added 17.3-17.6 preliminary models

Author: PeterLi2016

ARM/Ch.17/17.3_flight_simulator.stan

@@ -0,0 +1,31 @@
+data {
+  int<lower=0> N;
+  int<lower=0> n_treatment;
+  int<lower=0> n_airport;
+  int<lower=0,upper=n_treatment> treatment[N];
+  int<lower=0,upper=n_airport> airport[N];
+}
+parameters {
+  real<lower=0> sigma;
+  real<lower=0> sigma_gamma;
+  real<lower=0> sigma_delta;
+  vector[n_treatment] gamma;
+  vector[n_airport] delta;
+}
+model {
+  vector[N] y_hat;
+
+  sigma ~ uniform(0, 100);
+  sigma_gamma ~ uniform(0, 100);
+  sigma_delta ~ uniform(0, 100);
+
+  mu ~ normal(0, 100);
+  
+  gamma ~ normal(0, sigma_gamma);
+  delta ~ normal(0, sigma_delta);
+
+  for (i in 1:N)
+    y_hat[i] <- mu + gamma[treatment[i]] + delta[airport[i]];
+
+  y ~ normal(y_hat, sigma);
+}

ARM/Ch.17/17.4_multilevel_logistic.stan

@@ -0,0 +1,67 @@
+data {
+  int<lower=0> N;
+  int<lower=0> n_age;
+  int<lower=0> n_edu;
+  int<lower=0> n_region;
+  int<lower=0> n_state;
+
+  int<lower=0, upper=1> female[N];
+  int<lower=0, upper=1> black[N];
+  int<lower=0, upper=n_age> age[N];
+  int<lower=0, upper=n_edu> edu[N];
+  int<lower=0, upper=n_state> region[N];
+  int<lower=0, upper=n_state> state[N];
+}
+parameters {
+  real<lower=0> sigma;
+  real<lower=0> sigma_age;
+  real<lower=0> sigma_edu;
+  real<lower=0> sigma_state;
+  real<lower=0> sigma_region;
+  real<lower=0> sigma_age_edu;
+
+  real b_0;
+  real b_female;
+  real b_black;
+  real b_female_black;
+
+  real b_v_prev;
+
+  vector[n_age] b_age;
+  vector[n_edu] b_edu;
+  vector[n_region] b_region;
+  matrix[n_age,n_edu] b_age_edu;
+
+  vector[n_state] b_hat;
+}
+model {
+  vector[N] p;
+  vector[n_state] b_state_hat;
+
+  b_0 ~ normal(0, 100);
+  b_female ~ normal(0, 100);
+  b_black ~ normal(0, 100);
+  b_female_black ~ normal(0, 100);
+
+  b_age ~ normal(0, sigma_age);
+  b_edu ~ normal(0, sigma_edu);
+  b_region ~ normal(0, sigma_region);
+
+  for (j in 1:n_age)
+    b_age_edu[j,] ~ normal(0, sigma_age_edu);
+
+  b_v_prev ~ normal(0, 100);
+
+  for (j in 1:n_state)
+    b_state_hat[j] <- b_region[region[j]] + b_v_prev * v_prev[j];
+
+  b_hat ~ normal(b_state_hat, sigma_state);
+
+  for (i in 1:N)
+    p[i] <- max(0, min(1, inv_logit(b_0 + b_female*female[i] 
+      + b_black*black[i] + b_female_black*female[i]*black[i] +
+      b_age[age[i]] + b_edu[edu[i]] + b_age_edu[age[i],edu[i]] +
+      b_state[state[i]])));
+
+  y ~ binomial(1, p);
+}

ARM/Ch.17/17.5_multilevel_poisson.stan

@@ -0,0 +1,42 @@
+data {
+  int<lower=0> N;
+  int<lower=0> n_eth;
+  int<lower=0> n_precint;
+
+  int<lower=0, upper=n_precint> precint[N];
+  int<lower=0, upper=n_eth> eth[N];
+  vector offeset[N];
+  vector stops[N];
+}
+parameters {
+  real mu;
+  real<lower=0> sigma_epsilon;
+  real<lower=0> sigma_eth;
+  real<lower=0> sigma_precint;
+
+  vector[n_eth] b_eth;
+  vector[n_precint] b_precint;
+  vector[N] epsilon;
+}
+model {
+  real mu_adj;
+  vector[n_eth] b_eth_adj;
+  vector[n_precint] b_precint_adj;
+
+  mu ~ normal(0, 100);
+  mu_adj <- mu + mean(b_eth) + mean(b_precint);
+
+  b_eth ~ normal(0, sigma_eth);
+  b_eth_adj <- b_eth - mean(b_eth);
+
+  b_precint ~ normal(0, sigma_precint);
+  b_precint_adj <- b_precint - mean(b_precint);
+
+  epsilon ~ normal(0, sigma_epsilon);
+
+  for (i in 1:N)
+    lambda[i] <- offeset[i] + mu + b_eth[eth[i]] + b_precint[precint[i]]
+      + epsilon[i];
+
+  stops ~ poisson_log(lambda);
+}

ARM/Ch.17/17.6_multilevel_ordered_categorical.stan

@@ -0,0 +1,46 @@
+data {
+  int<lower=0> N;
+  int<lower=0> n_cut;
+  int<lower=0> n_player;
+
+  int<lower=0, upper=n_player> player[N];
+  vector y[N];
+}
+parameters {
+  vector[n_cut] mu_c;
+  real mu_log_s;
+
+  vector<lower=0>[n_cut] sigma_c;
+  real<lower=0> sigma_log_s;
+
+  matrix[n_player,2] C;
+  vector[n_player] s;
+}
+model {
+  real mu_adj;
+  matrix[N,n_cut] Q;
+  matrix[N,n_cut] P;
+
+  mu_c ~ normal(0, 1000);
+  mu_log_s ~ normal(0, 100);
+
+  for (i in 1:n_player) {
+    C[i,1] ~ normal(mu_c[1], sigma_c[1]) T[0,C[i,2]];
+    C[i,2] ~ normal(mu_c[2], sigma_c[1]) T[C[i,1],100];
+    s[i] ~ lognormal(mu_log_s, sigma_log_s) T[1,100];
+  }
+
+  for (i in 1:N) {
+    for (i_cut in 1:n_cut)
+      Q[i,i_cut] <- inv_logit((x[i] - C[player[i],i_cut])/s[player[i]]);
+
+    P[i,1] <- 1 - Q[i,1];
+    P[i,n_cut+1] <- Q[i,n_cut];
+    for (i_cut in 2:n_cut)
+      P[i,i_cut] <- Q[i,i_cut-1] - Q[i,i_cut];
+  }
+
+  for (i in 1:N)
+    y[i] ~ categorical(P[i,]);
+
+}