Format data

cpg2 <- data.frame(matrix(array(0), nrow = nrow(cpg1)*4, ncol = 4))
names(cpg2) <- c("ID", "Prod", "Rating", "Cond")
for(i in 1:nrow(cpg1)) {
  indx <- ((i-1)*4 + 1):(i*4)
  cpg2$ID[indx] <- cpg1$ResponseId[i]
  cpg2$Prod[indx[1]] <- 1
  cpg2$Rating[indx[1]] <- ifelse(!is.na(cpg1$Q1[i]), cpg1$Q1[i], cpg1$Q26[i])
  cpg2$Cond[indx[1]] <- ifelse(!is.na(cpg1$Q1[i]), 0, 1)
  cpg2$Prod[indx[2]] <- 2
  cpg2$Rating[indx[2]] <- ifelse(!is.na(cpg1$Q27[i]), cpg1$Q27[i], cpg1$Q28[i])
  cpg2$Cond[indx[2]] <- ifelse(!is.na(cpg1$Q27[i]), 0, 1)
  cpg2$Prod[indx[3]] <- 3
  cpg2$Rating[indx[3]] <- ifelse(!is.na(cpg1$Q29[i]), cpg1$Q29[i], cpg1$Q30[i])
  cpg2$Cond[indx[3]] <- ifelse(!is.na(cpg1$Q29[i]), 0, 1)
  cpg2$Prod[indx[4]] <- 4
  cpg2$Rating[indx[4]] <- ifelse(!is.na(cpg1$Q31[i]), cpg1$Q31[i], cpg1$Q32[i])
  cpg2$Cond[indx[4]] <- ifelse(!is.na(cpg1$Q31[i]), 0, 1)
}
cpg2$Prod <- factor(cpg2$Prod)
cpg2$Cond <- factor(cpg2$Cond)

Analyze data

library(brms)
## Loading required package: Rcpp
## Loading 'brms' package (version 2.22.0). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').
## 
## Attaching package: 'brms'
## The following object is masked from 'package:stats':
## 
##     ar
cpgmod1 <- brm(Rating ~ (1|ID) + Prod + Cond, data = cpg2)
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.4.4.1)’
## using SDK: ‘MacOSX26.1.sdk’
## clang -arch arm64 -std=gnu2x -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG   -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/Rcpp/include/"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppEigen/include/"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppEigen/include/unsupported"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/StanHeaders/include/src/"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/StanHeaders/include/"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppParallel/include/"  -I"/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG  -DBOOST_DISABLE_ASSERTS  -DBOOST_PENDING_INTEGER_LOG2_HPP  -DSTAN_THREADS  -DUSE_STANC3 -DSTRICT_R_HEADERS  -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION  -D_HAS_AUTO_PTR_ETC=0  -include '/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp'  -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1   -I/opt/R/arm64/include    -fPIC  -falign-functions=64 -Wall -g -O2  -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
##   679 | #include <cmath>
##       |          ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1: 
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## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.55 seconds.
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## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
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summary(cpgmod1)
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: Rating ~ (1 | ID) + Prod + Cond 
##    Data: cpg2 (Number of observations: 492) 
##   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
##          total post-warmup draws = 4000
## 
## Multilevel Hyperparameters:
## ~ID (Number of levels: 123) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.72      0.10     0.54     0.92 1.00     1408     2348
## 
## Regression Coefficients:
##           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     4.82      0.16     4.51     5.13 1.00     4748     3106
## Prod2        -0.73      0.18    -1.07    -0.37 1.00     5950     3270
## Prod3        -0.08      0.18    -0.44     0.26 1.00     5970     3410
## Prod4         0.03      0.18    -0.30     0.38 1.00     5964     2807
## Cond1        -0.26      0.14    -0.52     0.02 1.00     6599     2847
## 
## Further Distributional Parameters:
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     1.41      0.05     1.32     1.52 1.00     3216     3335
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).