Statsmodels Python general statistical model library

Understanding oneself 2020-11-13 10:09:26
statsmodels python general statistical model


See before sklearn The linear model doesn't have R Fang ,F test , Regression coefficient T Test and other indicators , So I saw statsmodels This library , Looking at the output of the library is really nostalgic ..



1 install

pip install statsmodels

But it's possible to report a mistake :

ImportError: cannot import name 'factorial' from 'scipy.misc'
(E:\Anaconda3.7\lib\site-packages\scipy\misc\__init__.py)

with scipy Version mismatch , The author deleted the previous pip uninstall statsmodels, Just reinstall it again :

pip install --pre statsmodels -i https://pypi.tuna.tsinghua.edu.cn/simple

2 Introduction to relevant models

Relevant documents can be found in :https://www.statsmodels.org/stable/examples/index.html

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The models included are :

2.1 Linear model

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2.2 Discrete choice model (Discrete Choice Model, DCM)

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Reference resources : Discrete choice model (Discrete Choice Model, DCM) brief introduction —— One of

Discrete choice model (Discrete Choice Model, DCM) It's widely used in economics and sociology .
for example , When consumers buy a car, they usually compare several different brands , Like Ford 、 Honda 、 The public , wait .
If consumers choose Ford as Y=1, Choose Honda as Y=2, Choose Volkswagen as Y=3; So when studying what kind of car brand consumers choose , Because the dependent variable is not a continuous variable (Y=1, 2, 3), The traditional linear regression model has some limitations ( see DCM Series article No 2 piece ).
Another example , In the field of traffic safety research , The severity of traffic accidents is usually divided into 3 Categories: :

  • (1) Only property damage (Property Damage Only, PDO),
  • (2) injured (Injury),
  • (3) Death (Fatality);
    Studying all kinds of factors ( Like the slope of the road 、 Curve curvature, etc 、 Age of car 、 light 、 Weather conditions, etc ) When it affects the severity of the accident , Because of the dependent variable ( The severity of the accident ) It's a discrete variable ( only 3 An option ), Using discrete selection model can provide an effective modeling approach .
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2.3 Nonparametric statistics

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2.4 Generalized linear model - Generalized Linear Models

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2.5 Steady return ——Robust Regression

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2.6 Generalized estimating equation

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2.7 variance analysis

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2.8 Time series analysis ——Time Series Analysis

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2.9 Space measurement is necessary : State space model ——State space models

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2.10 Multivariate statistical model —— factor / Principal component analysis

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3 The related model demo

3.1 linear regression model

May refer to :https://www.statsmodels.org/stable/examples/notebooks/generated/ols.html

# Linear model
import statsmodels.api as sm
import numpy as np
x = np.linspace(0,10,100)
y = 3*x + np.random.randn()+ 10
# Fit and summarize OLS model
X = sm.add_constant(x)
mod = sm.OLS(y,X)
result = mod.fit()
print('Parameters: ', result .params)
print('Standard errors: ', result .bse)
print('Predicted values: ', result .predict())
print(result.summary())
# Forecast data
print(result.predict(X[:5]))

The output is super familiar .

  • result.params It's the regression coefficient
  • result.summary() Print out the correlation coefficients of the model
    among , Prediction time , If no parameters are given result.predict(), Default is X

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3.2 Generalized linear model ——GLM

Reference resources :https://www.statsmodels.org/stable/examples/notebooks/generated/glm.html

import statsmodels.formula.api as smf
star98 = sm.datasets.star98.load_pandas().data
formula = 'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \
PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'
dta = star98[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP',
'PCTCHRT', 'PCTYRRND', 'PERMINTE', 'AVYRSEXP', 'AVSALK',
'PERSPENK', 'PTRATIO', 'PCTAF']].copy()
endog = dta['NABOVE'] / (dta['NABOVE'] + dta.pop('NBELOW'))
del dta['NABOVE']
dta['SUCCESS'] = endog
mod1 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit()
mod1.summary()
mod1.predict(dta)

formula It's a regular formula , All that is X/Y The data are all in one dataframe In .
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print('Total number of trials:', data.endog[0].sum())
print('Parameters: ', res.params)
print('T-values: ', res.tvalues)

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Including the regression coefficient ,T Test value

3.3 Steady return

Reference resources :https://www.statsmodels.org/stable/examples/notebooks/generated/robust_models_0.html

nsample = 50
x1 = np.linspace(0, 20, nsample)
X = np.column_stack((x1, (x1-5)**2))
X = sm.add_constant(X)
sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger
beta = [5, 0.5, -0.0]
y_true2 = np.dot(X, beta)
y2 = y_true2 + sig*1. * np.random.normal(size=nsample)
y2[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample)
X2 = X[:,[0,1]]
res2 = sm.OLS(y2, X2).fit()
print(res2.params)
print(res2.bse)
resrlm2 = sm.RLM(y2, X2).fit()
print(resrlm2.params)
print(resrlm2.bse)
print(resrlm2.summary())

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4 other

4.1 What is the result of the model CSV export ?

Can pass as_csv() Export the model

resrlm2 = sm.RLM(y, x).fit()
resrlm2.summary()
with open( 'model_rlm.csv', 'w') as fh:
fh.write(resrlm2.summary().as_csv())

But the format of the export is strange :
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4.2 Draw model pictures and save

import statsmodels.api as sm
import numpy as np
import matplotlib.pyplot as plt
# Prepare the data
x = np.linspace(0,10,100)
y = 3*x + np.random.randn()+ 10
# Fit and summarize OLS model
res = sm.OLS(y,x).fit()
print(res.params)
print(res.summary())
# Steady return
resrlm = sm.RLM(y, x).fit()
# drawing
fig, ax = plt.subplots(figsize=(8,6))
ax.plot(x, y, 'o', label="truey ")
ax.plot(x, res.predict(), 'o', label="ols") # res2.predict(X2) == res2.predict()
ax.plot(x, resrlm.predict(), 'b-', label="rlm")# resrlm2.predict(X2) == resrlm2.predict()
legend = ax.legend(loc="best")
# Figure saving
plt.savefig( 'image.jpg')

4.3 Get model output parameters quickly :P test 、F test 、P statistic

def get_model_param(res2,name = 'all'):
model_param_dict = {'name':name, # The name of the model
'rsquared':res2.rsquared, # R Fang
'fvalue':res2.fvalue, # F value , The whole model
'f_pvalue':res2.f_pvalue, # P value , The whole model
'params':res2.params[0], # Regression coefficient
'pvalues':res2.pvalues[0], # Regression coefficient P test 0.000
'tvalues':res2.tvalues[0]} # Regression coefficient T test 276.571
return model_param_dict
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