")

##                                        2.5 %     97.5 %
## .sig01                                    NA         NA
## .sig02                                    NA         NA
## .sigma                                    NA         NA
## (Intercept)                      0.477999275 0.55798110
## typicality_condition_c          -0.006796469 0.03230111
## age_mo_c                         0.008216234 0.02640510
## mean_target_looking_baseline     0.048065511 0.13430643
## typicality_condition_c:age_mo_c -0.008583667 0.01792521

Following the analytic strategy for Aim 2, we also fit a linear mixed-effects model predicting proportion target looking during the critical window from age, typicality condition, and their interaction (all centered), while also controlling for proportion target looking during the baseline window. The model included by-participant and by-item random intercepts. We found a significant effect of age (\(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(88.56) = 3.33\), \(p = .001\)) and looking during the baseline window (\(\hat{\beta} = 0.09\), 95% CI \([0.05, 0.13]\), \(t(3041.49) = 4.14\), \(p < .001\)). However, there was no significant interaction between age and typicality (\(\hat{\beta} = 0.00\), 95% CI \([-0.01, 0.02]\), \(t(3011.43) = 0.69\), \(p = .490\)).

Continuous effect of target AND distractor typicality

m_5_6_1_continuous_td <- lmer(mean_target_looking_critical ~ 1 + target_typicality_z * distractor_typicality_z + mean_target_looking_baseline +
            (1+target_typicality_z : distractor_typicality_z|sub_num) +
            (1|target_category),
          data=trial_corrected_accuracy,control=lmerControl(optimizer="bobyqa"))
summary(m_5_6_1_continuous_td)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## mean_target_looking_critical ~ 1 + target_typicality_z * distractor_typicality_z +  
##     mean_target_looking_baseline + (1 + target_typicality_z:distractor_typicality_z |  
##     sub_num) + (1 | target_category)
##    Data: trial_corrected_accuracy
## Control: lmerControl(optimizer = "bobyqa")
## 
## REML criterion at convergence: 899.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.46820 -0.62454  0.04141  0.71024  2.11417 
## 
## Random effects:
##  Groups          Name                                        Variance  Std.Dev.
##  sub_num         (Intercept)                                 0.0036335 0.06028 
##                  target_typicality_z:distractor_typicality_z 0.0006615 0.02572 
##  target_category (Intercept)                                 0.0012362 0.03516 
##  Residual                                                    0.0755362 0.27484 
##  Corr 
##       
##  -0.61
##       
##       
## Number of obs: 3086, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                               Estimate Std. Error         df
## (Intercept)                                    0.54995    0.02378    8.27618
## target_typicality_z                           -0.02842    0.01041 2903.23367
## distractor_typicality_z                        0.03778    0.01039 2907.84852
## mean_target_looking_baseline                   0.08481    0.02198 3027.67824
## target_typicality_z:distractor_typicality_z   -0.03431    0.01060   64.42116
##                                             t value Pr(>|t|)    
## (Intercept)                                  23.128 8.19e-09 ***
## target_typicality_z                          -2.731 0.006350 ** 
## distractor_typicality_z                       3.635 0.000282 ***
## mean_target_looking_baseline                  3.858 0.000117 ***
## target_typicality_z:distractor_typicality_z  -3.236 0.001914 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trgt__ dstr__ mn_t__
## trgt_typcl_ -0.027                     
## dstrctr_ty_ -0.014 -0.866              
## mn_trgt_lk_ -0.451  0.083 -0.087       
## trgt_ty_:__ -0.390 -0.020  0.135 -0.004

confint(m_5_6_1_continuous_td,method="Wald")

##                                                   2.5 %       97.5 %
## .sig01                                               NA           NA
## .sig02                                               NA           NA
## .sig03                                               NA           NA
## .sig04                                               NA           NA
## .sigma                                               NA           NA
## (Intercept)                                  0.50334128  0.596551800
## target_typicality_z                         -0.04881197 -0.008024322
## distractor_typicality_z                      0.01741192  0.058148376
## mean_target_looking_baseline                 0.04172028  0.127893020
## target_typicality_z:distractor_typicality_z -0.05509629 -0.013533334

check_collinearity(m_5_6_1_continuous_td)

## # Check for Multicollinearity
## 
## Low Correlation
## 
##                                         Term  VIF   VIF 95% CI Increased SE
##                          target_typicality_z 4.16 [3.91, 4.42]         2.04
##                      distractor_typicality_z 4.23 [3.98, 4.51]         2.06
##                 mean_target_looking_baseline 1.01 [1.00, 1.73]         1.00
##  target_typicality_z:distractor_typicality_z 1.06 [1.03, 1.12]         1.03
##  Tolerance Tolerance 95% CI
##       0.24     [0.23, 0.26]
##       0.24     [0.22, 0.25]
##       0.99     [0.58, 1.00]
##       0.94     [0.90, 0.97]

#there is some concerning multicollinearity for the main effects of target and distractor typicality

Finally, we investigated the influence of both target and distractor typicality using z-scored adult typicality ratings. We fit a linear mixed-effects model predicting proportion target looking during the critical window from target typicality ratings (z-scored), distractor typicality ratings (z-scored), and their interaction, while also controlling for proportion target looking during the baseline window. The model included by-participant and by-item random effects, as well as by-participant random slope for the interaction between target and distractor typicality (more complex random effects structures yielded a singular fit, albeit with comparable results). There was an interaction between target and distractor typicality, \(\hat{\beta} = -0.03\), 95% CI \([-0.06, -0.01]\), \(t(64.42) = -3.24\), \(p = .002\). Proportion target looking during the critical window increased as distractor typicality increased (\(\hat{\beta} = 0.04\), 95% CI \([0.02, 0.06]\), \(t(2907.85) = 3.64\), \(p < .001\)), and this effect was larger when the target was more atypical (see Figure below).

# figure explaining the interaction
p1 <- ggplot(trial_corrected_accuracy,aes(target_typicality_z,mean_target_looking_baseline))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0.5, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  scale_color_manual(values=pal[c(3,4)])+
  xlab("Target Typicality (z-scored adult ratings)")+
  ylab("Mean Prop Target Looking\nBaseline Window")+
  theme(legend.position="none")
p2 <- ggplot(trial_corrected_accuracy,aes(distractor_typicality_z,mean_target_looking_baseline))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0.5, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  scale_color_manual(values=pal[c(3,4)])+
  xlab("Distractor Typicality (z-scored adult ratings)")+
  ylab("Mean Prop Target Looking\nBaseline Window")+
  theme(legend.position="none")
p3 <- ggplot(trial_corrected_accuracy,aes(target_typicality_z,mean_target_looking_critical))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0.5, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  scale_color_manual(values=pal[c(3,4)])+
  xlab("Target Typicality (z-scored adult ratings)")+
  ylab("Mean Prop Target Looking\nCritical Window")+
  theme(legend.position="none")
p4 <- ggplot(trial_corrected_accuracy,aes(distractor_typicality_z,mean_target_looking_critical))+
    geom_point(aes(color=condition),alpha=0.2)+
    geom_hline(yintercept=0.5, linetype="dashed")+
    geom_smooth(method="lm",color="black")+
  facet_wrap(~condition,scales = "free")+
  scale_color_manual(values=pal[c(3,4)])+
  xlab("Distractor Typicality (z-scored adult ratings)")+
  ylab("Mean Prop Target Looking\nCritical Window")+
  theme(legend.position="none")

(p1+p2)/(p3+p4)+
  plot_annotation(tag_levels = 'A')+
  theme(plot.tag = element_text(size = 18))

ggsave(here::here("..","figures","interaction_continuous_distractor_typicality_window.png"),width=10.5,height=9,bg = "white")

5.6.2. Predicting target looking from the interaction of trial window and typicality

Typicality Condition * Trial Window interaction

#pivot the dataset longer to incorporate trial window as a predictor
trial_corrected_accuracy_long_window <- trial_corrected_accuracy %>%
  ungroup() %>%
  #pivot longer 
  pivot_longer(cols=c(mean_target_looking_baseline,mean_target_looking_critical),names_to = "trial_window",values_to = "prop_target_looking") %>%
  #clean up trial window
  mutate(trial_window=str_remove(trial_window,"mean_target_looking_")) %>%
  mutate(trial_window_c = case_when(
    trial_window=="critical" ~ 0.5,
    trial_window=="baseline" ~ -0.5))

# fit a linear mixed-effects model predicting proportion target looking from the interaction of trial window and typicality
#the model had singular fits when including additional random slopes for typicality condition and/or trial window (though results were qualitatively equivalent)
m_5_6_2 <- lmer(prop_target_looking ~ 1 + typicality_condition_c*trial_window_c +
            (1|sub_num) +
            (1+trial_window_c|target_category),
          data=trial_corrected_accuracy_long_window)
summary(m_5_6_2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_target_looking ~ 1 + typicality_condition_c * trial_window_c +  
##     (1 | sub_num) + (1 + trial_window_c | target_category)
##    Data: trial_corrected_accuracy_long_window
## 
## REML criterion at convergence: 725.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.41988 -0.60843  0.01828  0.64687  2.17264 
## 
## Random effects:
##  Groups          Name           Variance  Std.Dev. Corr 
##  sub_num         (Intercept)    0.0002083 0.01443       
##  target_category (Intercept)    0.0013635 0.03693       
##                  trial_window_c 0.0001874 0.01369  -0.39
##  Residual                       0.0652269 0.25540       
## Number of obs: 6172, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                        Estimate Std. Error        df t value
## (Intercept)                           5.266e-01  1.881e-02 3.043e+00  27.990
## typicality_condition_c                7.558e-03  6.506e-03 6.118e+03   1.162
## trial_window_c                        7.502e-02  9.441e-03 2.995e+00   7.947
## typicality_condition_c:trial_window_c 1.093e-02  1.300e-02 6.082e+03   0.841
##                                       Pr(>|t|)    
## (Intercept)                           9.01e-05 ***
## typicality_condition_c                 0.24541    
## trial_window_c                         0.00418 ** 
## typicality_condition_c:trial_window_c  0.40051    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) typc__ trl_w_
## typclty_cn_  0.000              
## tril_wndw_c -0.276  0.000       
## typclt__:__  0.000  0.000  0.001

confint(m_5_6_2,method="Wald")

##                                             2.5 %     97.5 %
## .sig01                                         NA         NA
## .sig02                                         NA         NA
## .sig03                                         NA         NA
## .sig04                                         NA         NA
## .sigma                                         NA         NA
## (Intercept)                            0.48976857 0.56352276
## typicality_condition_c                -0.00519343 0.02030849
## trial_window_c                         0.05652038 0.09352862
## typicality_condition_c:trial_window_c -0.01455489 0.03642298

We fit a linear mixed-effects model predicting proportion target looking from trial window (baseline vs. critical; centered), typicality condition (centered), and their interaction. We included by-participant and by-word random intercepts. We also included a by-word random slope for trial window (more complex random effects structures yielded singular fits). There was a significant effect of trial window, \(\hat{\beta} = 0.08\), 95% CI \([0.06, 0.09]\), \(t(2.99) = 7.95\), \(p = .004\), indicating successful word recognition (i.e., proportion target looking increased for the critical window compared to the baseline window) However, as in the main analyses, we found no significant trial window by typicality interaction, \(\hat{\beta} = 0.01\), 95% CI \([-0.01, 0.04]\), \(t(6082.30) = 0.84\), \(p = .401\).

# Figure
# summarize average accuracy within participant
subj_corrected_target_looking_by_window <- trial_corrected_accuracy_long_window  %>%
  group_by(sub_num, condition,trial_window) %>%
  summarize(N=n(),
            average_prop_target_looking=mean(prop_target_looking,na.rm=TRUE)
  )
#then summarize across participants
avg_corrected_target_looking_by_window <- subj_corrected_target_looking_by_window  %>%
  group_by(condition,trial_window) %>%
  summarize(N=n(),
            mean_prop_target_looking=mean(average_prop_target_looking,na.rm=TRUE),
            ci=qt(0.975, N-1)*sd(average_prop_target_looking,na.rm=T)/sqrt(N),
            lower_ci=mean_prop_target_looking-ci,
            upper_ci=mean_prop_target_looking+ci
  )

#Create a plot
set.seed(1)
jitterer <- position_jitter(width = .05,seed=1)
overall_typicality_trial_window_plot <- ggplot(subj_corrected_target_looking_by_window,aes(x=trial_window,y=average_prop_target_looking, fill=trial_window))+
  geom_half_violin(data=filter(subj_corrected_target_looking_by_window, trial_window=="baseline"),position = position_nudge(x = -.1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="l")+
  geom_half_violin(data=filter(subj_corrected_target_looking_by_window, trial_window=="critical"),position = position_nudge(x = .1, y = 0), width=1,trim = FALSE, alpha = .8,color=NA,side="r")+
  geom_path(aes(group=sub_num),color="black",fill=NA,alpha=0.15,size=0.75,position=jitterer)+
  geom_point(aes(color=trial_window,group=sub_num), size = 1.5, alpha=0.15,position=jitterer)+
  geom_point(data=avg_corrected_target_looking_by_window,aes(y=mean_prop_target_looking),color="black",size=3)+
  geom_line(data=avg_corrected_target_looking_by_window,aes(y=mean_prop_target_looking,group=1),color="black",size=1.5)+
  geom_errorbar(data=avg_corrected_target_looking_by_window,aes(y=mean_prop_target_looking,ymin=lower_ci,ymax=upper_ci),width=0,size=1.2,color="black")+
  geom_hline(yintercept=0.5,linetype="dashed")+
  theme(legend.position="none")+
  xlab("Trial Window")+
  ylab("Proportion Target Looking")+
  theme(axis.title.x = element_text(face="bold", size=20),
        axis.text.x  = element_text(size=14),
        axis.title.y = element_text(face="bold", size=20),
        axis.text.y  = element_text(size=16),
        strip.text.x = element_text(size = 16,face="bold"))+
  facet_wrap(~condition)


overall_typicality_trial_window_plot

ggsave(here::here("..","figures","trial_window_prop_looking_by_typicality.png"),width=7,height=6,bg = "white")

Continuous Typicality Ratings * Trial Window

m_5_6_2_continuous <- lmer(prop_target_looking ~ 1 + target_typicality_z*trial_window_c +
            (1|sub_num) +
            (1+trial_window_c|target_category),
          data=trial_corrected_accuracy_long_window)
summary(m_5_6_2_continuous)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_target_looking ~ 1 + target_typicality_z * trial_window_c +  
##     (1 | sub_num) + (1 + trial_window_c | target_category)
##    Data: trial_corrected_accuracy_long_window
## 
## REML criterion at convergence: 726.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.42934 -0.60480  0.01884  0.64418  2.16465 
## 
## Random effects:
##  Groups          Name           Variance  Std.Dev. Corr 
##  sub_num         (Intercept)    0.0002091 0.01446       
##  target_category (Intercept)    0.0013842 0.03721       
##                  trial_window_c 0.0002041 0.01428  -0.28
##  Residual                       0.0652092 0.25536       
## Number of obs: 6172, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                     Estimate Std. Error        df t value
## (Intercept)                        5.267e-01  1.895e-02 3.041e+00  27.789
## target_typicality_z                2.639e-03  3.345e-03 6.120e+03   0.789
## trial_window_c                     7.511e-02  9.658e-03 2.995e+00   7.777
## target_typicality_z:trial_window_c 1.108e-02  6.657e-03 5.129e+03   1.665
##                                    Pr(>|t|)    
## (Intercept)                        9.26e-05 ***
## target_typicality_z                 0.43020    
## trial_window_c                      0.00445 ** 
## target_typicality_z:trial_window_c  0.09606 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) trgt__ trl_w_
## trgt_typcl_  0.001              
## tril_wndw_c -0.201  0.000       
## trgt_ty_:__  0.000 -0.001  0.006

confint(m_5_6_2_continuous,method="Wald")

##                                           2.5 %      97.5 %
## .sig01                                       NA          NA
## .sig02                                       NA          NA
## .sig03                                       NA          NA
## .sig04                                       NA          NA
## .sigma                                       NA          NA
## (Intercept)                         0.489514289 0.563806072
## target_typicality_z                -0.003917715 0.009196184
## trial_window_c                      0.056182331 0.094042430
## target_typicality_z:trial_window_c -0.001966444 0.024126558

Similarly, there was no significant interaction between trial window and typicality when treating typicality as a continuous predictor (based on z-scored adult ratings), \(\hat{\beta} = 0.01\), 95% CI \([0.00, 0.02]\), \(t(5129.00) = 1.66\), \(p = .096\).

Age * Typicality * Trial Window Interaction

m_5_6_2_age_int <- lmer(prop_target_looking ~ 1 + typicality_condition_c*trial_window_c*age_mo_c +
            (1|sub_num) +
            (1+trial_window_c|target_category),
          data=trial_corrected_accuracy_long_window)
summary(m_5_6_2_age_int)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_target_looking ~ 1 + typicality_condition_c * trial_window_c *  
##     age_mo_c + (1 | sub_num) + (1 + trial_window_c | target_category)
##    Data: trial_corrected_accuracy_long_window
## 
## REML criterion at convergence: 732
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.58319 -0.60302  0.01998  0.64816  2.16090 
## 
## Random effects:
##  Groups          Name           Variance  Std.Dev. Corr 
##  sub_num         (Intercept)    8.646e-05 0.009298      
##  target_category (Intercept)    1.371e-03 0.037028      
##                  trial_window_c 1.995e-04 0.014125 -0.35
##  Residual                       6.506e-02 0.255068      
## Number of obs: 6172, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                                 Estimate Std. Error        df
## (Intercept)                                    5.264e-01  1.883e-02 3.015e+00
## typicality_condition_c                         7.576e-03  6.500e-03 6.118e+03
## trial_window_c                                 7.411e-02  9.597e-03 2.999e+00
## age_mo_c                                       7.900e-03  2.308e-03 8.321e+01
## typicality_condition_c:trial_window_c          1.098e-02  1.300e-02 6.079e+03
## typicality_condition_c:age_mo_c                2.552e-03  4.407e-03 6.118e+03
## trial_window_c:age_mo_c                        1.856e-02  4.406e-03 6.078e+03
## typicality_condition_c:trial_window_c:age_mo_c 4.406e-03  8.812e-03 6.077e+03
##                                                t value Pr(>|t|)    
## (Intercept)                                     27.964 9.68e-05 ***
## typicality_condition_c                           1.166 0.243832    
## trial_window_c                                   7.722 0.004520 ** 
## age_mo_c                                         3.423 0.000965 ***
## typicality_condition_c:trial_window_c            0.845 0.398212    
## typicality_condition_c:age_mo_c                  0.579 0.562534    
## trial_window_c:age_mo_c                          4.212 2.57e-05 ***
## typicality_condition_c:trial_window_c:age_mo_c   0.500 0.617097    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##                     (Intr) typc__ trl_w_ ag_m_c typclty_cndtn_c:t__
## typclty_cn_          0.000                                         
## tril_wndw_c         -0.253  0.000                                  
## age_mo_c            -0.006  0.005  0.000                           
## typclty_cndtn_c:t__  0.000  0.000  0.001  0.000                    
## typclty_cndtn_c:g__  0.001 -0.034  0.000  0.002  0.000             
## trl_wnd_:__          0.000  0.000 -0.023  0.000  0.005             
## typ__:__:__          0.000  0.000  0.003  0.000 -0.034             
##                     typclty_cndtn_c:g__ tr__:__
## typclty_cn_                                    
## tril_wndw_c                                    
## age_mo_c                                       
## typclty_cndtn_c:t__                            
## typclty_cndtn_c:g__                            
## trl_wnd_:__          0.000                     
## typ__:__:__          0.000               0.002

confint(m_5_6_2_age_int,method="Wald")

##                                                       2.5 %     97.5 %
## .sig01                                                   NA         NA
## .sig02                                                   NA         NA
## .sig03                                                   NA         NA
## .sig04                                                   NA         NA
## .sigma                                                   NA         NA
## (Intercept)                                     0.489529817 0.56332395
## typicality_condition_c                         -0.005163418 0.02031552
## trial_window_c                                  0.055299431 0.09291779
## age_mo_c                                        0.003376168 0.01242474
## typicality_condition_c:trial_window_c          -0.014491637 0.03645173
## typicality_condition_c:age_mo_c                -0.006085328 0.01118957
## trial_window_c:age_mo_c                         0.009922319 0.02719462
## typicality_condition_c:trial_window_c:age_mo_c -0.012865403 0.02167741

There was also no three-way interaction between age, trial window, and typicality, \(\hat{\beta} = 0.00\), 95% CI \([-0.01, 0.02]\), \(t(6077.38) = 0.50\), \(p = .617\). Note that, consistent with alternative analytic strategies, there was a significant age by trial window interaction, suggesting that word recognition improved with age, \(\hat{\beta} = 0.02\), 95% CI \([0.01, 0.03]\), \(t(6078.41) = 4.21\), \(p < .001\).

Below is a quick and dirty plot depicting the age effect

#quick plot of the age effect
ggplot(trial_corrected_accuracy_long_window, aes(age_mo,prop_target_looking,color=trial_window,linetype=condition))+
  geom_hline(yintercept=0.5,linetype="dashed")+
  geom_smooth(method="loess")

Continuous effect of target AND distractor typicality w/ trial window

m_5_6_2_continuous_td <- lmer(prop_target_looking ~ 1 + target_typicality_z*distractor_typicality_z*trial_window_c +
            (1|sub_num) +
            (1+trial_window_c|target_category),
          data=trial_corrected_accuracy_long_window)
summary(m_5_6_2_continuous_td)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## prop_target_looking ~ 1 + target_typicality_z * distractor_typicality_z *  
##     trial_window_c + (1 | sub_num) + (1 + trial_window_c | target_category)
##    Data: trial_corrected_accuracy_long_window
## 
## REML criterion at convergence: 701
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.56191 -0.60783  0.02477  0.64758  2.31574 
## 
## Random effects:
##  Groups          Name           Variance  Std.Dev. Corr
##  sub_num         (Intercept)    0.0002184 0.01478      
##  target_category (Intercept)    0.0013310 0.03648      
##                  trial_window_c 0.0002408 0.01552  0.04
##  Residual                       0.0646516 0.25427      
## Number of obs: 6172, groups:  sub_num, 84; target_category, 4
## 
## Fixed effects:
##                                                              Estimate
## (Intercept)                                                 5.409e-01
## target_typicality_z                                        -3.497e-02
## distractor_typicality_z                                     4.061e-02
## trial_window_c                                              1.051e-01
## target_typicality_z:distractor_typicality_z                -1.734e-02
## target_typicality_z:trial_window_c                          4.801e-03
## distractor_typicality_z:trial_window_c                      2.787e-03
## target_typicality_z:distractor_typicality_z:trial_window_c -3.587e-02
##                                                            Std. Error
## (Intercept)                                                 1.941e-02
## target_typicality_z                                         6.787e-03
## distractor_typicality_z                                     6.777e-03
## trial_window_c                                              1.482e-02
## target_typicality_z:distractor_typicality_z                 6.626e-03
## target_typicality_z:trial_window_c                          1.339e-02
## distractor_typicality_z:trial_window_c                      1.338e-02
## target_typicality_z:distractor_typicality_z:trial_window_c  1.295e-02
##                                                                    df t value
## (Intercept)                                                 3.578e+00  27.872
## target_typicality_z                                         6.077e+03  -5.153
## distractor_typicality_z                                     6.073e+03   5.992
## trial_window_c                                              1.206e+01   7.093
## target_typicality_z:distractor_typicality_z                 6.005e+03  -2.618
## target_typicality_z:trial_window_c                          2.481e+03   0.358
## distractor_typicality_z:trial_window_c                      2.515e+03   0.208
## target_typicality_z:distractor_typicality_z:trial_window_c  1.159e+03  -2.769
##                                                            Pr(>|t|)    
## (Intercept)                                                2.58e-05 ***
## target_typicality_z                                        2.65e-07 ***
## distractor_typicality_z                                    2.19e-09 ***
## trial_window_c                                             1.23e-05 ***
## target_typicality_z:distractor_typicality_z                 0.00887 ** 
## target_typicality_z:trial_window_c                          0.72006    
## distractor_typicality_z:trial_window_c                      0.83498    
## target_typicality_z:distractor_typicality_z:trial_window_c  0.00571 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##                    (Intr) trgt__ dstr__ trl_w_ trgt_typclty_z:d__
## trgt_typcl_         0.009                                        
## dstrctr_ty_        -0.043 -0.865                                 
## tril_wndw_c         0.017  0.000  0.000                          
## trgt_typclty_z:d__ -0.286 -0.023  0.143  0.000                   
## trgt_typclty_z:t__  0.000  0.000  0.000  0.001  0.000            
## dstrct__:__         0.000  0.000  0.000 -0.090  0.000            
## trg__:__:__         0.000  0.000  0.000 -0.731  0.000            
##                    trgt_typclty_z:t__ d__:__
## trgt_typcl_                                 
## dstrctr_ty_                                 
## tril_wndw_c                                 
## trgt_typclty_z:d__                          
## trgt_typclty_z:t__                          
## dstrct__:__        -0.862                   
## trg__:__:__         0.008              0.116

confint(m_5_6_2_continuous_td,method="Wald")

##                                                                  2.5 %
## .sig01                                                              NA
## .sig02                                                              NA
## .sig03                                                              NA
## .sig04                                                              NA
## .sigma                                                              NA
## (Intercept)                                                 0.50286423
## target_typicality_z                                        -0.04827622
## distractor_typicality_z                                     0.02732843
## trial_window_c                                              0.07604565
## target_typicality_z:distractor_typicality_z                -0.03033187
## target_typicality_z:trial_window_c                         -0.02145040
## distractor_typicality_z:trial_window_c                     -0.02343037
## target_typicality_z:distractor_typicality_z:trial_window_c -0.06126074
##                                                                  97.5 %
## .sig01                                                               NA
## .sig02                                                               NA
## .sig03                                                               NA
## .sig04                                                               NA
## .sigma                                                               NA
## (Intercept)                                                 0.578935321
## target_typicality_z                                        -0.021669854
## distractor_typicality_z                                     0.053894778
## trial_window_c                                              0.134117759
## target_typicality_z:distractor_typicality_z                -0.004359042
## target_typicality_z:trial_window_c                          0.031051603
## distractor_typicality_z:trial_window_c                      0.029003946
## target_typicality_z:distractor_typicality_z:trial_window_c -0.010482963

In order to explore the influence of both target and distractor typicality (analogously to the analyses in 5.3.), we fit a model including the interaction between continuous target image typicality (adult norms, z-scored), continuous distractor image typicality (adult norms, z-scored), trial window (centered), and their interaction. The model included by-participant and by-word random intercepts, as well as a by-word random slope for trial window. There was a significant three-way interaction between target typicality, distractor typicality, and trial window, \(\hat{\beta} = -0.04\), 95% CI \([-0.06, -0.01]\), \(t(1158.74) = -2.77\), \(p = .006\). There was a significant overall effect of distractor typicality on target looking, \(\hat{\beta} = 0.04\), 95% CI \([0.03, 0.05]\), \(t(6072.94) = 5.99\), \(p < .001\), and this effect was stronger when the target was more atypical, \(\hat{\beta} = -0.02\), 95% CI \([-0.03, 0.00]\), \(t(6005.27) = -2.62\), \(p = .009\). The three-way interaction indicates that this interaction between distractor and target typicality was stronger in the critical window than in the baseline window, i.e., target looking increased as distractor typicality increased, and this effect was stronger in the critical window than in the baseline window when the target was atypical.

5.7. Predicting target looking from the visual similarity between target and distractor

We also conducted an exploratory analysis investigating the degree to which the visual similarity between the target image and the distractor image affected infants’ word recognition. We predicted that recognizing the target should be more difficult (i.e., lower proportion looking to the target during the critical window) the more (visually) similar the distractor image was to the target image. To obtain an estimate of visual similarity between each target and distractor image pair, we used DreamSim (https://dreamsim-nights.github.io/; Fu et al., 2023) to generate predictions of perceptual distance between each image pair. In this metric, lower distance indicates higher perceptual similarity, i.e. the lower the distance between two images, the more similar they are. We then used this distance metric as a predictor in a linear mixed-effects model predicting trial-by-trial proportion target looking during the critical window. See the analysis script categories_dreamsim_distances.R for further details on the analyses.

Session Info

sessionInfo()

## R version 4.3.2 (2023-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Sonoma 14.4.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/New_York
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] patchwork_1.2.0       agreement_0.0.0.9003  performance_0.10.9   
##  [4] broom_1.0.5           sessioninfo_1.2.2     ggimage_0.3.3        
##  [7] effectsize_0.8.6      papaja_0.1.2          tinylabels_0.2.4     
## [10] broom.mixed_0.2.9.4   JWileymisc_1.4.1      multilevelTools_0.1.1
## [13] car_3.1-2             carData_3.0-5         gghalves_0.1.4       
## [16] wesanderson_0.3.7     TOSTER_0.8.0          lmerTest_3.1-3       
## [19] lme4_1.1-35.1         Matrix_1.6-5          readxl_1.4.3         
## [22] here_1.0.1            cowplot_1.1.3         janitor_2.2.0        
## [25] lubridate_1.9.3       forcats_1.0.0         stringr_1.5.1        
## [28] dplyr_1.1.4           purrr_1.0.2           readr_2.1.5          
## [31] tidyr_1.3.1           tibble_3.2.1          ggplot2_3.5.0        
## [34] tidyverse_2.0.0      
## 
## loaded via a namespace (and not attached):
##   [1] splines_4.3.2        polspline_1.1.24     ggplotify_0.1.2     
##   [4] cellranger_1.1.0     datawizard_0.9.1     rpart_4.1.21        
##   [7] lifecycle_1.0.4      rstatix_0.7.2        rprojroot_2.0.4     
##  [10] vroom_1.6.5          globals_0.16.2       lattice_0.21-9      
##  [13] MASS_7.3-60          insight_0.19.8       ggdist_3.3.1        
##  [16] backports_1.4.1      magrittr_2.0.3       Hmisc_5.1-1         
##  [19] sass_0.4.8           rmarkdown_2.25       jquerylib_0.1.4     
##  [22] yaml_2.3.8           minqa_1.2.6          multcomp_1.4-25     
##  [25] abind_1.4-5          quadprog_1.5-8       yulab.utils_0.1.4   
##  [28] nnet_7.3-19          TH.data_1.1-2        sandwich_3.1-0      
##  [31] listenv_0.9.1        MatrixModels_0.5-3   parallelly_1.37.0   
##  [34] codetools_0.2-19     tidyselect_1.2.0     shape_1.4.6         
##  [37] farver_2.1.1         stats4_4.3.2         base64enc_0.1-3     
##  [40] jsonlite_1.8.8       fst_0.9.8            mitml_0.4-5         
##  [43] Formula_1.2-5        survival_3.5-7       iterators_1.0.14    
##  [46] emmeans_1.10.0       systemfonts_1.0.5    foreach_1.5.2       
##  [49] tools_4.3.2          ragg_1.2.7           Rcpp_1.0.12         
##  [52] glue_1.7.0           mnormt_2.1.1         gridExtra_2.3       
##  [55] pan_1.9              xfun_0.42            mgcv_1.9-0          
##  [58] distributional_0.4.0 ggthemes_5.1.0       withr_3.0.0         
##  [61] numDeriv_2016.8-1.1  fastmap_1.1.1        boot_1.3-28.1       
##  [64] fansi_1.0.6          SparseM_1.81         digest_0.6.34       
##  [67] timechange_0.3.0     R6_2.5.1             gridGraphics_0.5-1  
##  [70] estimability_1.5     textshaping_0.3.7    mice_3.16.0         
##  [73] colorspace_2.1-0     utf8_1.2.4           generics_0.1.3      
##  [76] data.table_1.15.0    robustbase_0.99-2    htmlwidgets_1.6.4   
##  [79] parameters_0.21.5    pkgconfig_2.0.3      gtable_0.3.4        
##  [82] furrr_0.3.1          htmltools_0.5.7      lavaan_0.6-17       
##  [85] multcompView_0.1-10  scales_1.3.0         snakecase_0.11.1    
##  [88] ggfun_0.1.4          knitr_1.45           rstudioapi_0.15.0   
##  [91] tzdb_0.4.0           coda_0.19-4.1        checkmate_2.3.1     
##  [94] nlme_3.1-163         nloptr_2.0.3         cachem_1.0.8        
##  [97] zoo_1.8-12           parallel_4.3.2       foreign_0.8-85      
## [100] pillar_1.9.0         grid_4.3.2           vctrs_0.6.5         
## [103] VGAM_1.1-10          ggpubr_0.6.0         jomo_2.7-6          
## [106] xtable_1.8-4         cluster_2.1.4        htmlTable_2.4.2     
## [109] evaluate_0.23        pbivnorm_0.6.0       extraoperators_0.3.0
## [112] magick_2.8.3         mvtnorm_1.2-4        cli_3.6.2           
## [115] compiler_4.3.2       crayon_1.5.2         rlang_1.1.3         
## [118] rms_6.7-1            ggsignif_0.6.4       labeling_0.4.3      
## [121] fs_1.6.3             stringi_1.8.3        psych_2.4.1         
## [124] assertthat_0.2.1     munsell_0.5.0        glmnet_4.1-8        
## [127] bayestestR_0.13.2    quantreg_5.97        fstcore_0.9.18      
## [130] hms_1.1.3            bit64_4.0.5          future_1.33.1       
## [133] highr_0.10           memoise_2.0.1        bslib_0.6.1         
## [136] bit_4.0.5            DEoptimR_1.1-3