Merge pull request #198 from andrjohns/feature/arm_ch8

Update ARM Ch.8 Models

Author: rok-cesnovar

ARM/Ch.8/grades.stan

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

ARM/Ch.8/roaches.stan

@@ -7,14 +7,13 @@ data {
   int y[N];
 }
 transformed data {
-  vector[N] log_expo;
-
-  log_expo = log(exposure2);
+  vector[N] log_expo = log(exposure2);
+  matrix[N,3] x = [roach1', treatment', senior']';
 }
 parameters {
-  vector[4] beta;
+  real alpha;
+  vector[3] beta;
 } 
 model {
-  y ~ poisson_log(log_expo + beta[1] + beta[2] * roach1 + beta[3] * treatment
-                  + beta[4] * senior);
+  y ~ poisson_log_glm(x, alpha + log_expo, beta);
 }

ARM/Ch.8/roaches_overdispersion.stan

@@ -7,25 +7,16 @@ data {
   int y[N];
 }
 transformed data {
-  vector[N] log_expo;
-
-  log_expo = log(exposure2);
+  vector[N] log_expo = log(exposure2);
+  matrix[N,3] x = [roach1', senior', treatment']';
 }
 parameters {
-  vector[4] beta;
-  vector[N] lambda;
-  real<lower=0> tau;
-} 
-transformed parameters {
+  real alpha;
+  vector[3] beta;
   real<lower=0> sigma;
-
-  sigma = 1.0 / sqrt(tau);
+  vector<multiplier=sigma>[N] lambda;
 }
 model {
-  tau ~ gamma(0.001, 0.001);
-  for (i in 1:N) {
-    lambda[i] ~ normal(0, sigma);
-    y[i] ~ poisson_log(lambda[i] + log_expo[i] + beta[1] + beta[2]*roach1[i] 
-                       + beta[3]*senior[i] + beta[4]*treatment[i]);
-  }
+  lambda ~ normal(0, sigma);
+  y ~ poisson_log_glm(x, alpha + lambda + log_expo, beta);
 }

ARM/Ch.8/unemployment.stan

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

ARM/Ch.8/y_x.stan

@@ -1,12 +1,13 @@
 data {
   int<lower=0> N; 
-  vector[N] x;
+  matrix[N,1] x;
   vector[N] y;
 }
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 } 
 model {
-  y ~ normal(beta[1] + beta[2] * x,sigma);
+  y ~ normal_id_glm(x, alpha, beta, sigma);
 }