使用bambi进行泊松回归得到不正确的结果？

Question

我正在尝试使用bambi (版本0.1.0)来建立一个简单的泊松回归模型。然而，与直接的pymc3或statsmodels实现相比，结果不同，我似乎不知道如何解释bambi给我的系数。测试代码如下。我是否指定了错误的模型，或者我不应该依赖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

我很抱歉回复太慢了；我没有订阅bambi标签(但现在我订阅了)，只是刚刚看到了这个。这确实是一个错误(详情见here)。我刚刚为它打开了一个PR，所以如果你从代码库克隆，这个问题应该就解决了(我会发布一个新的PyPI版本)。我知道这在这一点上可能对您没有多大用处，但还是要感谢您标记它。如果您在将来遇到任何类似的问题，请在GitHub代码库上使用open an issue，因为这肯定会落入错误领域。