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mitzimorrismitzimorris
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9 files changed

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‎jupyter/radon/img/multilevel_models_fig_11_1.png‎

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‎jupyter/radon/radon.ipynb‎

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‎jupyter/radon/stan/normal_glm.stan‎

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/* normal linear regression model */
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data {
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int<lower=0> N; // number of observations
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int<lower=1> M; // number of predictors
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matrix[N, M] xs;
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vector[N] y;
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}
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parameters {
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real alpha;
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vector beta[M];
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real<lower=0> sigma;
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}
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model {
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y ~ normal_glm_id(xs, alpha, beta, sigma);
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sigma ~ normal(0, 10); // override default uniform(-inf, +inf)
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}

jupyter/radon/stan/radon_complete_pool.stan renamed to jupyter/radon/stan/radon_cp.stan

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real<lower=0> sigma;
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}
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model {
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sigma ~ normal(0, 5);
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y ~ normal(alpha + beta * x, sigma);
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alpha ~ normal(0, 10);
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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}
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generated quantities {
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array[N] real y_rep = normal_rng(alpha + beta * x, sigma);
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}
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jupyter/radon/stan/radon_no_pool.stan renamed to jupyter/radon/stan/radon_np.stan

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int<lower=1> N; // observations
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int<lower=1> J; // counties
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array[N] int<lower=1, upper=J> county;
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vector[N] x;
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vector[N] y;
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vector[N] x; // floor
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vector[N] y; // radon
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}
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parameters {
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real beta;
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vector[J] alpha;
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real beta;
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real<lower=0> sigma;
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}
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model {
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sigma ~ normal(0, 5);
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y ~ normal(alpha[county] + beta * x, sigma);
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alpha ~ normal(0, 10);
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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}
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generated quantities {
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array[N] real y_rep = normal_rng(alpha[county] + beta * x, sigma);
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}

‎jupyter/radon/stan/radon_np_uranium.stan‎

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data {
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int<lower=1> N; // observations
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int<lower=1> J; // counties
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array[N] int<lower=1, upper=J> county;
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vector[N] y; // radon
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vector[N] x; // floor
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vector[N] u; // uranium
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}
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parameters {
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vector[J] alpha;
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vector[2] beta;
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real<lower=0> sigma;
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}
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model {
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y ~ normal(alpha[county] + beta[1] * x + beta[2] * u, sigma);
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alpha ~ normal(0, 10);
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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}
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generated quantities {
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array[N] real y_rep = normal_rng(alpha[county] + beta[1] * x + beta[2] * u, sigma);
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}

‎jupyter/radon/stan/radon_np_uranium_glm_id_normal.stan‎

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data {
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int<lower=1> N; // observations
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int<lower=1> J; // counties
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array[N] int<lower=1, upper=J> county;
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vector[N] y; // radon
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vector[N] x; // floor
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vector[N] u; // uranium
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}
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transformed data {
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matrix[N, 2] xs = [x', u']';
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}
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parameters {
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vector[J] alpha;
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vector[2] beta;
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real<lower=0> sigma;
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}
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transformed parameters {
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vector[N] alphas = alpha[county];
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}
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model {
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y ~ normal_id_glm(xs, alphas, beta, sigma);
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alpha ~ normal(0, 10);
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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}

‎jupyter/radon/stan/radon_pp_alpha.stan‎

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data {
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int<lower=1> N; // observations
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int<lower=1> J; // counties
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array[N] int<lower=1, upper=J> county;
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vector[N] x;
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vector[N] y;
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}
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parameters {
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real mu_alpha;
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real<lower=0> sigma_alpha;
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vector<offset=mu_alpha, multiplier=sigma_alpha>[J] alpha; // non-centered parameterization
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real beta;
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real<lower=0> sigma;
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}
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model {
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y ~ normal(alpha[county] + beta * x, sigma);
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alpha ~ normal(mu_alpha, sigma_alpha); // partial-pooling
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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mu_alpha ~ normal(0, 10);
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sigma_alpha ~ normal(0, 10);
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}
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generated quantities {
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array[N] real y_rep = normal_rng(alpha[county] + beta * x, sigma);
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}

‎jupyter/radon/stan/radon_pp_uranium.stan‎

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data {
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int<lower=1> N; // observations
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int<lower=1> J; // counties
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array[N] int<lower=1, upper=J> county;
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vector[N] y; // radon
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vector[N] x; // floor
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vector[N] u; // uranium
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}
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transformed data {
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matrix[N, 2] xs = [x', u']';
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}
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parameters {
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real mu_alpha;
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real<lower=0> sigma_alpha;
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vector<offset=mu_alpha, multiplier=sigma_alpha>[J] alpha; // non-centered parameterization
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vector[2] beta;
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real<lower=0> sigma;
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}
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transformed parameters {
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vector[N] alphas = alpha[county];
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}
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model {
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y ~ normal_id_glm(xs, alphas, beta, sigma);
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alpha ~ normal(mu_alpha, sigma_alpha); // partial-pooling
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beta ~ normal(0, 10);
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sigma ~ normal(0, 10);
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mu_alpha ~ normal(0, 10);
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sigma_alpha ~ normal(0, 10);
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}
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generated quantities {
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array[N] real y_rep = normal_rng(alpha[county] + beta * xs, sigma);
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}

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