From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida  

 

you are kindly asked to include the complete citation if you used this material in a publication

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Code 5.19 Logistic model in Python using Stan

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import numpy as np
import pystan
import statsmodels.api as sm

from scipy.stats import uniform, bernoulli

​

# Data
np.random.seed(13979)                                        # set seed to replicate example
nobs= 5000                                                           # number of obs in model 

x1 = bernoulli.rvs(0.6, size=nobs)
x2 = uniform.rvs(size=nobs) 

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beta0 = 2.0
beta1 = 0.75
beta2 = -5.

​

xb = beta0 + beta1 * x1 + beta2 * x2     
exb = 1.0/(1 + np.exp(-xb))                                 # logit link function

by = bernoulli.rvs(exb, size=nobs)

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mydata = {}
mydata['Y'] = by
mydata['N'] = nobs
mydata['X'] = sm.add_constant(np.column_stack((x1, x2)))
mydata['K'] = 3
mydata['logN'] = np.log(nobs)

# Fit
stan_code = """
data{
    int<lower=0> N;
    int<lower=0> K;
    int Y[N];
    matrix[N,K] X;
    real logN;
}
parameters{
    vector[K] beta;
}
transformed parameters{
    vector[N] eta;

    eta = X * beta;
}
model{

    Y ~ bernoulli_logit(eta);
}
generated quantities{
    real LLi[N];
    real AIC;
    real BIC;
    real LogL;
    vector[N] etanew;
    real<lower=0, upper=1.0> pnew[N];

    etanew = X * beta;

    for (i in 1:N){ 
        pnew[i] = inv_logit(etanew[i]);
        LLi[i] = bernoulli_lpmf(1|pnew[i]);
    }

    LogL = sum(LLi);
    AIC = -2 * LogL + 2 * K; 
    BIC = -2 * LogL + logN * K; 
}
"""

fit = pystan.stan(model_code=stan_code, data=mydata, iter=10000, chains=3,
                           warmup=5000, n_jobs=1)

​

# Output
lines = list(range(8)) + [2 * nobs + 8, 2 * nobs + 9, 2 * nobs + 10]

output = str(fit).split('\n')

for i in lines:
    print(output[i])   
 

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