N Parameters
The question is: What is the causal effect of postcards on voting in the 2026 election? Do those effects vary by political engagement? I have cleaned the data and also did an exploratory plot of civil engagement and voting. I then examined stability, representativeness and unconfoundedness. One problem is that voters in Michigan might not represent voters io Texas. I then made a brm model with the equation: voted ~ age_z + sex + treatment + voter_class + treatment * voter_class.
\[y_{i} = \beta_{0} + \beta_{1} age\_z + \beta_{2}male_i + \beta_{3}civic\_duty_i + \\ \beta_{4}hawthorne_i + \beta_{5}self_i + \beta_{6}neighbors_i + \\ \beta_{7}Sometimes\ vote_i + \beta_{8}Always\ vote_i + \\ \beta_{9}civic\_duty_i Sometimes\ vote_i + \beta_{10}hawthorne_i Sometimes\ vote_i + \\ \beta_{11}self_i Sometimes\ vote_i + \beta_{11}neighbors_i Sometimes\ vote_i + \\ \beta_{12}civic\_duty_i Always\ vote_i + \beta_{13}hawthorne_i Always\ vote_i + \\ \beta_{14}self_i Always\ vote_i + \beta_{15}neighbors_i Always\ vote_i + \epsilon_{i}\]
Family: gaussian
Links: mu = identity; sigma = identity
Formula: voted ~ age_z + sex + treatment + voter_class + treatment * voter_class
Data: ch10_data (Number of observations: 34408)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Regression Coefficients:
Estimate Est.Error l-95% CI
Intercept 0.15 0.01 0.13
age_z 0.03 0.00 0.03
sexMale 0.00 0.00 -0.01
treatmentCivicDuty -0.01 0.02 -0.05
treatmentHawthorne 0.01 0.02 -0.03
treatmentSelf 0.05 0.02 0.01
treatmentNeighbors 0.03 0.02 -0.01
voter_classSometimesVote 0.13 0.01 0.11
voter_classAlwaysVote 0.30 0.01 0.28
treatmentCivicDuty:voter_classSometimesVote 0.01 0.02 -0.04
treatmentHawthorne:voter_classSometimesVote 0.01 0.02 -0.04
treatmentSelf:voter_classSometimesVote 0.01 0.02 -0.04
treatmentNeighbors:voter_classSometimesVote 0.06 0.02 0.01
treatmentCivicDuty:voter_classAlwaysVote 0.02 0.03 -0.04
treatmentHawthorne:voter_classAlwaysVote 0.02 0.03 -0.03
treatmentSelf:voter_classAlwaysVote 0.01 0.03 -0.05
treatmentNeighbors:voter_classAlwaysVote 0.05 0.03 -0.00
u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.17 1.00 2294 2660
age_z 0.04 1.00 5580 3437
sexMale 0.01 1.00 5631 2634
treatmentCivicDuty 0.03 1.00 2253 2176
treatmentHawthorne 0.06 1.00 2290 2808
treatmentSelf 0.09 1.00 2141 2142
treatmentNeighbors 0.08 1.00 2336 2404
voter_classSometimesVote 0.15 1.00 2192 2768
voter_classAlwaysVote 0.32 1.00 2322 2723
treatmentCivicDuty:voter_classSometimesVote 0.06 1.00 2145 2357
treatmentHawthorne:voter_classSometimesVote 0.06 1.00 2303 2724
treatmentSelf:voter_classSometimesVote 0.05 1.00 2133 2486
treatmentNeighbors:voter_classSometimesVote 0.10 1.00 2427 2811
treatmentCivicDuty:voter_classAlwaysVote 0.07 1.00 2374 2617
treatmentHawthorne:voter_classAlwaysVote 0.07 1.00 2500 2700
treatmentSelf:voter_classAlwaysVote 0.06 1.00 2262 2771
treatmentNeighbors:voter_classAlwaysVote 0.10 1.00 2796 2718
Further Distributional Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.45 0.00 0.45 0.46 1.00 6566 2856
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).