Study3_Number_of_Trials_Until_Testing_by_Preference.R

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# Number of Trials Until Testing by Preference #
################################################

# Import Libraries
library("tidyverse")
library('lmerTest')

# Import data
Number_of_Trials_Until_Testing_by_Preference <- as_tibble(read.csv("Study3_Number_of_Trials_Until_Testing_by_Preference.csv"))

# preview data
head(Number_of_Trials_Until_Testing_by_Preference)

# data dictionary:
## "Participant" = participant number
## "Function_Exposure" = denotes if participant was assigned to function exposure treatment (see study 3 methods for details); 1=yes, 0=no
## "Function" = Function number (range 1-6; refer to payoff function figure)
## "Preferred_Policy_at_Start" = notes policy preference at start. 1 = randomized to preferred policy at start of learning task; 0 = non preferred policy at start; -88 = neutral policy (i.e., no opportunity for preference or not)
## "Trial_Number_of_First_Test" = Notes what trial number a participant made first test (i.e., change/switch) for a given policy/function; Note "NA"s mean a participant never tested a policy/function. Also note that trial 1-10 were learning trials, where a participant did not have control yet.

# Subtract 10 from trial number, to reflect trial # that participant actually had control of economic policies. 
Number_of_Trials_Until_Testing_by_Preference$first_test_adj <- 
  Number_of_Trials_Until_Testing_by_Preference$Trial_Number_of_First_Test - 10

# Descriptives: When did participants first test policies across randomized policy at start
# 1="Preferred policy at Start"
# 0="Non-preferred policy at start"
aggregate(Number_of_Trials_Until_Testing_by_Preference$first_test_adj, 
          by=list(Number_of_Trials_Until_Testing_by_Preference$Preferred_Policy_at_Start),
          mean, na.rm=T) %>% 
  rename("Preferred_Policy_at_Start" = "Group.1",
         "Mean_Trial_Number_of_First_Test" = "x")


# Re-scale to improve model convergence (z-score with min. value of 1)
Number_of_Trials_Until_Testing_by_Preference$first_test_adj_centered <- 
  scale(Number_of_Trials_Until_Testing_by_Preference$first_test_adj, center=TRUE)
Number_of_Trials_Until_Testing_by_Preference$first_test_adj_centered_fixed <- 
  Number_of_Trials_Until_Testing_by_Preference$first_test_adj_centered + 
  abs(min(Number_of_Trials_Until_Testing_by_Preference$first_test_adj_centered,na.rm=T)) + 
  1

# Analysis 1: number of trials until testing: preferred vs non-preferred at start (omitted neutral policies)
Number_of_Trials_Until_Testing_by_Preference_omit_neutral <- Number_of_Trials_Until_Testing_by_Preference %>% 
  filter(!Preferred_Policy_at_Start==-88)

# Effects coding for analysis
Number_of_Trials_Until_Testing_by_Preference$Preferred_Policy_at_Start2 <-
  ifelse(Number_of_Trials_Until_Testing_by_Preference$Preferred_Policy_at_Start==1,.5,-.5)
Number_of_Trials_Until_Testing_by_Preference$Function_Exposure2 <- 
  ifelse(Number_of_Trials_Until_Testing_by_Preference$Function_Exposure==1,.5,-.5)


# Model: preferred vs non-preferred at start
m1 <- glmer(first_test_adj_centered_fixed ~ Preferred_Policy_at_Start2*Function_Exposure2 + (1+Preferred_Policy_at_Start2|Participant),
            data=Number_of_Trials_Until_Testing_by_Preference, family=Gamma(link='inverse'))
summary(m1)

# Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
# Family: Gamma  ( inverse )
# Formula: first_test_adj_centered_fixed ~ Preferred_Policy_at_Start2 *  
#   Function_Exposure2 + (1 + Preferred_Policy_at_Start2 | Participant)
# Data: Number_of_Trials_Until_Testing_by_Preference
# 
# AIC      BIC   logLik deviance df.resid 
# 591.1    623.2   -287.6    575.1      396 
# 
# Scaled residuals: 
#   Min      1Q  Median      3Q     Max 
# -1.8673 -0.2911 -0.1617  0.3305  4.7969 
# 
# Random effects:
#   Groups      Name                       Variance Std.Dev. Corr 
# Participant (Intercept)                0.01558  0.1248        
# Preferred_Policy_at_Start2 0.05711  0.2390   -0.19
# Residual                               0.11247  0.3354        
# Number of obs: 404, groups:  Participant, 78
# 
# Fixed effects:
#   Estimate Std. Error t value Pr(>|z|)    
# (Intercept)                                    0.72677    0.02490  29.184  < 2e-16 ***
#   Preferred_Policy_at_Start2                    -0.30467    0.04664  -6.532 6.49e-11 ***
#   Function_Exposure2                             0.02506    0.04582   0.547    0.584    
# Preferred_Policy_at_Start2:Function_Exposure2  0.08372    0.08755   0.956    0.339    
# ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# Correlation of Fixed Effects:
#   (Intr) Pr_P__S2 Fnc_E2
# Prfrr_P__S2 -0.151                
# Fnctn_Exps2  0.074 -0.013         
# P_P__S2:F_E -0.021  0.064   -0.161