Hierarchical Modeling with Aggregated Data

Hello!

I am attempting to build a hierarchical model in STAN. My hierarchy is national → businesses → states → locations. I have data at the location-day level and it seems impossible for my code to run (for a number of reasons I’m sure). I’m been playing around with the idea of aggregating my data up to the state level and weighting my regression based on the number of locations in those states. I want to be able to leverage the data on locations but also have code that runs quickly. Do we think there is a better way to accomplish what I’ve set out to do in the code below?

``````data {
int N_obs; // Number of observations
int nG; // Number of States
int nR; // Number of businesses
array[N_obs] int G; // State ID for each observation
array[N_obs] int R; // Business ID for each observation

int nX_direct; // Number of constrained predictors
int nX_unconstrained; // Number of unconstrained predictors
matrix[N_obs, nX_direct] x_con; // Constrained predictors matrix
matrix[N_obs, nX_unconstrained] x_uncon; // Unconstrained predictors matrix
array[N_obs] real y; // Dependent variable vector
vector[N_obs] weights; // Weights for each observation - number of locations in a state!
}

parameters {
array[nR] vector[nX_unconstrained] beta_r_uncon; // Unconstrained coefficients at business level
array[nG] vector<lower=0>[nX_direct] beta_r_con; // Constrained coefficients at business level
array[nG] vector[nX_unconstrained] beta_g_uncon; // Unconstrained coefficients at state level
array[nG] vector<lower=0>[nX_direct] beta_g_con; // Constrained coefficients at state level

vector<lower=0>[nX_direct] sigma_g_con; // SDs for state-specific constrained coefficients
vector<lower=0>[nX_unconstrained] sigma_g_uncon; // SDs for state-specific unconstrained coefficients

cholesky_factor_corr[nX_direct] L_r_con; // Cholesky factor of correlation matrix for business constrained coefficients
cholesky_factor_corr[nX_unconstrained] L_r_uncon; // Cholesky factor for business unconstrained coefficients

real<lower=0> sigma; // Population-level SD for sales
}

transformed parameters {
vector[N_obs] mu;

for (i in 1:N_obs) {
mu[i] = dot_product(x_con_[i], beta_g_con[G[i]]) + dot_product(x_uncon[i], beta_g_uncon[G[i]]);
}
}

model {
// Priors
for (r in 1:nR) {
beta_r_con[r] ~ normal(0, 1); // Retailer-level constrained predictors
beta_r_uncon[r] ~ normal(0, 1); // Retailer-level unconstrained predictors
}
L_r_con ~ lkj_corr_cholesky(2.0);
L_r_uncon ~ lkj_corr_cholesky(2.0);

sigma_g_con ~ exponential(1);
sigma_g_uncon ~ exponential(1);
sigma ~ exponential(1);

// stat-level effects conditional on retailer effects
for (g in 1:nG) {
beta_g_con[g] ~ multi_normal_cholesky(beta_r_con[R[g]], diag_pre_multiply(sigma_g_con, L_r_con));
beta_g_uncon[g] ~ normal(beta_r_uncon[R[g]], sigma_g_uncon); // Assuming independence across predictors for simplicity
}