In [418]:
%matplotlib inline
import matplotlib.pyplot as plt
In [420]:
import pandas as pd
In [34]:
df = pd.read_csv('/Users/chengjun/github/cjc2016/data/tianya_bbs_threads_list.txt', sep = "\t", header=None)
df[:2]
Out[34]:
In [60]:
df=df.rename(columns = {0:'title', 1:'link', 2:'author',3:'author_page', 4:'click', 5:'reply', 6:'time'})
df[:5]
Out[60]:
In [55]:
da = pd.read_csv('/Users/chengjun/github/cjc2016/data/tianya_bbs_threads_author_info.txt', sep = "\t", header=None)
da[:2]
Out[55]:
In [61]:
da=da.rename(columns = {0:'author_page', 1:'followed_num', 2:'fans_num',3:'post_num', 4:'comment_num'})
da[:5]
Out[61]:
In [435]:
data = pd.concat([df,da], axis=1)
len(data)
Out[435]:
In [436]:
data[:3]
Out[436]:
In [437]:
type(data.time[0])
Out[437]:
In [438]:
# extract date from datetime
date = map(lambda x: x[:10], data.time)
data['date'] = pd.to_datetime(date)
In [439]:
# convert str to datetime format
data.time = pd.to_datetime(data.time)
data['month'] = data.time.dt.month
data['year'] = data.time.dt.year
data['day'] = data.time.dt.day
type(data.time[0])
Out[439]:
In [440]:
data[:3]
Out[440]:
http://statsmodels.sourceforge.net/
Statsmodels is a Python module that allows users to explore data, estimate statistical models, and perform statistical tests.
An extensive list of descriptive statistics, statistical tests, plotting functions, and result statistics are available for different types of data and each estimator.
Researchers across fields may find that statsmodels fully meets their needs for statistical computing and data analysis in Python.
In [325]:
import statsmodels.api as sm
In [326]:
' '.join(dir(sm))
Out[326]:
In [327]:
' '.join(dir(sm.stats))
Out[327]:
In [370]:
data.describe()
Out[370]:
In [162]:
import numpy as np
np.mean(data.click), np.std(data.click), np.sum(data.click)
Out[162]:
In [328]:
# 不加权的变量描述
d1 = sm.stats.DescrStatsW(data.click, weights=[1 for i in data.click])
d1.mean, d1.var, d1.std, d1.sum
Out[328]:
In [329]:
# 加权的变量描述
d1 = sm.stats.DescrStatsW(data.click, weights=data.reply)
d1.mean, d1.var, d1.std, d1.sum
Out[329]:
In [163]:
np.median(data.click)
Out[163]:
In [176]:
plt.hist(data.click)
plt.show()
In [186]:
plt.hist(data.reply, color = 'green')
plt.show()
In [185]:
plt.hist(np.log(data.click+1), color='green')
plt.hist(np.log(data.reply+1), color='red')
plt.show()
In [170]:
# Plot the height and weight to see
plt.boxplot([np.log(data.click+1)])
plt.show()
In [152]:
# Plot the height and weight to see
plt.boxplot([data.click, data.reply])
plt.show()
In [172]:
def transformData(dat):
results = []
for i in dat:
if i != 'na':
results.append( int(i))
else:
results.append(0)
return results
In [441]:
data.fans_num = transformData(data.fans_num)
data.followed_num = transformData(data.followed_num )
data.post_num = transformData(data.post_num )
data.comment_num = transformData(data.comment_num )
In [379]:
# Plot the height and weight to see
plt.boxplot([np.log(data.click+1), np.log(data.reply+1),
np.log(data.fans_num+1), np.log(data.followed_num + 1)],
labels = ['$Click$', '$Reply$', '$Fans$', '$Followed$'])
plt.show()
In [380]:
fig = plt.figure(figsize=(12,4))
data.boxplot(return_type='dict')
plt.yscale('log')
plt.show()
In [381]:
' '.join(dir(data))
Out[381]:
In [454]:
from pandas.tools import plotting
#fig = plt.figure(figsize=(10, 10))
plotting.scatter_matrix(data[['click', 'reply', 'post_num','comment_num']])
plt.show()
In [450]:
' '.join(dir(plotting))
Out[450]:
In [455]:
import seaborn
seaborn.pairplot(data, vars=['click', 'reply', 'post_num', 'comment_num'],
kind='reg')
Out[455]:
In [458]:
seaborn.pairplot(data, vars=['click', 'reply', 'post_num'],
kind='reg', hue='year')
Out[458]:
In [457]:
seaborn.lmplot(y='reply', x='click', data=data)
Out[457]:
In [323]:
from scipy import stats
stats.ttest_ind(data.click, data.reply)
Out[323]:
In [324]:
sm.stats.ttest_ind(data.click, data.reply)
# test statistic, pvalue and degrees of freedom
Out[324]:
In [278]:
data.year.value_counts()
Out[278]:
In [292]:
d = data.year.value_counts()
dd = pd.DataFrame(d)
dd = dd.sort_index(axis=0, ascending=True)
dd
Out[292]:
In [351]:
dd.index
Out[351]:
In [362]:
dd_date_str = map(lambda x: str(x) +'-01-01', dd.index)
dd_date_str
Out[362]:
In [363]:
dd_date = pd.to_datetime(dd_date_str)
dd_date
Out[363]:
In [365]:
plt.plot(dd_date, dd.year, 'r-o')
plt.show()
In [384]:
ds = dd.cumsum()
ds
Out[384]:
In [397]:
d = data.year.value_counts()
dd = pd.DataFrame(d)
dd = dd.sort_index(axis=0, ascending=True)
ds = dd.cumsum()
def getDate(dat):
dat_date_str = map(lambda x: str(x) +'-01-01', dat.index)
dat_date = pd.to_datetime(dat_date_str)
return dat_date
ds.date = getDate(ds)
dd.date = getDate(dd)
plt.plot(ds_date, ds.year, 'g-s', label = '$Cumulative\: Number\:of\: Threads$')
plt.plot(dd_date, dd.year, 'r-o', label = '$Yearly\:Number\:of\:Threads$')
plt.legend(loc=2,numpoints=1,fontsize=13)
plt.show()
In [398]:
dg = data.groupby('year').sum()
dg
Out[398]:
In [400]:
dgs = dg.cumsum()
dgs
Out[400]:
In [414]:
def getDate(dat):
dat_date_str = map(lambda x: str(x) +'-01-01', dat.index)
dat_date = pd.to_datetime(dat_date_str)
return dat_date
dg.date = getDate(dg)
In [413]:
fig = plt.figure(figsize=(12,5))
plt.plot(dg.date, dg.click, 'r-o', label = '$Yearly\:Number\:of\:Clicks$')
plt.plot(dg.date, dg.reply, 'g-s', label = '$Yearly\:Number\:of\:Replies$')
plt.plot(dg.date, dg.fans_num, 'b->', label = '$Yearly\:Number\:of\:Fans$')
plt.yscale('log')
plt.legend(loc=4,numpoints=1,fontsize=13)
plt.show()
In [276]:
data.groupby('year')['click'].sum()
Out[276]:
In [275]:
data.groupby('year')['click'].mean()
Out[275]:
https://en.wikipedia.org/wiki/Chi-squared_test
Parameters:
Suppose there is a city of 1 million residents with four neighborhoods: A, B, C, and D. A random sample of 650 residents of the city is taken and their occupation is recorded as "blue collar", "white collar", or "no collar". The null hypothesis is that each person's neighborhood of residence is independent of the person's occupational classification. The data are tabulated as:
| A | B | C | D | Total | |
|---|---|---|---|---|---|
| White collar | 90 | 60 | 104 | 95 | 349 |
| Blue collar | 30 | 50 | 51 | 20 | 151 |
| No coloar | 30 | 40 | 45 | 35 | 150 |
| Total | 150 | 150 | 200 | 150 | 650 |
Let us take the sample living in neighborhood A, 150/650, to estimate what proportion of the whole 1 million people live in neighborhood A. Similarly we take 349/650 to estimate what proportion of the 1 million people are white-collar workers. By the assumption of independence under the hypothesis we should "expect" the number of white-collar workers in neighborhood A to be
$ \frac{150}{650} \frac{349}{650} 650 = 80.54 $
Then in that "cell" of the table, we have
$\frac{(\text{observed}-\text{expected})^2}{\text{expected}} = \frac{(90-80.54)^2}{80.54}$.
The sum of these quantities over all of the cells is the test statistic. Under the null hypothesis, it has approximately a chi-square distribution whose number of degrees of freedom are
$ (\text{number of rows}-1)(\text{number of columns}-1) = (3-1)(4-1) = 6. $
If the test statistic is improbably large according to that chi-square distribution, then one rejects the null hypothesis of independence.
In [428]:
from scipy.stats import chisquare
chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8])
Out[428]:
In [427]:
from scipy.stats import chisqprob, chi2
# p_value = chi2.sf(chi_statistic, df)
print chisqprob(3.94,1), 1 - chi2.cdf(3.94,1)
In [168]:
print np.corrcoef(data.click, data.reply)
In [ ]:
In [383]:
data.corr()
Out[383]:
In [13]:
plt.plot(df.click, df.reply, 'r-o')
plt.show()
In [16]:
plt.plot(df.click, df.reply, 'gs')
plt.xlabel('$Clicks$', fontsize = 20)
plt.ylabel('$Replies$', fontsize = 20)
plt.xscale('log')
plt.yscale('log')
plt.title('$Allowmetric\,Law$', fontsize = 20)
plt.show()
In [19]:
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
In [20]:
# Load data
dat = sm.datasets.get_rdataset("Guerry", "HistData").data
# Fit regression model (using the natural log of one of the regressors)
results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit()
In [21]:
# Inspect the results
print results.summary()
In [137]:
reg = smf.ols('reply ~ click + followed_num', data=data).fit()
In [138]:
print reg.summary()
In [207]:
reg1 = smf.ols('np.log(reply+1) ~ np.log(click+1) +np.log(followed_num+1)+month', data=data).fit()
print reg1.summary()
In [208]:
sm.graphics.plot_partregress('reply', 'click', ['followed_num'], data=data, obs_labels=False)
Out[208]:
In [209]:
fig = plt.figure(figsize=(12,8))
fig = sm.graphics.plot_partregress_grid(reg1, fig = fig)
plt.show()
In [429]:
import statsmodels.api as sm
from statsmodels.formula.api import ols
moore = sm.datasets.get_rdataset("Moore", "car",
cache=True) # load data
data = moore.data
data = data.rename(columns={"partner.status" :
"partner_status"}) # make name pythonic
In [434]:
data[:5]
Out[434]:
In [430]:
moore_lm = ols('conformity ~ C(fcategory, Sum)*C(partner_status, Sum)',
data=data).fit()
In [432]:
fig = plt.figure(figsize=(12,8))
fig = sm.graphics.plot_partregress_grid(moore_lm, fig = fig)
plt.show()
In [431]:
table = sm.stats.anova_lm(moore_lm, typ=2) # Type 2 ANOVA DataFrame
print table