We need one observation per line. Variables are: Rating ID (factor) Artist (factor) Cond (factor; condition: 0 = Title on top, 1 = Artist on top)
acr <- data.frame(matrix(array(0), nrow = nrow(acdat)*5, ncol = 4))
names(acr) <- c("ID", "Artist", "Rating", "Cond")
for(i in 1:nrow(acdat)) {
indx <- ((i-1)*5 + 1):(i*5)
acr$ID[indx] <- acdat$ResponseId[i]
acr$Artist[indx[1]] <- 1
acr$Rating[indx[1]] <- ifelse(!is.na(acdat$Q1[i]), acdat$Q1[i], acdat$Q26[i])
acr$Cond[indx[1]] <- ifelse(!is.na(acdat$Q1[i]), 0, 1)
acr$Artist[indx[2]] <- 2
acr$Rating[indx[2]] <- ifelse(!is.na(acdat$Q27[i]), acdat$Q27[i], acdat$Q28[i])
acr$Cond[indx[2]] <- ifelse(!is.na(acdat$Q27[i]), 0, 1)
acr$Artist[indx[3]] <- 3
acr$Rating[indx[3]] <- ifelse(!is.na(acdat$Q29[i]), acdat$Q29[i], acdat$Q30[i])
acr$Cond[indx[3]] <- ifelse(!is.na(acdat$Q29[i]), 0, 1)
acr$Artist[indx[4]] <- 4
acr$Rating[indx[4]] <- ifelse(!is.na(acdat$Q31[i]), acdat$Q31[i], acdat$Q32[i])
acr$Cond[indx[4]] <- ifelse(!is.na(acdat$Q31[i]), 0, 1)
acr$Artist[indx[5]] <- 5
acr$Rating[indx[5]] <- ifelse(!is.na(acdat$Q33[i]), acdat$Q33[i], acdat$Q12[i])
acr$Cond[indx[5]] <- ifelse(!is.na(acdat$Q33[i]), 0, 1)
}
acr$Artist <- factor(acr$Artist)
acr$Cond <- factor(acr$Cond)Analysis will control for artist with fixed effects. Random effects on ID.
Model 1 does not show evidence of an effect of artist-title order. Model 2 examines if the effect is heterogeneous (improves rating for some and decreases it for others). No evidence of heterogeneity. Model 3 examines if the effect of artist-title order is moderated by artist/album. No evidence of this, either.
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':
##
## armod1 <- brm(Rating ~ (1|ID) + Artist + Cond, data = acr)## Compiling Stan program...## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
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## /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>
## | ^~~~~~~
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## Chain 4:summary(mod1)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Rating ~ (1 | ID) + Artist + Cond
## Data: acr (Number of observations: 1530)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~ID (Number of levels: 306)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.71 0.05 0.61 0.81 1.00 1730 2248
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 4.37 0.10 4.19 4.56 1.00 3482 3185
## Artist2 -0.88 0.11 -1.10 -0.65 1.00 4377 3116
## Artist3 -0.28 0.11 -0.50 -0.07 1.00 4386 3548
## Artist4 -1.16 0.11 -1.39 -0.94 1.00 4189 3193
## Artist5 -0.42 0.11 -0.64 -0.20 1.00 4263 3171
## Cond1 0.01 0.08 -0.13 0.17 1.00 6347 2795
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.40 0.03 1.35 1.46 1.00 3590 3222
##
## 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).mod2 <- brm(Rating ~ (1|ID) + Artist + (1|Cond), data = acr)## 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:
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## /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.
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## Chain 4:## Warning: There were 271 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.## Warning: Examine the pairs() plot to diagnose sampling problems## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-esssummary(mod2)## Warning: There were 271 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Rating ~ (1 | ID) + Artist + (1 | Cond)
## Data: acr (Number of observations: 1530)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~Cond (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.29 0.39 0.00 1.32 1.02 356 363
##
## ~ID (Number of levels: 306)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.71 0.06 0.60 0.82 1.02 248 713
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 4.41 0.20 4.05 4.87 1.03 205 76
## Artist2 -0.88 0.11 -1.10 -0.66 1.00 893 912
## Artist3 -0.28 0.12 -0.50 -0.06 1.01 430 1592
## Artist4 -1.17 0.12 -1.39 -0.95 1.00 925 1561
## Artist5 -0.42 0.12 -0.65 -0.19 1.01 309 326
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.41 0.03 1.35 1.46 1.01 1190 1395
##
## 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).mod3 <- brm(Rating ~ (1|ID) + Artist + Cond + Artist:Cond, data = acr)## 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##
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## Chain 4:summary(mod3)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Rating ~ (1 | ID) + Artist + Cond + Artist:Cond
## Data: acr (Number of observations: 1530)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~ID (Number of levels: 306)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.71 0.05 0.61 0.81 1.00 1858 2709
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 4.36 0.12 4.11 4.59 1.00 1315 2274
## Artist2 -0.82 0.16 -1.14 -0.51 1.00 1765 2861
## Artist3 -0.23 0.16 -0.55 0.08 1.00 1683 2930
## Artist4 -1.22 0.16 -1.54 -0.90 1.00 1890 2768
## Artist5 -0.38 0.16 -0.70 -0.06 1.00 1729 2825
## Cond1 0.04 0.17 -0.29 0.37 1.00 1147 2226
## Artist2:Cond1 -0.11 0.24 -0.58 0.36 1.00 1563 2295
## Artist3:Cond1 -0.09 0.24 -0.56 0.38 1.00 1576 2243
## Artist4:Cond1 0.11 0.24 -0.36 0.58 1.00 1620 2328
## Artist5:Cond1 -0.07 0.24 -0.53 0.38 1.00 1500 2640
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.41 0.03 1.35 1.46 1.00 3722 2979
##
## 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).