regression-models
Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations.
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- choxos/BiostatAgent
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- 10 janvier 2026 à 18:48
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SKILL.md
Instructions source · Aperçu en lecture seule- name
- regression-models
- description
- Bayesian regression models including linear, logistic, Poisson, negative binomial, and robust regression with Stan and JAGS implementations.
# Regression Models
## Linear Regression
### Stan
```stan
data {
int<lower=0> N;
int<lower=0> K;
matrix[N, K] X;
vector[N] y;
}
parameters {
real alpha;
vector[K] beta;
real<lower=0> sigma;
}
model {
alpha ~ normal(0, 10);
beta ~ normal(0, 5);
sigma ~ exponential(1);
y ~ normal(alpha + X * beta, sigma);
}
generated quantities {
array[N] real y_rep;
for (n in 1:N)
y_rep[n] = normal_rng(alpha + X[n] * beta, sigma);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dnorm(mu[i], tau)
mu[i] <- alpha + inprod(X[i,], beta[])
}
alpha ~ dnorm(0, 0.001)
for (k in 1:K) { beta[k] ~ dnorm(0, 0.001) }
tau ~ dgamma(0.001, 0.001)
sigma <- 1/sqrt(tau)
}
```
## Logistic Regression
### Stan
```stan
data {
int<lower=0> N;
int<lower=0> K;
matrix[N, K] X;
array[N] int<lower=0,upper=1> y;
}
parameters {
real alpha;
vector[K] beta;
}
model {
alpha ~ normal(0, 2.5);
beta ~ normal(0, 2.5);
y ~ bernoulli_logit(alpha + X * beta);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dbern(p[i])
logit(p[i]) <- alpha + inprod(X[i,], beta[])
}
alpha ~ dnorm(0, 0.4) # SD ≈ 1.58
for (k in 1:K) { beta[k] ~ dnorm(0, 0.4) }
}
```
## Poisson Regression
### Stan
```stan
model {
alpha ~ normal(0, 5);
beta ~ normal(0, 2.5);
y ~ poisson_log(alpha + X * beta);
}
```
### JAGS
```
model {
for (i in 1:N) {
y[i] ~ dpois(lambda[i])
log(lambda[i]) <- alpha + inprod(X[i,], beta[])
}
}
```
## Negative Binomial (Overdispersed Counts)
### Stan
```stan
parameters {
real alpha;
vector[K] beta;
real<lower=0> phi; // Overdispersion
}
model {
phi ~ exponential(1);
y ~ neg_binomial_2_log(alpha + X * beta, phi);
}
```
## Robust Regression (Student-t Errors)
### Stan
```stan
parameters {
real alpha;
vector[K] beta;
real<lower=0> sigma;
real<lower=1> nu; // Degrees of freedom
}
model {
nu ~ gamma(2, 0.1); // Prior on df
y ~ student_t(nu, alpha + X * beta, sigma);
}
```
## QR Decomposition (For Correlated Predictors)
```stan
transformed data {
matrix[N, K] Q = qr_thin_Q(X) * sqrt(N - 1.0);
matrix[K, K] R = qr_thin_R(X) / sqrt(N - 1.0);
matrix[K, K] R_inv = inverse(R);
}
parameters {
vector[K] theta;
real<lower=0> sigma;
}
model {
y ~ normal(Q * theta, sigma);
}
generated quantities {
vector[K] beta = R_inv * theta;
}
```
## Prior Recommendations
| Parameter | Weakly Informative | Reference |
|-----------|-------------------|-----------|
| Intercept | `normal(0, 10)` | Scale of outcome |
| Coefficients | `normal(0, 2.5)` | Gelman et al. |
| SD (sigma) | `exponential(1)` | Half-normal alternative |
| Logistic coef | `normal(0, 2.5)` | ~4 logit units = extreme |
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