Merge pull request #193 from andrjohns/feature/arm_ch3

ARM Ch.3 Models Update

Author: rok-cesnovar

ARM/Ch.3/kidiq_interaction.stan

@@ -2,17 +2,18 @@ data {
   int<lower=0> N;
   vector<lower=0, upper=200>[N] kid_score;
   vector<lower=0, upper=200>[N] mom_iq;
-  vector<lower=0, upper=1>[N] mom_hs;}
+  vector<lower=0, upper=1>[N] mom_hs;
+}
 transformed data {           // interaction
-  vector[N] inter;
-  inter = mom_hs .* mom_iq;
+  vector[N] inter = mom_hs .* mom_iq;
+  matrix[N, 3] x = [mom_hs', mom_iq', inter']';
 }
 parameters {
-  vector[4] beta;
+  real alpha;
+  vector[3] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  kid_score ~ normal(beta[1] + beta[2] * mom_hs + beta[3] * mom_iq
-                     + beta[4] * inter, sigma);
+  kid_score ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.3/kidiq_multi_preds.stan

@@ -4,11 +4,15 @@ data {
   vector<lower=0, upper=200>[N] mom_iq;
   vector<lower=0, upper=1>[N] mom_hs;
 }
+transformed data {
+  matrix[N, 2] x = [mom_hs', mom_iq']';
+}
 parameters {
-  vector[3] beta;
+  real alpha;
+  vector[2] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  kid_score ~ normal(beta[1] + beta[2] * mom_hs + beta[3] * mom_iq, sigma);
+  kid_score ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.3/kidiq_prediction.stan

@@ -6,16 +6,19 @@ data {
   real<lower=0, upper=1> mom_hs_new;           // for prediction
   real<lower=0, upper=200> mom_iq_new;
 }
+transformed data {
+  matrix[N, 2] x = [mom_hs', mom_iq']';
+  row_vector[2] x_new = [mom_hs_new, mom_iq_new];
+}
 parameters {
-  vector[3] beta;
+  real alpha;
+  vector[2] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  kid_score ~ normal(beta[1] + beta[2] * mom_hs + beta[3] * mom_iq, sigma);
+  kid_score ~ normal_id_glm(x, alpha, beta, sigma);
 }
 generated quantities {       // prediction
-  real kid_score_pred;
-  kid_score_pred = normal_rng(beta[1] + beta[2] * mom_hs_new
-                               + beta[3] * mom_iq_new, sigma);
+  real kid_score_pred = normal_rng(alpha + x_new * beta, sigma);
 }

ARM/Ch.3/kidiq_validation.stan

@@ -4,11 +4,15 @@ data {
   vector<lower=0, upper=1>[N] hs;
   vector<lower=0, upper=200>[N] afqt;
 }
+transformed data {
+  matrix[N,2] x = [hs', afqt']';
+}
 parameters {
-  vector[3] beta;
+  real alpha;
+  vector[2] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  ppvt ~ normal(beta[1] + beta[2] * hs + beta[3] * afqt, sigma);
+  ppvt ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.3/kidscore_momhs.stan

@@ -3,11 +3,15 @@ data {
   vector<lower=0, upper=200>[N] kid_score;
   vector<lower=0, upper=1>[N] mom_hs;
 }
+transformed data {
+  matrix[N,1] x = [mom_hs']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  kid_score ~ normal(beta[1] + beta[2] * mom_hs, sigma);
+  kid_score ~ normal_id_glm(x, alpha, beta, sigma);
 }

ARM/Ch.3/kidscore_momiq.stan

@@ -3,11 +3,15 @@ data {
   vector<lower=0, upper=200>[N] kid_score;
   vector<lower=0, upper=200>[N] mom_iq;
 }
+transformed data {
+  matrix[N,1] x = [mom_iq']';
+}
 parameters {
-  vector[2] beta;
+  real alpha;
+  vector[1] beta;
   real<lower=0> sigma;
 }
 model {
   sigma ~ cauchy(0, 2.5);
-  kid_score ~ normal(beta[1] + beta[2] * mom_iq, sigma);
+  kid_score ~ normal_id_glm(x, alpha, beta, sigma);
 }