-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathFullModel_HierPart_Winter_2FE_NoSummer.stan
192 lines (155 loc) · 7.11 KB
/
FullModel_HierPart_Winter_2FE_NoSummer.stan
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
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)
int<lower=1> n_cov_gamma; // number of fixed effects in winter (gamma) model MINUS 1 for summer index
// 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
matrix[n_obs,n_cov_gamma] X_winter; // matrix 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
vector[n_cov_gamma] 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]);
}