regression-modelslisted

# 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 (Ov