Read in and filter data

dataset <- read.csv("data_experiment1.csv",sep=";")

# Percent of trials where the path was left
table(dataset$path_left)/nrow(dataset)
## 
##         no        yes 
## 0.92766798 0.07233202
dataset <- subset(dataset,path_left=="no")

dataset$subject_nr <- as.factor(dataset$subject_nr)

Load libraries

library(lme4)
library(afex)
library(reshape2)
library(BayesFactor)
library(ggplot2)

# Set ggplot theme
theme_set(theme_classic()+ 
  theme(
    axis.line = element_line(colour = "black"),
    axis.ticks = element_line(colour = "black"),
    axis.text = element_text(colour = "black"),
    panel.border = element_rect(colour = "black", fill=NA)
  ))

Create variables

# Determine choice congruency
dataset$congruency <- ifelse(dataset$response == dataset$direction, 1,0)
dataset$congruency <- factor(dataset$congruency,levels=c(0,1),labels=c("incongruent","congruent"))
contrasts(dataset$congruency) <- c(0,1)

# Calculate logRT
dataset$logRT <- log10(dataset$response_time)

Choice analyses

Choice rates per participant

choice_rates <- dcast(
  dataset,subject_nr+distance+direction~"percent_right",mean,value.var="response_right")

dcast(choice_rates,distance+direction~"percent_right",mean,value.var="percent_right")
##   distance direction percent_right
## 1    equal      left     0.5556805
## 2    equal     right     0.5359645
## 3  unequal      left     0.4273087
## 4  unequal     right     0.6185367

Generalized linear mixed model predicting choice right on trial level

  • Mixed model on trial level predicting probability of saying right
  • Using a binomial link function
  • Specifying a random intercept per participant
  • Dummy coding the effects of direction and distance
  • Baseline condition for direction is always direction left
  • Baseline condition for distance is varied

Baseline: equal distance, direction left

# Set contrasts
contrasts(dataset$direction) <- c(0,1)
contrasts(dataset$distance) <- c(0,1)

# Model results
model_choices_baseline_ed <- glmer(
  response_right~(1|subject_nr)+direction*distance,data=dataset,family="binomial")
summary(model_choices_baseline_ed)
## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
##  Family: binomial  ( logit )
## Formula: response_right ~ (1 | subject_nr) + direction * distance
##    Data: dataset
## 
##      AIC      BIC   logLik deviance df.resid 
##  12785.7  12821.5  -6387.9  12775.7     9383 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5143 -1.0552  0.7480  0.9041  1.3472 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.03493  0.1869  
## Number of obs: 9388, groups:  subject_nr, 115
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           0.20837    0.04583   4.547 5.45e-06 ***
## direction1           -0.04879    0.05923  -0.824     0.41    
## distance1            -0.50433    0.05959  -8.463  < 2e-16 ***
## direction1:distance1  0.82412    0.08396   9.816  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) drctn1 dstnc1
## direction1  -0.660              
## distance1   -0.657  0.508       
## drctn1:dst1  0.466 -0.706 -0.710
# Odds ratio table
coef_baseline_ed <- summary(model_choices_baseline_ed)$coefficients
ci_coef_baseline_ed <- confint(model_choices_baseline_ed,level = .95)
## Computing profile confidence intervals ...
model_table_baseline_ed <- cbind(
  exp(coef_baseline_ed[,1]),
  exp(ci_coef_baseline_ed[-1,1]),
  exp(ci_coef_baseline_ed[-1,2]),
  coef_baseline_ed[,3:4]
)
colnames(model_table_baseline_ed)<-c("OR","CIl","CIu","z","p")
model_table_baseline_ed
##                             OR       CIl       CIu          z            p
## (Intercept)          1.2316712 1.1259721 1.3478545  4.5468623 5.445159e-06
## direction1           0.9523775 0.8479638 1.0695833 -0.8237874 4.100604e-01
## distance1            0.6039116 0.5372564 0.6786262 -8.4632635 2.599974e-17
## direction1:distance1 2.2798793 1.9342450 2.6880323  9.8159689 9.611017e-23
# write.table(model_table_baseline_ed,"glmer_table_ed_exp1.csv",sep=";",dec=".")

Baseline: unequal distance, direction left

# Set contrasts
contrasts(dataset$direction) <- c(0,1)
contrasts(dataset$distance) <- c(1,0)

# Model results
model_choices_baseline_ud <- glmer(
  response_right~(1|subject_nr)+direction*distance,data=dataset,family="binomial")
summary(model_choices_baseline_ud)
## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
##  Family: binomial  ( logit )
## Formula: response_right ~ (1 | subject_nr) + direction * distance
##    Data: dataset
## 
##      AIC      BIC   logLik deviance df.resid 
##  12785.7  12821.5  -6387.9  12775.7     9383 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5143 -1.0552  0.7480  0.9041  1.3472 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.03493  0.1869  
## Number of obs: 9388, groups:  subject_nr, 115
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          -0.29596    0.04544  -6.513 7.36e-11 ***
## direction1            0.77533    0.05949  13.033  < 2e-16 ***
## distance1             0.50434    0.05959   8.463  < 2e-16 ***
## direction1:distance1 -0.82414    0.08396  -9.816  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) drctn1 dstnc1
## direction1  -0.651              
## distance1   -0.649  0.497       
## drctn1:dst1  0.461 -0.709 -0.710
# Odds ratios
coef_baseline_ud <- summary(model_choices_baseline_ud)$coefficients
ci_coef_baseline_ud <- confint(model_choices_baseline_ud,level = .95)
## Computing profile confidence intervals ...
model_table_baseline_ud <- cbind(
  exp(coef_baseline_ud[,1]),
  exp(ci_coef_baseline_ud[-1,1]),
  exp(ci_coef_baseline_ud[-1,2]),
  coef_baseline_ud[,3:4]
)
colnames(model_table_baseline_ud)<-c("OR","CIl","CIu","z","p")
model_table_baseline_ud
##                             OR       CIl       CIu         z            p
## (Intercept)          0.7438197 0.6802378 0.8130435 -6.513128 7.360195e-11
## direction1           2.1713172 1.9327788 2.4403638 13.032915 7.951047e-39
## distance1            1.6558880 1.4735653 1.8613089  8.463070 2.604297e-17
## direction1:distance1 0.4386106 0.3720193 0.5169976 -9.816130 9.595645e-23
# write.table(model_table_baseline_ud,"glmer_table_ud_exp1.csv",sep=";",dec=".")

Figure

# Extract CIs from model using confint
trial_model <- glmer(response_right~(1|subject_nr)+0+interaction(direction,distance),data=dataset,family="binomial")
trial_model_ci <- confint(trial_model)
## Computing profile confidence intervals ...
table_trial_model <- data.frame(
  direction = rep(c("Left","Right"),2),
  distance = rep(c("Equal","Unequal"),each=2),
  logodds = fixef(trial_model),
  logodds_lower = trial_model_ci[-1,1],
  logodds_upper = trial_model_ci[-1,2]
  )

table_trial_model$p <-
  with(table_trial_model,
       exp(logodds)/(1+exp(logodds)))

table_trial_model$p_lower <-
  with(table_trial_model,
       exp(logodds_lower)/(1+exp(logodds_lower)))

table_trial_model$p_upper <-
  with(table_trial_model,
       exp(logodds_upper)/(1+exp(logodds_upper)))

rownames(table_trial_model) <- NULL

table_trial_model
##   direction distance    logodds logodds_lower logodds_upper         p   p_lower   p_upper
## 1      Left    Equal  0.2083772    0.11864677     0.2985140 0.5519066 0.5296269 0.5740792
## 2     Right    Equal  0.1595730    0.07141151     0.2480087 0.5398088 0.5178453 0.5616863
## 3      Left  Unequal -0.2959607   -0.38531285    -0.2069706 0.4265452 0.4048461 0.4484413
## 4     Right  Unequal  0.4793731    0.39008043     0.5693459 0.6175998 0.5963021 0.6386122
# write.table(table_trial_model,"figure_table_exp1.csv",sep=";",dec=".")

ggplot(table_trial_model,aes(x=direction,y=p,group=distance,linetype=distance))+
  geom_errorbar(aes(ymin=p_lower,ymax=p_upper),stat="identity",width=.15,linetype="solid")+
  geom_line(stat="identity")+
  geom_point(stat="identity",size=2,shape=16)+
  xlab("Direction")+ ylab("Probability of right-side option choices")+
  coord_cartesian(ylim=c(.3,.7))+
  scale_linetype(name="Distance")+
  theme(legend.justification=c(1,0), legend.position=c(.95,.05))

# ggsave("figure_exp1.png",width=8.5,height=8.5, unit="cm",dpi=600)
# ggsave("figure_exp1.eps",width=8.5,height=8.5, unit="cm")

Bayes factors for choice rates

BF of direction in equal distance condition

BF_choice_ed_0 <- lmBF(percent_right ~ subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates,distance=="equal"))
BF_choice_ed_1 <- lmBF(percent_right ~ direction + subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates,distance=="equal"))

BF_choice_ed_1/BF_choice_ed_0
## Bayes factor analysis
## --------------
## [1] direction + subject_nr : 0.2992372 ±0.85%
## 
## Against denominator:
##   percent_right ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for choice rates (not reported, just used to check that
# results using choice rates replicate trial level analyses - this is the case)
summary(lmer(percent_right~(1|subject_nr)+direction,
             data=subset(choice_rates,distance=="equal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: percent_right ~ (1 | subject_nr) + direction
##    Data: subset(choice_rates, distance == "equal")
## 
## REML criterion at convergence: -275.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2059 -0.5668  0.0334  0.5704  2.5803 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.002016 0.0449  
##  Residual               0.014861 0.1219  
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##                 Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)      0.55568    0.01211 224.79000  45.870   <2e-16 ***
## directionright  -0.01972    0.01608 114.00000  -1.226    0.223    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## directnrght -0.664

BF of direction in unequal distance condition

BF_choice_ud_0 <- lmBF(percent_right ~ subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates,distance=="unequal"))
BF_choice_ud_1 <- lmBF(percent_right ~ direction + subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates,distance=="unequal"))

BF_choice_ud_1/BF_choice_ud_0
## Bayes factor analysis
## --------------
## [1] direction + subject_nr : 1.814095e+15 ±0.82%
## 
## Against denominator:
##   percent_right ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for choice rates (not reported, just used to check that
# results using choice rates replicate trial level analyses - this is the case)
summary(lmer(percent_right~(1|subject_nr)+direction,
             data=subset(choice_rates,distance=="unequal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: percent_right ~ (1 | subject_nr) + direction
##    Data: subset(choice_rates, distance == "unequal")
## 
## REML criterion at convergence: -188.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.43834 -0.75692  0.00566  0.69434  2.43584 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.00000  0.0000  
##  Residual               0.02452  0.1566  
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##                 Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)      0.42731    0.01460 228.00000  29.261   <2e-16 ***
## directionright   0.19123    0.02065 228.00000   9.259   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## directnrght -0.707

Reaction time analyses

Data aggregation and descriptives

RT

mean_rt <- dcast(
  dataset,subject_nr+distance+congruency~"mean_rt",mean,value.var="response_time")
dcast(mean_rt,distance+congruency~"mean_rt",mean,value.var="mean_rt")
##   distance  congruency  mean_rt
## 1    equal incongruent 4580.579
## 2    equal   congruent 4535.029
## 3  unequal incongruent 4927.584
## 4  unequal   congruent 4266.021

logRT

mean_logrt <- dcast(
  dataset,subject_nr+distance+congruency~"mean_logrt",mean,value.var="logRT")
dcast(mean_logrt,distance+congruency~"mean_logrt",mean,value.var="mean_logrt")
##   distance  congruency mean_logrt
## 1    equal incongruent   3.628092
## 2    equal   congruent   3.624720
## 3  unequal incongruent   3.663636
## 4  unequal   congruent   3.594883

Analyses with untransformed RT

Linear mixed model for trial level RTs

Effect of congruency in unequal distance condition

model_RT_ud <- lmer(response_time~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="unequal")
summary(model_RT_ud)
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: response_time ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "unequal"
## 
## REML criterion at convergence: 82260
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4567 -0.5565 -0.1414  0.3729 10.2763 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1624596  1275    
##  Residual               1814884  1347    
## Number of obs: 4746, groups:  subject_nr, 115
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4877.54     122.98  123.00   39.66   <2e-16 ***
## congruency1  -627.19      41.19 5186.00  -15.22   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.200
mixed(response_time~(1|subject_nr)+congruency,data=subset(dataset,distance=="unequal"))
## Contrasts set to contr.sum for the following variables: subject_nr, congruency
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Mixed Model Anova Table (Type 3 tests, KR-method)
## 
## Model: response_time ~ (1 | subject_nr) + congruency
## Data: subset
## Data: dataset
## Data: distance == "unequal"
##       Effect         df          F p.value
## 1 congruency 1, 4646.72 231.78 ***  <.0001
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
confint(model_RT_ud, level = .95)
## Computing profile confidence intervals ...
##                 2.5 %    97.5 %
## .sig01      1116.1901 1457.5478
## .sigma      1320.0558 1374.9389
## (Intercept) 4635.5226 5119.2995
## congruency1 -707.9979 -546.4799

Effect of congruency in equal distance condition

model_RT_ed <- lmer(response_time~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="equal")
summary(model_RT_ed)
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: response_time ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "equal"
## 
## REML criterion at convergence: 81291.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2690 -0.5225 -0.1322  0.3308 13.2604 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1628121  1276    
##  Residual               2178768  1476    
## Number of obs: 4642, groups:  subject_nr, 115
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4577.21     122.92  121.00  37.239   <2e-16 ***
## congruency1   -40.04      43.90 6238.00  -0.912    0.362    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.176
mixed(response_time~(1|subject_nr)+congruency,data=subset(dataset,distance=="equal"))
## Contrasts set to contr.sum for the following variables: subject_nr, congruency
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]
## Mixed Model Anova Table (Type 3 tests, KR-method)
## 
## Model: response_time ~ (1 | subject_nr) + congruency
## Data: subset
## Data: dataset
## Data: distance == "equal"
##       Effect         df    F p.value
## 1 congruency 1, 4534.41 0.83     .36
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
confint(model_RT_ed, level = .95)
## Computing profile confidence intervals ...
##                 2.5 %     97.5 %
## .sig01      1116.3424 1460.21531
## .sigma      1446.0142 1506.83530
## (Intercept) 4335.3486 4818.93310
## congruency1 -126.0836   46.03641

Bayes factors for mean RTs

BF of congruency in unequal distance condition

BF_rt_ud_0 <- lmBF(mean_rt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt,distance=="unequal"))
BF_rt_ud_1 <- lmBF(mean_rt ~ congruency + subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt,distance=="unequal"))

BF_rt_ud_1/BF_rt_ud_0
## Bayes factor analysis
## --------------
## [1] congruency + subject_nr : 1.537824e+16 ±0.82%
## 
## Against denominator:
##   mean_rt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for mean RTs (not reported, just used to check
# that results on aggregate data replicate trial level analyses - this is the case)
summary(lmer(mean_rt~(1|subject_nr)+congruency,
             data=subset(mean_rt,distance=="unequal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: mean_rt ~ (1 | subject_nr) + congruency
##    Data: subset(mean_rt, distance == "unequal")
## 
## REML criterion at convergence: 3768.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.61940 -0.37675 -0.06654  0.31584  2.65742 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1593417  1262.3  
##  Residual                210816   459.1  
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4927.58     125.26  128.10   39.34   <2e-16 ***
## congruency1  -661.56      60.55  116.07  -10.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.242

BF of congruency in equal distance condition

BF_rt_ed_0 <- lmBF(mean_rt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt,distance=="equal"))
BF_rt_ed_1 <- lmBF(mean_rt ~ congruency + subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt,distance=="equal"))

BF_rt_ed_1/BF_rt_ed_0
## Bayes factor analysis
## --------------
## [1] congruency + subject_nr : 0.2282974 ±4.03%
## 
## Against denominator:
##   mean_rt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for mean RTs (not reported, just used to check
# that results on aggregate data replicate trial level analyses - this is the case)
summary(lmer(mean_rt~(1|subject_nr)+congruency,
             data=subset(mean_rt,distance=="equal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: mean_rt ~ (1 | subject_nr) + congruency
##    Data: subset(mean_rt, distance == "equal")
## 
## REML criterion at convergence: 3713.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6583 -0.3768 -0.0478  0.3679  4.7702 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1670843  1293    
##  Residual                127483   357    
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4580.58     125.05  122.37  36.630   <2e-16 ***
## congruency1   -45.55      47.09  116.44  -0.967    0.335    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.188

Analyses with logRT

Linear mixed model for trial level logRTs

Effect of congruency in unequal distance condition

model_logRT_ud <- lmer(logRT~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="unequal")
summary(model_logRT_ud)
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: logRT ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "unequal"
## 
## REML criterion at convergence: -6979
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2430 -0.6509 -0.0702  0.5808  4.9893 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.01620  0.1273  
##  Residual               0.01217  0.1103  
## Number of obs: 4746, groups:  subject_nr, 115
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  3.657e+00  1.214e-02  1.200e+02  301.10   <2e-16 ***
## congruency1 -6.363e-02  3.375e-03  4.641e+03  -18.86   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.166
confint(model_logRT_ud,level = .95)
## Computing profile confidence intervals ...
##                   2.5 %      97.5 %
## .sig01       0.11156693  0.14540086
## .sigma       0.10810129  0.11259593
## (Intercept)  3.63306662  3.68085306
## congruency1 -0.07025299 -0.05702219

Effect of congruency in equal distance condition

model_logRT_ed <- lmer(logRT~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="equal")
summary(model_logRT_ed)
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: logRT ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "equal"
## 
## REML criterion at convergence: -6920.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2266 -0.6362 -0.0656  0.5413  5.8910 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.01457  0.1207  
##  Residual               0.01193  0.1092  
## Number of obs: 4642, groups:  subject_nr, 115
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  3.628e+00  1.148e-02  1.180e+02 315.923   <2e-16 ***
## congruency1 -2.125e-03  3.249e-03  4.530e+03  -0.654    0.513    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.139
confint(model_logRT_ed,level = .95)
## Computing profile confidence intervals ...
##                    2.5 %     97.5 %
## .sig01       0.105770586 0.13793281
## .sigma       0.107004393 0.11150532
## (Intercept)  3.605292795 3.65047872
## congruency1 -0.008493756 0.00424534

Bayes factors for mean logRTs

BF of congruency in unequal distance condition

BF_logrt_ud_0 <- lmBF(mean_logrt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_logrt,distance=="unequal"))
BF_logrt_ud_1 <- lmBF(mean_logrt ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=subset(mean_logrt,distance=="unequal"))

BF_logrt_ud_1/BF_logrt_ud_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 5.410858e+19 ±1.64%
## 
## Against denominator:
##   mean_logrt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for mean logRTs (not reported, just used to check
# that results on aggregate data replicate trial level analyses - this is the case)
summary(lmer(mean_logrt~(1|subject_nr)+congruency,
             data=subset(mean_logrt,distance=="unequal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: mean_logrt ~ (1 | subject_nr) + congruency
##    Data: subset(mean_logrt, distance == "unequal")
## 
## REML criterion at convergence: -460.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.73360 -0.34127 -0.00776  0.35173  2.75201 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.01506  0.12274 
##  Residual               0.00174  0.04171 
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)   3.66364    0.01209 126.41000   303.1   <2e-16 ***
## congruency1  -0.06875    0.00550 114.00000   -12.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.228

BF of congruency in equal distance condition

BF_logrt_ed_0 <- lmBF(mean_logrt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_logrt,distance=="equal"))
BF_logrt_ed_1 <- lmBF(mean_logrt ~ subject_nr+ congruency, whichRandom = "subject_nr",
             data=subset(mean_logrt,distance=="equal"))

BF_logrt_ed_1/BF_logrt_ed_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 0.2115193 ±1.71%
## 
## Against denominator:
##   mean_logrt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS
# linear mixed model for mean logRTs (not reported, just used to check
# that results replicate trial level analyses - this is the case)
summary(lmer(mean_logrt~(1|subject_nr)+congruency,
             data=subset(mean_logrt,distance=="equal")))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: mean_logrt ~ (1 | subject_nr) + congruency
##    Data: subset(mean_logrt, distance == "equal")
## 
## REML criterion at convergence: -555.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.6424 -0.4453  0.0003  0.4437  2.8307 
## 
## Random effects:
##  Groups     Name        Variance  Std.Dev.
##  subject_nr (Intercept) 0.0151284 0.1230  
##  Residual               0.0007784 0.0279  
## Number of obs: 230, groups:  subject_nr, 115
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)   3.628092   0.011761 119.720000 308.486   <2e-16 ***
## congruency1  -0.003372   0.003679 114.000000  -0.916    0.361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.156

Initiation time analysis in equal distance condition

Data aggregation and descriptives

mean_initiation_time <- dcast(data = subset(dataset,distance=="equal"),
  subject_nr+congruency~"mean_initiation_time",mean,value.var="initiation_time")
dcast(mean_initiation_time,congruency~"mean_initiation_time",mean,value.var="mean_initiation_time")
##    congruency mean_initiation_time
## 1 incongruent             594.2839
## 2   congruent             595.0745

Effect of congruency

# Linear mixed model on trial level
summary(lmer(initiation_time~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="equal"))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: initiation_time ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "equal"
## 
## REML criterion at convergence: 72877.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.6907 -0.4109 -0.0902  0.2009 17.1015 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 106771   326.8   
##  Residual               363198   602.7   
## Number of obs: 4642, groups:  subject_nr, 115
## 
## Fixed effects:
##              Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)  595.5569    32.9649  132.0000  18.066   <2e-16 ***
## congruency1    0.6324    17.9135 4663.0000   0.035    0.972    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.268
# Bayes factor for mean initiation times
BF_init_ed_0 <- lmBF(mean_initiation_time ~ subject_nr, whichRandom = "subject_nr",
             data=mean_initiation_time)
BF_init_ed_1 <- lmBF(mean_initiation_time ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=mean_initiation_time)

BF_init_ed_1/BF_init_ed_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 0.1493376 ±5.29%
## 
## Against denominator:
##   mean_initiation_time ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

Analyses for subset of participants

Descriptives

hypothesis <- unique(subset(dataset,select=c(subject_nr,hypothesis)))
table(hypothesis$hypothesis)
## 
##   0   1 
## 101  14
table(hypothesis$hypothesis)/nrow(hypothesis)
## 
##         0         1 
## 0.8782609 0.1217391

Choice rates per participant

choice_rates_sub <- dcast(
  subset(dataset,hypothesis==0),subject_nr+distance+direction~"percent_right",mean,value.var="response_right")
dcast(choice_rates_sub,distance+direction~"percent_right",mean,value.var="percent_right")
##   distance direction percent_right
## 1    equal      left     0.5620005
## 2    equal     right     0.5420748
## 3  unequal      left     0.4233469
## 4  unequal     right     0.6263610
# Refactor subject_nr to get rid of non-existing levels
choice_rates_sub$subject_nr <- factor(choice_rates_sub$subject_nr)

Generalized linear mixed model predicting choice right on trial level

Baseline: equal distance, direction left

contrasts(dataset$direction) <- c(0,1)
contrasts(dataset$distance) <- c(0,1)
summary(glmer(response_right~(1|subject_nr)+direction*distance,
              data=dataset,family="binomial",subset=hypothesis==0))
## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
##  Family: binomial  ( logit )
## Formula: response_right ~ (1 | subject_nr) + direction * distance
##    Data: dataset
##  Subset: hypothesis == 0
## 
##      AIC      BIC   logLik deviance df.resid 
##  11136.9  11172.0  -5563.4  11126.9     8195 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5394 -1.0648  0.7376  0.8931  1.3675 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.03589  0.1895  
## Number of obs: 8200, groups:  subject_nr, 101
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           0.23294    0.04922   4.733 2.21e-06 ***
## direction1           -0.04489    0.06346  -0.707    0.479    
## distance1            -0.54633    0.06390  -8.550  < 2e-16 ***
## direction1:distance1  0.87144    0.09002   9.681  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) drctn1 dstnc1
## direction1  -0.660              
## distance1   -0.656  0.508       
## drctn1:dst1  0.466 -0.705 -0.710

Baseline: unequal distance, direction left

contrasts(dataset$direction) <- c(0,1)
contrasts(dataset$distance) <- c(1,0)
summary(glmer(response_right~(1|subject_nr)+direction*distance,
              data=dataset,family="binomial",subset=hypothesis==0))
## Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
##  Family: binomial  ( logit )
## Formula: response_right ~ (1 | subject_nr) + direction * distance
##    Data: dataset
##  Subset: hypothesis == 0
## 
##      AIC      BIC   logLik deviance df.resid 
##  11136.9  11172.0  -5563.4  11126.9     8195 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5393 -1.0648  0.7376  0.8931  1.3675 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.03589  0.1895  
## Number of obs: 8200, groups:  subject_nr, 101
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          -0.31340    0.04878  -6.424 1.32e-10 ***
## direction1            0.82655    0.06383  12.949  < 2e-16 ***
## distance1             0.54634    0.06391   8.549  < 2e-16 ***
## direction1:distance1 -0.87145    0.09003  -9.679  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) drctn1 dstnc1
## direction1  -0.649              
## distance1   -0.648  0.496       
## drctn1:dst1  0.460 -0.709 -0.710

Bayes factors for choice rates

BF of direction in equal distance condition

BF_choicerates_ed_0 <- lmBF(percent_right ~ subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates_sub,distance=="equal"))
BF_choicerates_ed_1 <- lmBF(percent_right ~ subject_nr+ direction, whichRandom = "subject_nr",
             data=subset(choice_rates_sub,distance=="equal"))

BF_choicerates_ed_1/BF_choicerates_ed_0
## Bayes factor analysis
## --------------
## [1] subject_nr + direction : 0.296616 ±0.9%
## 
## Against denominator:
##   percent_right ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

BF of direction in unequal distance condition

BF_choicerates_ud_0 <- lmBF(percent_right ~ subject_nr, whichRandom = "subject_nr",
             data=subset(choice_rates_sub,distance=="unequal"))
BF_choicerates_ud_1 <- lmBF(percent_right ~ subject_nr + direction, whichRandom = "subject_nr",
             data=subset(choice_rates_sub,distance=="unequal"))

BF_choicerates_ud_1/BF_choicerates_ud_0
## Bayes factor analysis
## --------------
## [1] subject_nr + direction : 3.454584e+14 ±1.25%
## 
## Against denominator:
##   percent_right ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

Linear mixed model for trial level RTs

Effect of congruency in unequal distance condition

summary(lmer(response_time~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="unequal"&hypothesis==0))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: response_time ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "unequal" & hypothesis == 0
## 
## REML criterion at convergence: 71865
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4648 -0.5505 -0.1407  0.3726 10.2830 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1692658  1301    
##  Residual               1815939  1348    
## Number of obs: 4146, groups:  subject_nr, 101
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4802.45     133.87  108.00   35.88   <2e-16 ***
## congruency1  -601.82      44.24 5203.00  -13.60   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.199

Effect of congruency in equal distance condition

summary(lmer(response_time~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="equal"&hypothesis==0))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: response_time ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "equal" & hypothesis == 0
## 
## REML criterion at convergence: 70991.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2732 -0.5133 -0.1302  0.3201 12.3961 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 1729778  1315    
##  Residual               2174857  1475    
## Number of obs: 4054, groups:  subject_nr, 101
## 
## Fixed effects:
##             Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)  4526.93     134.97  105.70  33.541   <2e-16 ***
## congruency1   -53.34      46.92 2277.20  -1.137    0.256    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.171

Bayes factors for mean RTs

Aggregate data

mean_rt_sub <- dcast(
  subset(dataset,hypothesis==0),subject_nr+distance+congruency~"mean_rt",mean,value.var="response_time")
dcast(mean_rt_sub,distance+congruency~"mean_rt",mean,value.var="mean_rt")
##   distance  congruency  mean_rt
## 1    equal incongruent 4530.915
## 2    equal   congruent 4471.710
## 3  unequal incongruent 4859.326
## 4  unequal   congruent 4216.152
# Refactor subject_nr to get rid of non-existing levels
mean_rt_sub$subject_nr <- factor(mean_rt_sub$subject_nr)

BF of congruency in unequal distance condition

BF_congr_ud_0 <- lmBF(mean_rt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt_sub,distance=="unequal"))
BF_congr_ud_1 <- lmBF(mean_rt ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=subset(mean_rt_sub,distance=="unequal"))

BF_congr_ud_1/BF_congr_ud_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 7.68179e+12 ±1.23%
## 
## Against denominator:
##   mean_rt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

BF of congruency in equal distance condition

BF_congr_ed_0 <- lmBF(mean_rt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_rt_sub,distance=="equal"))
BF_congr_ed_1 <- lmBF(mean_rt ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=subset(mean_rt_sub,distance=="equal"))

BF_congr_ed_1/BF_congr_ed_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 0.3228291 ±15.61%
## 
## Against denominator:
##   mean_rt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

Linear mixed model for trial level logRTs

Effect of congruency in unequal distance condition

summary(lmer(logRT~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="unequal"&hypothesis==0))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: logRT ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "unequal" & hypothesis == 0
## 
## REML criterion at convergence: -6045.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.2230 -0.6506 -0.0753  0.5863  4.9647 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.0172   0.1312  
##  Residual               0.0123   0.1109  
## Number of obs: 4146, groups:  subject_nr, 101
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  3.649e+00  1.335e-02  1.050e+02  273.39   <2e-16 ***
## congruency1 -6.283e-02  3.642e-03  4.053e+03  -17.25   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.164

Effect of congruency in equal distance condition

summary(lmer(logRT~(1|subject_nr)+congruency,
             data=dataset,subset=distance=="equal"&hypothesis==0))
## Linear mixed model fit by REML 
## t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
## Formula: logRT ~ (1 | subject_nr) + congruency
##    Data: dataset
##  Subset: distance == "equal" & hypothesis == 0
## 
## REML criterion at convergence: -5994
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2063 -0.6325 -0.0645  0.5340  5.8518 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_nr (Intercept) 0.01559  0.1248  
##  Residual               0.01205  0.1098  
## Number of obs: 4054, groups:  subject_nr, 101
## 
## Fixed effects:
##               Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)  3.621e+00  1.266e-02  1.030e+02 285.960   <2e-16 ***
## congruency1 -2.703e-03  3.494e-03  3.956e+03  -0.774    0.439    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## congruency1 -0.136

Bayes factors for mean logRTs

Aggregate data

mean_logrt_sub <- dcast(
  subset(dataset,hypothesis==0),subject_nr+distance+congruency~"mean_logrt",mean,value.var="logRT")
dcast(mean_logrt_sub,distance+congruency~"mean_logrt",mean,value.var="mean_logrt")
##   distance  congruency mean_logrt
## 1    equal incongruent   3.621526
## 2    equal   congruent   3.617408
## 3  unequal incongruent   3.656741
## 4  unequal   congruent   3.588046
# Refactor subject_nr to get rid of non-existing levels
mean_logrt_sub$subject_nr <- factor(mean_logrt_sub$subject_nr)

BF of congruency in unequal distance condition

BF_congr_lgrt_ud_0 <- lmBF(mean_logrt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_logrt_sub,distance=="unequal"))
BF_congr_lgrt_ud_1 <- lmBF(mean_logrt ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=subset(mean_logrt_sub,distance=="unequal"))

BF_congr_lgrt_ud_1/BF_congr_lgrt_ud_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 1.202168e+16 ±2.22%
## 
## Against denominator:
##   mean_logrt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS

BF of congruency in equal distance condition

BF_congr_lgrt_ed_0 <- lmBF(mean_logrt ~ subject_nr, whichRandom = "subject_nr",
             data=subset(mean_logrt_sub,distance=="equal"))
BF_congr_lgrt_ed_1 <- lmBF(mean_logrt ~ subject_nr + congruency, whichRandom = "subject_nr",
             data=subset(mean_logrt_sub,distance=="equal"))

BF_congr_lgrt_ed_1/BF_congr_lgrt_ed_0
## Bayes factor analysis
## --------------
## [1] subject_nr + congruency : 0.2456843 ±1.29%
## 
## Against denominator:
##   mean_logrt ~ subject_nr 
## ---
## Bayes factor type: BFlinearModel, JZS