Data Analysis

Load necessary libraries

library(tidyr)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(lme4)

## Loading required package: Matrix

## 
## Attaching package: 'Matrix'

## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack

# Load the cleaned data
dataset <- read.csv("anonymizedData.csv")

# Reshape the data from wide to long format
long_data <- dataset %>%
  tidyr::gather(key = "Question", value = "Response", Q1:Q224) %>%
  dplyr::mutate(Question = as.integer(gsub("Q", "", Question)))

# Ensure the data types are correct
long_data$Response <- as.numeric(long_data$Response)
long_data$Years_of_Musicianship <- as.numeric(long_data$Years_of_Musicianship)
long_data$Participant <- as.factor(long_data$Participant)
long_data$Question <- as.factor(long_data$Question)

# Fit the generalized linear mixed-effects model
model_glmer <- lme4::glmer(Response ~ Years_of_Musicianship + (1 | Participant) + (1 | Question), 
                     data = long_data, family = binomial)

# Display the summary of the model
summary(model_glmer)

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: Response ~ Years_of_Musicianship + (1 | Participant) + (1 | Question)
##    Data: long_data
## 
##      AIC      BIC   logLik deviance df.resid 
##   6160.2   6186.8  -3076.1   6152.2     5596 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -4.4688 -0.6890  0.3396  0.5967  3.4687 
## 
## Random effects:
##  Groups      Name        Variance Std.Dev.
##  Question    (Intercept) 1.8014   1.3422  
##  Participant (Intercept) 0.2565   0.5065  
## Number of obs: 5600, groups:  Question, 224; Participant, 25
## 
## Fixed effects:
##                        Estimate Std. Error z value Pr(>|z|)    
## (Intercept)            0.814390   0.188997   4.309 1.64e-05 ***
## Years_of_Musicianship -0.001953   0.025282  -0.077    0.938    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## Yrs_f_Mscns -0.672