Python 使用PYMC3的分层线性回归中的多层

我正在尝试使用PYMC3建立一个层次线性回归模型。在我的例子中，我想看看邮政编码是否为其他功能提供了有意义的结构。假设我使用以下模拟数据：

import pandas as pd
import numpy as np
import pymc3 as pm

data = pd.DataFrame({"postalcode": np.floor(np.random.uniform(low=10, high=99, size=1000)),
                 "x": np.random.normal(size=1000),
                 "y": np.random.normal(size=1000)})
data["postalcode"] = data["postalcode"].astype(int)

我生成10到99之间的邮政编码，以及正态分布的特征x和目标值y。现在，我为邮政编码级别1和级别2设置了索引：

def create_pc_index(level):
    pc = data["postalcode"].astype(str).str[0:level]
    unique_pc = pc.unique()
    pc_dict = dict(zip(unique_pc, range(0, len(unique_pc))))
    return pc_dict, pc.apply(lambda x: pc_dict[x]).values

pc1_dict, pc1_index = create_pc_index(1)
pc2_dict, pc2_index = create_pc_index(2) 

使用邮政编码的第一位数字作为分层属性可以很好地工作：

number_of_samples = 1000

x = data["x"]
y = data["y"]

with pm.Model() as model:
    sigma = pm.HalfCauchy('sigma', beta=10, testval=0.5, shape=1)
    mu_i = pm.Normal("mu_i", 5, sd=25, shape=1)
    intercept = pm.Normal('Intercept', mu_i, sd=1, shape=len(pc1_dict))

    mu_s = pm.Normal("mu_x", 0, sd=3, shape=1)
    x_coeffs = pm.Normal("x", mu_s, 1, shape=len(pc1_dict))

    mean = intercept[pc1_index] + x_coeffs[pc1_index] * x

    likelihood_mean = pm.Deterministic("mean", mean)
    likelihood = pm.Normal('y', mu=likelihood_mean, sd=sigma, observed=y)

    trace = pm.sample(number_of_samples)
    burned_trace = trace[number_of_samples/2:]

但是，如果我想在层次结构中添加第二层（在本例中，仅在截取上，暂时忽略x），我会遇到形状问题

with pm.Model() as model:
    sigma = pm.HalfCauchy('sigma', beta=10, testval=0.5, shape=1)
    mu_i_level_1 = pm.Normal("mu_i", 0, sd=25, shape=1)
    mu_i_level_2 = pm.Normal("mu_i_level_2", mu_i_level_1, sd=1, shape=len(pc1_dict))
    intercept = pm.Normal('Intercept', mu_i_level_2[pc1_index], sd=1, shape=len(pc2_dict))

    mu_s = pm.Normal("mu_x", 0, sd=3, shape=1)
    x_coeffs = pm.Normal("x", mu_s, 1, shape=len(pc1_dict))

    mean = intercept[pc2_index] + x_coeffs[pc1_index] * x

    likelihood_mean = pm.Deterministic("mean", mean)
    likelihood = pm.Normal('y', mu=likelihood_mean, sd=sigma, observed=y)

    trace = pm.sample(number_of_samples)
    burned_trace = trace[number_of_samples/2:]

错误消息是：

operands could not be broadcast together with shapes (89,) (1000,) 

如何在回归中正确建模多个级别？这只是形状尺寸正确的问题，还是我有更根本的错误

---

提前谢谢

我不认为截距的形状是

len（pc2\u dict）

而是

len（pc1\u dict）

。矛盾在于：

intercept = pm.Normal('Intercept', mu_i_level_2[pc1_index], sd=1, shape=len(pc2_dict))