PythonでGLMを当てはめるには？

Pythonで学ぶ一般化線形モデル

Ita Cirovic Donev

Data Science Consultant

statsmodels

statsmodelsのインポート
```
import statsmodels.api as sm
```
フォーミュラの利用
```
import statsmodels.formula.api as smf
```

glm() を直接使用

from statsmodels.formula.api import glm

モデル当てはめの流れ

モデルを記述 $\rightarrow \texttt{\color{#007AFF}{glm()}}$
モデルを当てはめ $\rightarrow \texttt{\color{#007AFF}{.fit()}}$
モデルを要約 $\rightarrow \texttt{\color{#007AFF}{.summary()}}$
予測を作成 $\rightarrow \texttt{\color{#007AFF}{.predict()}}$

モデルの記述

フォーミュラ方式

from statsmodels.formula.api import glm

model = glm(formula, data, family)

配列方式

import statsmodels.api as sm

X = sm.add_constant(X)
model = sm.glm(y, X, family)

Formula引数

$$\texttt{\color{#00A388}{response}} \sim \texttt{\color{#FF6138}{explanatory variable(s)}}$$ $$\texttt{\color{#00A388}{output}} \sim \texttt{\color{#FF6138}{input(s)}}$$

formula = 'y ~ x1 + x2'

$\texttt{\color{#FF6138}{C(x1)}}$ : x1をカテゴリ変数として扱う
$\texttt{\color{#FF6138}{-1}}$ : 切片を除く
$\texttt{\color{#FF6138}{x1:x2}}$ : x1とx2の交互作用のみ
$\texttt{\color{#FF6138}{x1*x2}}$ : 交互作用＋各主効果
$\texttt{\color{#FF6138}{np.log(x1)}}$ : ベクトル化関数を適用

Family引数

family = sm.families.____()

family関数:

$\texttt{\color{#007AFF}{Gaussian}(link = sm.families.links.\color{deeppink}{identity()})}$ $\rightarrow$ 既定のfamily
$\texttt{\color{#007AFF}{Binomial}(link = sm.families.links.\color{deeppink}{logit()})}$
- $\texttt{\color{deeppink}{probit()}}$, $\texttt{\color{deeppink}{cauchy()}}$, $\texttt{\color{deeppink}{log()}}$, $\texttt{\color{deeppink}{cloglog()}}$
$\texttt{\color{#007AFF}{Poisson}(link = sm.families.links.\color{deeppink}{log()})}$
- $\texttt{\color{deeppink}{identity()}}$, $\texttt{\color{deeppink}{sqrt()}}$

他の分布familyはstatsmodelsのサイトを参照。

モデルの要約

print(model_GLM.summary())

                 Generalized Linear Model Regression Results                  
=============================================================================
Dep. Variable:                      y  No. Observations:                  173
Model:                            GLM  Df Residuals:                      171
Model Family:                Binomial  Df Model:                            1
Link Function:                  logit  Scale:                          1.0000
Method:                          IRLS  Log-Likelihood:                -97.226
Date:                Mon, 21 Jan 2019  Deviance:                       194.45
Time:                        11:30:01  Pearson chi2:                     165.
No. Iterations:                     4  Covariance Type:             nonrobust
=============================================================================
                 coef    std err         z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------
Intercept    -12.3508      2.629    -4.698      0.000     -17.503      -7.199
width          0.4972      0.102     4.887      0.000       0.298       0.697
=============================================================================

回帰係数

$\texttt{\color{#007AFF}{.params}}$ は回帰係数を表示

model_GLM.params

Intercept   -12.350818
width         0.497231
dtype: float64

$\texttt{\color{#007AFF}{.conf\_int(alpha=0.05, cols=None)}}$ は信頼区間を表示

model_GLM.conf_int()

                   0         1
Intercept -17.503010 -7.198625
width       0.297833  0.696629

予測

予測用データに全ての変数を含める
$\texttt{\color{#007AFF}{.predict(\color{#FF931B}{test\_data})}}$ で予測を計算

model_GLM.predict(test_data)

0    0.029309
1    0.470299
2    0.834983
3    0.972363
4    0.987941

Let's practice!

Pythonで学ぶ一般化線形モデル