使用bambi進行泊松迴歸的結果不正確？

Question

我給bambi（版本0.1.0）一個簡單的泊松迴歸模型的嘗試。然而，與直接pymc3或statsmodels實現相比，結果不同，我似乎無法弄清楚如何解釋bambi給我的係數。測試代碼如下。我是否指定了模型錯誤，還是應該不依賴於bambi的自動先驗？

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）慢的回覆;我沒有訂閱[bambi]標籤（但現在是我），只是看到了這一點。這確實是一個錯誤（詳細信息是here）。我只是爲它開了一個PR，所以如果你從repo中克隆，問題應該解決（我會很好地發佈一個新的PyPI版本）。我意識到這一點對你來說可能沒有太大的用處，但是謝謝你的反對。如果您將來遇到類似問題，請在GitHub倉庫中登錄open an issue，因爲這絕對屬於bug區域。