## Family: gamma
## Links: mu = log
## Formula: true_time ~ 1 + s_rmi * s_time_in_game + (s_rmi * s_time_in_game | level) + (s_rmi * s_time_in_game | subject)
## Data: performance_and_rmi (Number of observations: 835)
## Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup draws = 8000
##
## Multilevel Hyperparameters:
## ~level (Number of levels: 10)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.23 0.06 0.14 0.38 1.00 2565 3489
## sd(s_rmi) 0.02 0.01 0.00 0.04 1.00 2669 1910
## sd(s_time_in_game) 0.01 0.01 0.00 0.04 1.00 2533 3800
## sd(s_rmi:s_time_in_game) 0.01 0.01 0.00 0.03 1.00 4149 4281
## cor(Intercept,s_rmi) 0.46 0.34 -0.34 0.93 1.00 6676 5487
## cor(Intercept,s_time_in_game) -0.14 0.38 -0.81 0.63 1.00 9942 5403
## cor(s_rmi,s_time_in_game) -0.29 0.41 -0.90 0.63 1.00 5304 5291
## cor(Intercept,s_rmi:s_time_in_game) 0.14 0.43 -0.71 0.86 1.00 9581 5886
## cor(s_rmi,s_rmi:s_time_in_game) 0.14 0.43 -0.73 0.86 1.00 8054 6433
## cor(s_time_in_game,s_rmi:s_time_in_game) -0.12 0.44 -0.85 0.75 1.00 6382 6267
##
## ~subject (Number of levels: 87)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.16 0.01 0.14 0.19 1.00 1438 2902
## sd(s_rmi) 0.03 0.01 0.02 0.05 1.00 1727 2814
## sd(s_time_in_game) 0.03 0.01 0.01 0.05 1.01 1216 922
## sd(s_rmi:s_time_in_game) 0.02 0.01 0.00 0.04 1.00 1640 2897
## cor(Intercept,s_rmi) 0.30 0.18 -0.05 0.64 1.00 5960 5075
## cor(Intercept,s_time_in_game) 0.22 0.20 -0.18 0.60 1.00 7303 3805
## cor(s_rmi,s_time_in_game) 0.35 0.28 -0.25 0.84 1.00 2225 2714
## cor(Intercept,s_rmi:s_time_in_game) 0.17 0.31 -0.51 0.75 1.00 7964 4376
## cor(s_rmi,s_rmi:s_time_in_game) 0.52 0.36 -0.42 0.95 1.00 2757 3914
## cor(s_time_in_game,s_rmi:s_time_in_game) 0.21 0.38 -0.59 0.84 1.00 4313 5722
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 5.05 0.08 4.89 5.20 1.00 1526 2545
## s_rmi -0.02 0.01 -0.04 -0.00 1.00 4257 5536
## s_time_in_game -0.00 0.01 -0.02 0.01 1.00 6664 5278
## s_rmi:s_time_in_game 0.00 0.01 -0.01 0.02 1.00 6316 5456
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 67.84 4.36 59.68 76.86 1.00 2583 4408
##
## 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).Game
Here is a video playthrough of each level.
Check out how data are tracked in real time.
Model
Here is where you can view more detail of the final model I summarized on the poster.
Model was fit with the brms package in R version 4.5.1. Visualization were completed using the ggplot2, tidybayes, bayesplot, and marginaleffects packages.
Model summary
Beta posteriors were shown on the poster, and variance posteriors for each groups’ random effect offsets are shown below.
Here is how model predicted relationships varied by subject.
Posterior Predictive Check
Here is a posterior predictive check to validate the model fit to the original data by level.
