In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.font_manager as fm
import statsmodels.api as sm
import statsmodels.formula.api as smf

data = pd.read_csv('~/Downloads/midoribon/data3a.csv')
fp = fm.FontProperties(fname='/Library/Fonts/Yu Gothic Medium.otf', size=12)

/Users/yusuke-nishioka/.anyenv/envs/pyenv/versions/3.6.1/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
  from pandas.core import datetools

説明変数なし¶

In [2]:

result = smf.glm(formula='y ~ 1', data=data, family=sm.families.Poisson()).fit()
result.summary()

Out[2]:

Generalized Linear Model Regression Results
Dep. Variable:	y	No. Observations:	100
Model:	GLM	Df Residuals:	99
Model Family:	Poisson	Df Model:	0
Link Function:	log	Scale:	1.0
Method:	IRLS	Log-Likelihood:	-237.64
Date:	Mon, 04 Sep 2017	Deviance:	89.507
Time:	21:09:36	Pearson chi2:	87.1
No. Iterations:	4

	coef	std err	z	P>\|z\|	[0.025	0.975]
Intercept	2.0580	0.036	57.586	0.000	1.988	2.128

In [3]:

# 最大対数尤度
result.llf

Out[3]:

-237.6432213092867

In [4]:

# 逸脱度
result.llf * -2

Out[4]:

475.2864426185734

In [5]:

# AIC
result.aic

Out[5]:

477.2864426185734

In [6]:

# 残差逸脱度
result.deviance

Out[6]:

89.506937569581382

In [7]:

# 最大逸脱度
result.null_deviance

Out[7]:

89.506937569581353

In [8]:

# 最小逸脱度
result.llf * (-2) - result.deviance

Out[8]:

385.77950504899201

体サイズ $x_{i}$ のみを説明変数に使用した場合¶

In [9]:

result = smf.glm(formula='y ~ x', data=data, family=sm.families.Poisson()).fit()
result.summary()

Out[9]:

Generalized Linear Model Regression Results
Dep. Variable:	y	No. Observations:	100
Model:	GLM	Df Residuals:	98
Model Family:	Poisson	Df Model:	1
Link Function:	log	Scale:	1.0
Method:	IRLS	Log-Likelihood:	-235.39
Date:	Mon, 04 Sep 2017	Deviance:	84.993
Time:	21:09:36	Pearson chi2:	83.8
No. Iterations:	4

	coef	std err	z	P>\|z\|	[0.025	0.975]
Intercept	1.2917	0.364	3.552	0.000	0.579	2.005
x	0.0757	0.036	2.125	0.034	0.006	0.145

In [10]:

# 最大対数尤度
result.llf

Out[10]:

-235.38625076986077

In [11]:

# 逸脱度
result.llf * -2

Out[11]:

470.77250153972153

In [12]:

# AIC
result.aic

Out[12]:

474.77250153972153

In [13]:

# 残差逸脱度
result.deviance

Out[13]:

84.992996490729567

In [14]:

# 最大逸脱度
result.null_deviance

Out[14]:

89.506937569581382

In [15]:

# 最小逸脱度
result.llf * (-2) - result.deviance

Out[15]:

385.77950504899195

施肥処理 $f_{i}$ のみを説明変数に使用した場合¶

In [16]:

result = smf.glm(formula='y ~ f', data=data, family=sm.families.Poisson()).fit()
result.summary()

Out[16]:

Generalized Linear Model Regression Results
Dep. Variable:	y	No. Observations:	100
Model:	GLM	Df Residuals:	98
Model Family:	Poisson	Df Model:	1
Link Function:	log	Scale:	1.0
Method:	IRLS	Log-Likelihood:	-237.63
Date:	Mon, 04 Sep 2017	Deviance:	89.475
Time:	21:09:36	Pearson chi2:	87.1
No. Iterations:	4

	coef	std err	z	P>\|z\|	[0.025	0.975]
Intercept	2.0516	0.051	40.463	0.000	1.952	2.151
f[T.T]	0.0128	0.071	0.179	0.858	-0.127	0.153

In [17]:

# 最大対数尤度
result.llf

Out[17]:

-237.62725696068685

In [18]:

# 逸脱度
result.llf * (-2)

Out[18]:

475.2545139213737

In [19]:

# AIC
result.aic

Out[19]:

479.2545139213737

In [20]:

# 残差逸脱度
result.deviance

Out[20]:

89.475008872381636

In [21]:

# 最大逸脱度
result.null_deviance

Out[21]:

89.506937569581382

In [22]:

# 最小逸脱度
result.llf * (-2) - result.deviance

Out[22]:

385.77950504899206

体サイズ $x_{i}$ と施肥処理 $f_{i}$ を説明変数に使用した場合¶

In [23]:

result = smf.glm(formula='y ~ x + f', data=data, family=sm.families.Poisson()).fit()
result.summary()

Out[23]:

Generalized Linear Model Regression Results
Dep. Variable:	y	No. Observations:	100
Model:	GLM	Df Residuals:	97
Model Family:	Poisson	Df Model:	2
Link Function:	log	Scale:	1.0
Method:	IRLS	Log-Likelihood:	-235.29
Date:	Mon, 04 Sep 2017	Deviance:	84.808
Time:	21:09:37	Pearson chi2:	83.8
No. Iterations:	4

	coef	std err	z	P>\|z\|	[0.025	0.975]
Intercept	1.2631	0.370	3.417	0.001	0.539	1.988
f[T.T]	-0.0320	0.074	-0.430	0.667	-0.178	0.114
x	0.0801	0.037	2.162	0.031	0.007	0.153

In [24]:

# 最大対数尤度
result.llf

Out[24]:

-235.29371924249369

In [25]:

# 逸脱度
result.llf * (-2)

Out[25]:

470.58743848498739

In [26]:

# AIC
result.aic

Out[26]:

476.58743848498739

In [27]:

# 残差逸脱度
result.deviance

Out[27]:

84.807933435995295

In [28]:

# 最大逸脱度
result.null_deviance

Out[28]:

89.506937569581353

In [29]:

# 最小逸脱度
result.llf * (-2) - result.deviance

Out[29]:

385.77950504899206

In [30]:

(result.llf * (-2) - result.deviance) / 2

Out[30]:

192.88975252449603

説明変数なし¶

体サイズxix_{i}のみを説明変数に使用した場合¶

施肥処理fif_{i}のみを説明変数に使用した場合¶

体サイズxix_{i}と施肥処理fif_{i}を説明変数に使用した場合¶

体サイズ $x_{i}$ のみを説明変数に使用した場合¶

施肥処理 $f_{i}$ のみを説明変数に使用した場合¶

体サイズ $x_{i}$ と施肥処理 $f_{i}$ を説明変数に使用した場合¶