Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal.R

#######################################
# Judgment Accuracy: Causal Functions #
#######################################

#import libraries
library('lmerTest') 
library("tidyverse")

# Import data
Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal <- as_tibble(read.csv("Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal.csv"))

# Preview data
head(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal)

# data dictionary:
## "Participant" = participant number
## "Function_Exposure_Treatment" = denotes whether or not participant received function exposure treatment (see Study 3 method section for details;), 0=no, 1=yes
## "Function" = function number (causal functions only; range 1-4; refer to payoff function figure)
## "Congruence" = denotes preference-congruence for a given policy/function
## "Ambiguity" = denotes ambiguity of function (low vs high)
## "Judgment_Accuracy" = values are the distance a final judgment was from the correct assessment value (3 possible values: 0-2); 0=correct judgment; 1=incorrect (policy A = policy B); 2=incorrect (e.g., Policy A < Policy B)

# Re-coded judgment accuracy so that correct=1 and incorrect judgment=0 
Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Judgment_Accuracy_Coded <-
  ifelse(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Judgment_Accuracy==0, 1, 0)

# Descriptives: average judgment accuracy across congruence and ambiguity
tapply(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Judgment_Accuracy_Coded,
       list(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Ambiguity,
            Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Congruence),
       mean,
       na.rm=TRUE) 

# Effects coding for model
Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Ambiguity2 <-
  ifelse(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Ambiguity=="Low",.5,-.5)
Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Function_Exposure_Treatment2 <-
  ifelse(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Function_Exposure_Treatment==1,.5,-.5)
Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Congruence2 <-
  ifelse(Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal$Congruence=="Congruent",.5,-.5)


#############################
# logistic regression model #
#############################

# model convergence issues, before settling on this model
m <- glmer(Judgment_Accuracy_Coded ~ Congruence2*Ambiguity2*Function_Exposure_Treatment2 + 
              (1|Participant),
            data=Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal, family="binomial")
summary(m)

# Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
# Family: binomial  ( logit )
# Formula: Judgment_Accuracy_Coded ~ Congruence2 * Ambiguity2 * Function_Exposure_Treatment2 +      (1 | Participant)
# Data: Study3_Judgments_of_Policy_Efficacy_after_the_Learning_Task_Causal
# 
# AIC      BIC   logLik deviance df.resid 
# 297.2    330.5   -139.6    279.2      291 
# 
# Scaled residuals: 
#   Min      1Q  Median      3Q     Max 
# -3.5590 -0.6939  0.2810  0.5547  4.2426 
# 
# Random effects:
#   Groups      Name        Variance Std.Dev.
# Participant (Intercept) 4e-14    2e-07   
# Number of obs: 300, groups:  Participant, 78
# 
# Fixed effects:
#   Estimate Std. Error z value Pr(>|z|)    
# (Intercept)                                          0.02477    0.17240   0.144    0.886    
# Congruence2                                          1.65521    0.34481   4.800 1.58e-06 ***
#   Ambiguity2                                           3.01146    0.34481   8.734  < 2e-16 ***
#   Function_Exposure_Treatment2                         0.30077    0.34481   0.872    0.383    
# Congruence2:Ambiguity2                              -0.70537    0.68961  -1.023    0.306    
# Congruence2:Function_Exposure_Treatment2            -0.80822    0.68961  -1.172    0.241    
# Ambiguity2:Function_Exposure_Treatment2             -0.71713    0.68961  -1.040    0.298    
# Congruence2:Ambiguity2:Function_Exposure_Treatment2 -1.01007    1.37920  -0.732    0.464    
# ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1