Varying intercepts Chimpanzees

In Statistical Rethinking Edition 1, the model below is called m10.4.

Data

import CSV

using TuringModels: project_root
using DataFrames

path = joinpath(project_root, "data", "chimpanzees.csv")
df = CSV.read(path, DataFrame; delim=';');

Model

using Turing

@model function m12_4(pulled_left, actor, condition, prosoc_left)
    # Total num of y
    N = length(pulled_left)

    # Separate σ priors for each actor
    σ_actor ~ truncated(Cauchy(0, 1), 0, Inf)

    # Number of unique actors in the data set
    N_actor = length(unique(actor)) #7

    # Vector of actors (1,..,7) which we'll set priors on
    α_actor ~ filldist(Normal(0, σ_actor), N_actor)

    # Prior for intercept, prosoc_left, and the interaction
    α ~ Normal(0, 10)
    βp ~ Normal(0, 10)
    βpC ~ Normal(0, 10)

    logitp = α .+ α_actor[actor] .+
            (βp .+ βpC * condition) .* prosoc_left

    pulled_left .~ BinomialLogit.(1, logitp)
end;

Output

chns = sample(
    m12_4(df.pulled_left, df.actor, df.condition, df.prosoc_left),
    NUTS(),
    1000
)

Chains MCMC chain (1000×23×1 Array{Float64, 3}):

Iterations        = 501:1:1500
Number of chains  = 1
Samples per chain = 1000
Wall duration     = 20.92 seconds
Compute duration  = 20.92 seconds
parameters        = σ_actor, α_actor[1], α_actor[2], α_actor[3], α_actor[4], α_actor[5], α_actor[6], α_actor[7], α, βp, βpC
internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size

Summary Statistics
  parameters      mean       std   naive_se      mcse        ess      rhat   ess_per_sec
      Symbol   Float64   Float64    Float64   Float64    Float64   Float64       Float64

     σ_actor    2.3051    0.9881     0.0312    0.0743   158.7163    1.0002        7.5861
  α_actor[1]   -1.2867    1.0601     0.0335    0.0965    92.5074    1.0069        4.4215
  α_actor[2]    4.1051    1.6267     0.0514    0.0756   379.9454    0.9999       18.1601
  α_actor[3]   -1.5682    1.0706     0.0339    0.0993    88.9685    1.0064        4.2524
  α_actor[4]   -1.5764    1.0534     0.0333    0.0977    92.9265    1.0050        4.4416
  α_actor[5]   -1.2777    1.0665     0.0337    0.0971    95.7129    1.0049        4.5748
  α_actor[6]   -0.3330    1.0581     0.0335    0.0966    92.7081    1.0058        4.4311
  α_actor[7]    1.2000    1.0951     0.0346    0.0998    93.1600    1.0074        4.4527
           α    0.5634    1.0382     0.0328    0.0967    89.5140    1.0068        4.2785
          βp    0.8177    0.2438     0.0077    0.0093   732.8422    1.0019       35.0274
         βpC   -0.1263    0.2853     0.0090    0.0101   792.4163    0.9998       37.8748

Quantiles
  parameters      2.5%     25.0%     50.0%     75.0%     97.5%
      Symbol   Float64   Float64   Float64   Float64   Float64

     σ_actor    1.1069    1.6692    2.0581    2.6542    4.8785
  α_actor[1]   -4.1357   -1.6900   -1.1658   -0.6658    0.5522
  α_actor[2]    1.5941    3.0604    3.7703    4.8946    8.1172
  α_actor[3]   -4.3841   -2.0164   -1.4599   -0.9437    0.1821
  α_actor[4]   -4.3581   -2.0031   -1.4407   -0.9603    0.1654
  α_actor[5]   -4.0121   -1.6895   -1.1536   -0.7022    0.5674
  α_actor[6]   -3.1881   -0.7475   -0.1801    0.2731    1.4832
  α_actor[7]   -1.4838    0.7121    1.3188    1.8460    3.0982
           α   -1.2412    0.0050    0.4453    0.9926    3.2768
          βp    0.3668    0.6379    0.8095    0.9873    1.2937
         βpC   -0.7055   -0.3144   -0.1180    0.0614    0.4223

using StatsPlots

StatsPlots.plot(chns)

"/home/runner/work/TuringModels.jl/TuringModels.jl/__site/assets/models/varying-intercepts-chimpanzees/code/output/chns.svg"

Original output

m124rethinking = "
             Mean StdDev lower 0.89 upper 0.89 n_eff Rhat
 a_actor[1]  -1.13   0.95      -2.62       0.27  2739    1
 a_actor[2]   4.17   1.66       1.80       6.39  3958    1
 a_actor[3]  -1.44   0.95      -2.90      -0.02  2720    1
 a_actor[4]  -1.44   0.94      -2.92      -0.04  2690    1
 a_actor[5]  -1.13   0.94      -2.58       0.31  2727    1
 a_actor[6]  -0.19   0.94      -1.64       1.25  2738    1
 a_actor[7]   1.34   0.97      -0.09       2.87  2889    1
 a            0.42   0.93      -1.00       1.81  2622    1
 bp           0.83   0.26       0.41       1.25  8594    1
 bpC         -0.13   0.30      -0.62       0.34  8403    1
 sigma_actor  2.26   0.94       1.07       3.46  4155    1
";