test_gp.R

# simulate GP ideal and fit it

require(rstan)
require(dplyr)
require(ggplot2)
require(forcats)
# classic ARMA stan model:

num_person <- 25
num_bills <- 200
alpha_int <- rnorm(num_person)
sigma <- 0.1
adj_in <- runif(num_person,-.8,.8)

t <- 100

# simulate the GP

alpha_true <- runif(n = num_person,2,3)
rho_true <- runif(n=num_person,2.5,5.5)
sigma_true <- runif(n=num_person,0.5,3)

N_total = num_person
x_total <- 20 * (0:(t - 1)) / (t - 1) - 10

simu_data <- list(alpha=alpha_true, rho=rho_true, sigma=sigma_true,
                  N=N_total, x=x_total, T=t)

sim_gauss <- "data {
  int<lower=1> N;
  int<lower=1> T;
  real x[T];

  real<lower=0> rho[N];
  real<lower=0> alpha[N];
  real<lower=0> sigma[N];
}

transformed data {
  //create one covariance matrix for each legislator
  matrix[T, T] cov[N];
  matrix[T, T] L_cov[N];
   for(n in 1:N) {
        cov[n] =   cov_exp_quad(x, alpha[n], rho[n])
                     + diag_matrix(rep_vector(1e-10, T));
        L_cov[n] = cholesky_decompose(cov[n]);
    }

   
}

parameters {}
model {}

generated quantities {
  matrix[N,T] f;
  for(n in 1:N) {
     f[n,] = multi_normal_cholesky_rng(rep_vector(0, T), L_cov[n])';
  }  
}"

simu_fit <- stan(model_code = sim_gauss, data=simu_data, iter=1,
                 chains=1, seed=494838, algorithm="Fixed_param")

# more realistic

Y <- rstan::extract(simu_fit)$f[1,,]

require(tidyr)
require(stringr)

y_plot <- as_data_frame(Y) %>% mutate(person=1:n()) %>% 
  gather(key=time,value=estimate,-person) %>% 
  mutate(time=as.numeric(str_extract(time,'[0-9]+')))

y_plot %>% 
  ggplot(aes(y=estimate,x=time)) +
  geom_line(aes(group=person),alpha=0.5) +
  theme(panel.grid = element_blank(),
        panel.background = element_blank())

# plot data

#relevel to consrain

person_points <- rep(1:num_person,times=num_bills)
bill_points <- rep(1:num_bills,each=num_person)

restrict_high <- sort.int(alpha_int,index.return = T,decreasing = T)$ix[1]
restrict_low <- sort.int(alpha_int,index.return = T,decreasing = F)$ix[1]

# generate time points

time_points <- rep(1:t,each=num_bills/t)
time_points <- time_points[bill_points]

absence_discrim <- rnorm(num_bills)
absence_diff <- rnorm(num_bills)

reg_discrim <- rnorm(num_bills)
reg_diff <- rnorm(num_bills)

pr_absence <- sapply(1:length(person_points),function(n) {
  Y[person_points[n],time_points[n]]*absence_discrim[bill_points[n]] - absence_diff[bill_points[n]]
}) %>% plogis()

pr_vote <- sapply(1:length(person_points),function(n) {
  Y[person_points[n],time_points[n]]*reg_discrim[bill_points[n]] - reg_diff[bill_points[n]]
}) %>% plogis()

absent <- as.numeric(runif(length(person_points))<pr_absence)
present <- as.numeric(runif(length(person_points))<pr_vote)

#outcome <- ifelse(absent==0,present,3)
outcome <- as.numeric(runif(length(person_points))<pr_vote)

person_points <- factor(person_points)
person_points <- fct_relevel(person_points,as.character(restrict_high),
                             after=num_person)

# need to adjust for full gaussian process inference.
# only non-missing for now


# now fit a model to the observed series

stan_code <- '
data {
int N;
int L;
int B;
int T;
int ll[N];
int bb[N];
int tt[N];
int outcome[N];
real id_diff;
real id_diff_high;
} 
parameters {
vector[L-1] alpha_free;
vector<lower=-0.8,upper=0.8>[L-1] adj_in_free;
vector[L] Y_start;
vector[T-1] Y_var;
vector[B] discrim;
vector[B] diff;
real<lower=0> sigma;
vector[1] high;
vector<lower=-0.8,upper=0.8>[1] adj_high;
}
transformed parameters {
vector[L] alpha;
vector[L] adj_in;
vector[1] low;
vector[L] Y[T];

low = high - id_diff;

alpha=append_row(alpha_free,high);
adj_in=append_row(adj_in_free,adj_high);

for(t in 1:T) {
if(t==1) {
Y[1] = Y_start;
} else {
Y[t] = alpha + adj_in .* Y[t-1] + sigma*Y_var[t-1];
}
}

}
model {
diff ~ normal(0,3);
discrim ~ normal(0,3);
alpha_free ~ normal(0,1);
adj_in_free ~ normal(0,2);
adj_high ~ normal(0,1);
sigma ~ exponential(1/.1);
high ~ normal(id_diff_high,.01);
Y_var ~ normal(0,1);
Y_start ~ normal(0,1);

for(n in 1:N) {
outcome[n] ~ bernoulli_logit(discrim[bb[n]] * (Y[tt[n],ll[n]]) - diff[bb[n]]);
}

}
'

to_stan <- stan_model(model_code = stan_code)

run_ar1 <- sampling(to_stan,data=list(N=length(outcome),
                                      L=nrow(Y),
                                      B=num_bills,
                                      T=t,
                                      ll=as.numeric(person_points),
                                      bb=bill_points,
                                      tt=time_points,
                                      outcome=outcome,
                                      id_diff=sort.int(alpha_int,index.return = T,decreasing = T)$x[1] -
                                        sort.int(alpha_int,index.return = T,decreasing = F)$x[1],
                                      id_diff_high=sort.int(alpha_int,index.return = T,decreasing = T)$x[1]),
                    chains=4,cores=4)



print(run_ar1)

all_res <- summary(run_ar1)

alpha <- all_res$summary[grepl(x=row.names(all_res$summary),
                               pattern='alpha\\['),
                         'mean']

alpha <- alpha[c(1:(restrict_high-1),num_person,(restrict_high):(num_person-1))]
cor(alpha,alpha_int)
adj_in_est <- all_res$summary[grepl(x=row.names(all_res$summary),
                                    pattern='adj_in\\['),
                              'mean']
adj_in_est <- adj_in_est[c(1:(restrict_high-1),num_person,(restrict_high):(num_person-1))]
cor(adj_in_est,adj_in)
Y_est <- all_res$summary[grepl(x=row.names(all_res$summary),
                               pattern='Y\\['),
                         'mean']

cor(Y_est,c(Y[c(1:(restrict_high-1),num_person,(restrict_high):(num_person-1)),]))

# now try a random walk model

alpha_int <- -1.25
sigma <- 0.1
adj_in <- 1

t <- 20


Y <-  .gen_ts_data(t=t,
                   adj_in=adj_in,
                   alpha_int=alpha_int,
                   sigma=sigma,
                   init_sides=0)


to_stan <- stan_model(model_code = stan_code)

run_rw <- sampling(to_stan,data=list(N=length(Y$t_11),
                                     Y=Y$t_11))