使用bambi进行泊松回归的结果不正确？

Question

我给bambi（版本0.1.0）一个简单的泊松回归模型的尝试。然而，与直接pymc3或statsmodels实现相比，结果不同，我似乎无法弄清楚如何解释bambi给我的系数。测试代码如下。我是否指定了模型错误，还是应该不依赖于bambi的自动先验？

import numpy as np 
import scipy.stats 
import pandas 
import patsy 
import statsmodels 
import pymc3 
import bambi 

%matplotlib inline 

# generate data 
num_subjects = 4 
mu = [5, 8, 10, 11] 
num_samples = [43, 60, 56, 38] 

counts = [scipy.stats.poisson.rvs(m,size=n,random_state=m) for m,n in zip(mu,num_samples)] 
counts = np.concatenate(counts) 
subject = np.repeat(np.arange(num_subjects), num_samples) 

df = pandas.DataFrame(np.vstack([subject,counts]).T, columns=['subject','counts']) 

# sample means 
print(df.groupby('subject').mean()) 

# subject 0 = 5.0 
# subject 1 = 7.4 
# subject 2 = 9.5 
# subject 3 = 10.0 


# fit with bambi 
model_bambi = bambi.Model(df) 
result_bambi = model_bambi.fit('counts ~ C(subject)', categorical=['subject'], family='poisson', chains=2) 

print(result_bambi.summary(hpd=None, diagnostics=None)) 

# resulting posterior means: 
# Intercept  9.3310 -> ? 
# C(subject)[T.1] 3.8171 -> ? 
# C(subject)[T.2] 4.4419 -> ? 
# C(subject)[T.3] 3.8652 -> ? 


# fit directly with pymc3 
with pymc3.Model() as model_pymc3: 
    pymc3.glm.GLM.from_formula("counts ~ C(subject)", df, family=pymc3.glm.families.Poisson()) 
    trace = pymc3.sample(2000, njobs=2, tune=500) 

pymc3.plot_posterior(trace, varnames=[x for x in trace.varnames if x[:2]!='mu']); 

# resulting posterior means: 
# Intercept  1.6065 -> mu = 5.0 = exp(1.6065) 
# C(subject)[T.1] 0.3990 -> mu = 7.4 = exp(1.6065+0.3990) 
# C(subject)[T.2] 0.6477 -> mu = 9.5 = exp(1.6065+0.6477) 
# C(subject)[T.3] 0.6977 -> mu = 10.0 = exp(1.6065+0.6977) 


# fit with statsmodels 
my, mx = patsy.dmatrices("counts ~ C(subject)", df, NA_action='raise') 
model_sm = statsmodels.api.GLM(my, mx, family=statsmodels.api.families.Poisson()) 
result_sm = model_sm.fit() 

print(result_sm.summary()) 

# resulting posterior means: 
# Intercept  1.6094 -> mu = 5.0 = exp(1.6094) 
# C(subject)[T.1] 0.3965 -> mu = 7.4 = exp(1.6094+0.3965) 
# C(subject)[T.2] 0.6456 -> mu = 9.5 = exp(1.6094+0.6456) 
# C(subject)[T.3] 0.6958 -> mu = 10.0 = exp(1.6094+0.6958) 

Answer 1

我很抱歉，（非常）慢的回复;我没有订阅[bambi]标签（但现在是我），只是看到了这一点。这确实是一个错误（详细信息是here）。我只是为它开了一个PR，所以如果你从repo中克隆，问题应该解决（我会很好地发布一个新的PyPI版本）。我意识到这一点对你来说可能没有太大的用处，但是谢谢你的反对。如果您将来遇到类似问题，请在GitHub仓库中登录open an issue，因为这绝对属于bug区域。