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FullModel_HierPart_Winter_1FE_NoSummer.stan
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FullModel_HierPart_Winter_1FE_NoSummer.stan
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data {
// dimensions of data
int<lower=1> n_counties; // number of counties included in summer breeding region
int<lower=1> n_years; // number of years
int<lower=1> n_cyw; // n_counties * n_years * n_weeks
int<lower=1> n_surveys; // number of summer surveys
int<lower=1> n_colonies; // number of supercolonies
int<lower=1> n_obs; // number of supercolony-year combinations
// indices
int<lower=1,upper=n_years> year_id[n_cyw]; // year id (1:15)
int<lower=1,upper=n_cyw> cyw_id[n_surveys]; // id for county-year-week combination
int<lower=1,upper=n_colonies> colony_id[n_obs]; // supercolony id (1:13)
int<lower=1> index_present[140]; // index indicating when monarchs were present in supercolonies
// number of regression coefficients
int<lower=1> n_cov_alpha; // number of fixed effects in county-level model (summer)
int<lower=1> n_cov_beta; // number of fixed effects in survey level model (summer)
// covariate data
matrix[n_cyw,n_cov_alpha] X_county; // matrix of covariates for summer county-level model (all standardized)
vector[n_cyw] week_st; // week, in county-level model (standardized)
matrix[n_surveys,n_cov_beta] X_survey; // matrix of covariates for summer survey-level model (all standardized)
vector<lower=0>[n_surveys] effort; // party hours spent on each survey, scaled by the mean
vector[n_obs] X_winter; // vector of covariates for winter model (all standardized)
// response data
int<lower=0> y_count[n_surveys]; // monarch count on each survey
vector<lower=0>[n_obs] area; // area occupied by monarchs in each supercolony, each year
}
parameters {
// regression coefficients
vector[n_cov_alpha] alphaFE; // betas associated with fixed effects in county-level model
vector[n_years] alpha_week; // mean effect of week
vector[n_years] alpha_week2; // mean effect of week^2
vector[n_cov_beta] betaFE; // betas associated with fixed effects in survey-level model
real gammaFE; // betas associated with fixed effects in winter model (not including coef for summer index)
// intercepts
real alpha0; // intercept in county-level model (mean expected count on NABA survey, on log scale)
vector<lower=0,upper=1>[n_colonies] pocc_mn; // intercepts in winter, logistic model (mean probability monarchs present at each colony)
vector[n_colonies] gamma0; // intercepts in winter (different for each colony), gamma model (mean area occupied when monarchs present, on log scale)
// overdispersion parameter for negative binomial
real <lower=0> phi;
// shape parameter in Gamma distribution in winter model
real<lower=0> shape;
}
transformed parameters {
// expected count (on an average NABA survey with average effort) in each county, year, week
vector<lower=0>[n_cyw] mu_county;
// expected count on each survey (as a function of survey type, effort, local land use)
vector<lower=0>[n_surveys] lambda;
// probability that monarchs are present in supercolony each year
vector<lower=0,upper=1>[n_obs] pocc;
// mean area occupied in December, conditional on monarch presence
vector<lower=0>[n_obs] mu_win;
// rate parameter for Gamma model (winter)
vector<lower=0>[n_obs] rate;
// Summer: County-level model
for(i in 1:n_cyw)
mu_county[i] = exp(alpha0 + alpha_week[year_id[i]] * week_st[i]
+ alpha_week2[year_id[i]] * week_st[i] * week_st[i]
+ X_county[i] * alphaFE);
// Summer: Survey-level model
for(i in 1:n_surveys)
lambda[i] = exp(log(mu_county[cyw_id[i]]) + log(effort[i])
+ X_survey[i] * betaFE);
// Winter: Logistic part of hurdle model
for(i in 1:n_obs)
pocc[i] = pocc_mn[colony_id[i]];
for(i in 1:n_obs)
mu_win[i] = exp(gamma0[colony_id[i]] + X_winter[i] * gammaFE);
rate = shape ./ mu_win;
}
model {
// priors on intercepts and regression coefficients (implicit U(0,1) prior on pocc_mn)
target += normal_lpdf(alphaFE | 0, sqrt(1000));
target += normal_lpdf(betaFE | 0, sqrt(1000));
target += normal_lpdf(gammaFE | 0, sqrt(1000));
target += normal_lpdf(alpha0 | 0, sqrt(1000));
target += normal_lpdf(alpha_week | 0, sqrt(1000));
target += normal_lpdf(alpha_week2 | 0, sqrt(1000));
target += normal_lpdf(gamma0 | 0, sqrt(1000));
// prior for overdisperion parameter in neg-binom
target += uniform_lpdf(phi | 0, 20);
// prior for shape parameter in Gamma model (winter)
target += gamma_lpdf(shape | 2, 2);
// Modeling counts in summer (Negative binomial distribution)
target += neg_binomial_2_lpmf(y_count | lambda, phi);
// Modeling area occupied in winter (Gamma hurdle model)
for(i in 1:n_obs)
{
if (area[i] == 0)
target += log1m(pocc[i]);
else
target += log(pocc[i]) + gamma_lpdf(area[i] | shape, rate[i]);
}
}
generated quantities {
vector[n_surveys] log_lik_summer;
real sum_log_lik;
vector[n_obs] log_lik_winter;
real win_log_lik;
vector<lower=0>[n_surveys] y_pred;
vector<lower=0,upper=1>[n_surveys] y_pred_0;
real<lower=0,upper=1> y_pred_prop0;
vector<lower=0>[n_surveys] sccount_pred;
real<lower=0> sccount_pred_mn;
real<lower=0> sccount_pred_max;
real<lower=0> sccount_pred_sd;
vector<lower=0,upper=1>[n_obs] p_unocc;
vector<lower=0,upper=1>[n_obs] area_pred_0;
real<lower=0,upper=1> area_pred_prop0;
vector<lower=0>[n_obs] area_pred;
real<lower=0> area_pred_mn;
real<lower=0> area_pred_max;
real<lower=0> area_pred_sd;
// calculating log-likelihood for model comparisons
for(i in 1:n_surveys)
{
log_lik_summer[i] = neg_binomial_2_lpmf(y_count[i] | lambda[i], phi);
}
for(i in 1:n_obs)
{
if (area[i] == 0)
log_lik_winter[i] = log1m(pocc[i]);
else
log_lik_winter[i] = log(pocc[i]) + gamma_lpdf(area[i] | shape, rate[i]);
}
sum_log_lik = sum(log_lik_summer);
win_log_lik = sum(log_lik_winter);
// fit stats: generating new counts (summer model)
for(i in 1:n_surveys)
{
if(lambda[i]>150){
y_pred[i] = neg_binomial_2_rng(150, phi);
} else {
y_pred[i] = neg_binomial_2_rng(lambda[i], phi);
}
y_pred_0[i] = !(y_pred[i]);
}
y_pred_prop0 = sum(y_pred_0) / n_surveys;
sccount_pred = y_pred ./ effort;
sccount_pred_mn = mean(sccount_pred);
sccount_pred_max = max(sccount_pred);
sccount_pred_sd = sd(sccount_pred);
// fit stats: generating new areas occupied (winter model)
// only comparing areas for sites where monarchs were observed 2004-2018 (can't have dynamic vector length)
p_unocc = 1 - pocc;
for(i in 1:n_obs)
{
area_pred_0[i] = bernoulli_rng(p_unocc[i]);
area_pred[i] = gamma_rng(shape, rate[i]);
}
area_pred_prop0 = sum(area_pred_0) / n_obs;
area_pred_mn = mean(area_pred[index_present]);
area_pred_max = max(area_pred[index_present]);
area_pred_sd = sd(area_pred[index_present]);
}