Updates ARM Ch10-Ch12 models

ARM/Ch.10/ideo_interactions.stan

@@ -5,14 +5,14 @@ data {
   vector[N] x;
 }
 transformed data {
-  vector[N] inter;
-
-  inter = party .* x;
+  vector[N] inter = party .* x;
+  matrix[N,3] cov = [party', x', inter']';
 }
 parameters {
-  vector[4] beta;
+  real alpha;
+  vector[3] beta;
   real<lower=0> sigma;
 } 
 model {
-  score1 ~ normal(beta[1] + beta[2] * party + beta[3] * x + beta[4] * inter,sigma);
+  score1 ~ normal_id_glm(cov, alpha, beta, sigma);
 }

ARM/Ch.10/ideo_reparam.stan

@@ -5,10 +5,14 @@ data {
   vector[N] z1; //z value for party 0, 0 otherwise 
   vector[N] z2; //z value for party 1, 0 otherwise 
 }
+transformed data {
+  matrix[N,3] x = [party', z1', z2']';
+}
 parameters {
-  vector[4] beta;
+  real alpha;
+  vector[3] beta;
   real<lower=0> sigma;
 } 
 model {
-  score1 ~ normal(beta[1] + beta[2] * party + beta[3] * z1 + beta[4] * z2,sigma);
+  score1 ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.10/ideo_two_pred.stan

@@ -4,10 +4,14 @@ data {
   vector[N] score1;
   vector[N] x;
 }
+transformed data {
+  matrix[N,2] cov = [party', x']';
+}
 parameters {
-  vector[3] beta;
+  real alpha;
+  vector[2] beta;
   real<lower=0> sigma;
 } 
 model {
-  score1 ~ normal(beta[1] + beta[2] * party + beta[3] * x,sigma);
+  score1 ~ normal_id_glm(cov, alpha, beta, sigma);
 }

ARM/Ch.10/sesame_multi_preds_3a.stan

@@ -10,20 +10,24 @@ transformed data {
   vector[N] site2; 
   vector[N] site3; 
   vector[N] site4; 
-  vector[N] site5; 
+  vector[N] site5;
+  matrix[N,7] x;
+
   for (i in 1:N) {
     site2[i] = site[i] == 2;
     site3[i] = site[i] == 3;
     site4[i] = site[i] == 4;
     site5[i] = site[i] == 5;
   }
+
+  x = [encouraged', pretest', site2', site3',
+       site4', site5', setting']';
 }
 parameters {
-  vector[8] beta;
+  real alpha;
+  vector[7] beta;
   real<lower=0> sigma;
 } 
 model {
-  watched ~ normal(beta[1] + beta[2] * encouraged + beta[3] * pretest 
-             + beta[4] * site2 + beta[5] * site3 + beta[6] * site4 
-             + beta[7] * site5 + beta[8] * setting,sigma);
+  watched ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.10/sesame_multi_preds_3b.stan

@@ -10,20 +10,24 @@ transformed data {
   vector[N] site2; 
   vector[N] site3; 
   vector[N] site4; 
-  vector[N] site5; 
+  vector[N] site5;
+  matrix[N,7] x;
+
   for (i in 1:N) {
     site2[i] = site[i] == 2;
     site3[i] = site[i] == 3;
     site4[i] = site[i] == 4;
     site5[i] = site[i] == 5;
   }
+
+  x = [watched_hat', pretest', site2', site3',
+       site4', site5', setting']';
 }
 parameters {
-  vector[8] beta;
+  real alpha;
+  vector[7] beta;
   real<lower=0> sigma;
 } 
 model {
-  y ~ normal(beta[1] + beta[2] * watched_hat + beta[3] * pretest 
-             + beta[4] * site2 + beta[5] * site3 + beta[6] * site4 
-             + beta[7] * site5 + beta[8] * setting,sigma);
+  y ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.10/sesame_one_pred_2b.stan

@@ -3,10 +3,14 @@ data {
   vector[N] watched_hat;
   vector[N] y;
 }
+transformed data {
+  matrix[N,1] x = [watched_hat']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 } 
 model {
-  y ~ normal(beta[1] + beta[2] * watched_hat,sigma);
+  y ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.10/sesame_one_pred_a.stan

@@ -3,10 +3,14 @@ data {
   vector[N] encouraged;
   vector[N] watched;
 }
+transformed data {
+  matrix[N,1] x = [encouraged']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 } 
 model {
-  watched ~ normal(beta[1] + beta[2] * encouraged,sigma);
+  watched ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.10/sesame_one_pred_b.stan

@@ -3,10 +3,14 @@ data {
   vector[N] encouraged;
   vector[N] y;
 }
+transformed data {
+  matrix[N,1] x = [encouraged']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 } 
 model {
-  y ~ normal(beta[1] + beta[2] * encouraged,sigma);
+  y ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.12/radon_complete_pool.stan

@@ -3,11 +3,15 @@ data {
   vector[N] x;
   vector[N] y;
 }
+transformed data {
+  matrix[N,1] cov = [x']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  y ~ normal(beta[1] + beta[2] * x, sigma);
+  y ~ normal_id_glm(cov, alpha, beta, sigma);
 }

ARM/Ch.12/radon_group.stan

@@ -6,27 +6,26 @@ data {
   vector[N] x;
   vector[N] y;
 }
+transformed data {
+  matrix[N,2] cov = [x', u']';
+}
 parameters {
-  vector[J] alpha;
-  vector[2] beta;
   real mu_alpha;
   real mu_beta;
   real<lower=0> sigma;
   real<lower=0> sigma_alpha;
   real<lower=0> sigma_beta;
+  vector<offset=mu_alpha, multiplier=sigma_alpha>[J] alpha;
+  vector<offset=mu_beta, multiplier=sigma_beta>[2] beta;
 }
 model {
-  vector[N] y_hat;
-  for (i in 1:N)
-    y_hat[i] = alpha[county[i]] + x[i] * beta[1] + u[i] * beta[2];
-
   alpha ~ normal(mu_alpha, sigma_alpha);
   beta ~ normal(mu_beta, sigma_beta);
   sigma ~ cauchy(0, 2.5);
-  mu_alpha ~ normal(0, 1);
+  mu_alpha ~ std_normal();
   sigma_alpha ~ cauchy(0, 2.5);
-  mu_beta ~ normal(0, 1);
+  mu_beta ~ std_normal();
   sigma_beta ~ cauchy(0, 2.5);
 
-  y ~ normal(y_hat, sigma);
+  y ~ normal_id_glm(cov, alpha[county], beta, sigma);
 }

ARM/Ch.12/radon_group_chr.stan

@@ -6,28 +6,22 @@ data {
   vector[N] x;
   vector[N] y;
 }
+transformed data {
+  matrix[N,2] cov = [x', u']';
+}
 parameters {
   vector[2] beta;
-  vector[J] eta;
-  real mu_b;
+  real mu_a;
   real<lower=0> sigma;
-  real<lower=0> sigma_b;
-}
-transformed parameters {
-  vector[J] b;
-  vector[N] y_hat;
-
-  b = mu_b + sigma_b * eta;
-
-  for (i in 1:N)
-    y_hat[i] = b[county[i]] + x[i] * beta[1] + u[i] * beta[2];
+  real<lower=0> sigma_a;
+  vector<offset=mu_a, multiplier=sigma_a>[J] alpha;
 }
 model {
-  mu_b ~ normal(0, 1);
-  eta ~ normal(0, 1);
+  mu_a ~ std_normal();
   beta ~ normal(0, 100);
   sigma ~ cauchy(0, 2.5);
-  sigma_b ~ cauchy(0, 2.5);
+  sigma_a ~ cauchy(0, 2.5);
+  alpha ~ normal(mu_a, sigma_a);
 
-  y ~ normal(y_hat, sigma);
+  y ~ normal_id_glm(cov, alpha[county], beta, sigma);
 }

ARM/Ch.12/radon_intercept.stan

@@ -5,20 +5,16 @@ data {
   vector[N] y;
 }
 parameters {
-  vector[J] a; # county intercepts
   real mu_a;
   real<lower=0> sigma_a;
   real<lower=0> sigma_y;
+  vector<offset=mu_a, multiplier=sigma_a>[J] a; # county intercepts
 }
 model {
-  vector[N] y_hat;
-  for (i in 1:N)
-    y_hat[i] = a[county[i]];
-
-  mu_a ~ normal(0, 1);
+  mu_a ~ std_normal();
   sigma_a ~ cauchy(0, 2.5);
   sigma_y ~ cauchy(0, 2.5);
-  a ~ normal (mu_a, sigma_a);
-  y ~ normal(y_hat, sigma_y);
+  a ~ normal(mu_a, sigma_a);
+  y ~ normal(a[county], sigma_y);
 }
 

ARM/Ch.12/radon_intercept_chr.stan

@@ -5,25 +5,17 @@ data {
   vector[N] y;
 }
 parameters {
-  vector[J] eta;
   real mu_a;
   real<lower=0> sigma_a;
   real<lower=0> sigma_y;
+  vector<offset=(10 * mu_a), multiplier=sigma_a>[J] alpha;
 }
-transformed parameters {
-  vector[J] a;
-  vector[N] y_hat;
 
-  a = 10 * mu_a + sigma_a * eta;
-
-  for (i in 1:N)
-    y_hat[i] = a[county[i]];
-}
 model {
-  mu_a ~ normal(0, 1);
-  eta ~ normal(0, 1);
+  mu_a ~ std_normal();
+  alpha ~ normal(10 * mu_a, sigma_a);
   sigma_a ~ cauchy(0, 2.5);
   sigma_y ~ cauchy(0, 2.5);
 
-  y ~ normal(y_hat, sigma_y);
+  y ~ normal(alpha[county], sigma_y);
 }

ARM/Ch.12/radon_no_pool.stan

@@ -5,23 +5,22 @@ data {
   vector[N] x;
   vector[N] y;
 }
+transformed data {
+  matrix[N,1] cov = [x']';
+}
 parameters {
-  vector[J] a;
-  real beta;
+  vector[1] beta;
   real<lower=0> sigma_a;
   real<lower=0> sigma_y;
   real mu_a;
+  vector<offset=mu_a, multiplier=sigma_a>[J] a;
 }
 model {
-  vector[N] y_hat;
-  for (i in 1:N)
-    y_hat[i] = beta * x[i] + a[county[i]];
-
-  beta ~ normal(0, 1);
-  mu_a ~ normal(0, 1);
+  beta ~ std_normal();
+  mu_a ~ std_normal();
   sigma_a ~ cauchy(0, 2.5);
   sigma_y ~ cauchy(0, 2.5);
 
   a ~ normal(mu_a, sigma_a);
-  y ~ normal(y_hat, sigma_y);
+  y ~ normal_id_glm(cov, a[county], beta, sigma_y);
 }

ARM/Ch.12/radon_no_pool_chr.stan

@@ -5,28 +5,22 @@ data {
   vector[N] x;
   vector[N] y;
 }
+transformed data {
+  matrix[N,1] cov = [x']';
+}
 parameters {
-  real beta;
-  vector[J] eta;
+  vector[1] beta;
   real mu_a;
   real<lower=0> sigma_a;
   real<lower=0> sigma_y;
-}
-transformed parameters {
-  vector[J] a;
-  vector[N] y_hat;
-
-  a = mu_a + sigma_a * eta;
-
-  for (i in 1:N)
-    y_hat[i] = beta * x[i] + a[county[i]];
+  vector<offset=mu_a, multiplier=sigma_a>[J] alpha;
 }
 model {
-  beta ~ normal(0, 1);
-  mu_a ~ normal(0, 1);
-  eta ~ normal(0, 1);
+  beta ~ std_normal();
+  mu_a ~ std_normal();
+  alpha ~ normal(mu_a, sigma_a);
   sigma_a ~ cauchy(0, 2.5);
   sigma_y ~ cauchy(0, 2.5);
 
-  y ~ normal(y_hat, sigma_y);
+  y ~ normal_id_glm(cov, alpha[county], beta, sigma_y);
 }