%matplotlib inline

from __future__ import print_function
from statsmodels.compat import urlopen
import numpy as np
np.set_printoptions(precision=4, suppress=True)
import statsmodels.api as sm
import pandas as pd
pd.set_option("display.width", 100)
import matplotlib.pyplot as plt
from statsmodels.formula.api import ols
from statsmodels.graphics.api import interaction_plot, abline_plot
from statsmodels.stats.anova import anova_lm

try:
    salary_table = pd.read_csv('salary.table')
except:  # recent pandas can read URL without urlopen
    url = 'http://stats191.stanford.edu/data/salary.table'
    fh = urlopen(url)
    salary_table = pd.read_table(fh)
    salary_table.to_csv('salary.table')

E = salary_table.E
M = salary_table.M
X = salary_table.X
S = salary_table.S

"""
Explanation: Interactions and ANOVA
Note: This script is based heavily on Jonathan Taylor's class notes http://www.stanford.edu/class/stats191/interactions.html
Download and format data:
End of explanation
"""


plt.figure(figsize=(6,6))
symbols = ['D', '^']
colors = ['r', 'g', 'blue']
factor_groups = salary_table.groupby(['E','M'])
for values, group in factor_groups:
    i,j = values
    plt.scatter(group['X'], group['S'], marker=symbols[j], color=colors[i-1],
               s=144)
plt.xlabel('Experience');
plt.ylabel('Salary');

"""
Explanation: Take a look at the data:
End of explanation
"""


formula = 'S ~ C(E) + C(M) + X'
lm = ols(formula, salary_table).fit()
print(lm.summary())

"""
Explanation: Fit a linear model:
End of explanation
"""


lm.model.exog[:5]

"""
Explanation: Have a look at the created design matrix:
End of explanation
"""


lm.model.data.orig_exog[:5]

"""
Explanation: Or since we initially passed in a DataFrame, we have a DataFrame available in
End of explanation
"""


lm.model.data.frame[:5]

"""
Explanation: We keep a reference to the original untouched data in
End of explanation
"""


infl = lm.get_influence()
print(infl.summary_table())

"""
Explanation: Influence statistics
End of explanation
"""


df_infl = infl.summary_frame()

df_infl[:5]

"""
Explanation: or get a dataframe
End of explanation
"""


resid = lm.resid
plt.figure(figsize=(6,6));
for values, group in factor_groups:
    i,j = values
    group_num = i*2 + j - 1  # for plotting purposes
    x = [group_num] * len(group)
    plt.scatter(x, resid[group.index], marker=symbols[j], color=colors[i-1],
            s=144, edgecolors='black')
plt.xlabel('Group');
plt.ylabel('Residuals');

"""
Explanation: Now plot the reiduals within the groups separately:
End of explanation
"""


interX_lm = ols("S ~ C(E) * X + C(M)", salary_table).fit()
print(interX_lm.summary())

"""
Explanation: Now we will test some interactions using anova or f_test
End of explanation
"""


from statsmodels.stats.api import anova_lm

table1 = anova_lm(lm, interX_lm)
print(table1)

interM_lm = ols("S ~ X + C(E)*C(M)", data=salary_table).fit()
print(interM_lm.summary())

table2 = anova_lm(lm, interM_lm)
print(table2)

"""
Explanation: Do an ANOVA check
End of explanation
"""


interM_lm.model.data.orig_exog[:5]

"""
Explanation: The design matrix as a DataFrame
End of explanation
"""


interM_lm.model.exog
interM_lm.model.exog_names

infl = interM_lm.get_influence()
resid = infl.resid_studentized_internal
plt.figure(figsize=(6,6))
for values, group in factor_groups:
    i,j = values
    idx = group.index
    plt.scatter(X[idx], resid[idx], marker=symbols[j], color=colors[i-1],
            s=144, edgecolors='black')
plt.xlabel('X');
plt.ylabel('standardized resids');

"""
Explanation: The design matrix as an ndarray
End of explanation
"""


drop_idx = abs(resid).argmax()
print(drop_idx)  # zero-based index
idx = salary_table.index.drop(drop_idx)

lm32 = ols('S ~ C(E) + X + C(M)', data=salary_table, subset=idx).fit()

print(lm32.summary())
print('\n')

interX_lm32 = ols('S ~ C(E) * X + C(M)', data=salary_table, subset=idx).fit()

print(interX_lm32.summary())
print('\n')


table3 = anova_lm(lm32, interX_lm32)
print(table3)
print('\n')


interM_lm32 = ols('S ~ X + C(E) * C(M)', data=salary_table, subset=idx).fit()

table4 = anova_lm(lm32, interM_lm32)
print(table4)
print('\n')

"""
Explanation: Looks like one observation is an outlier.
End of explanation
"""


try:
    resid = interM_lm32.get_influence().summary_frame()['standard_resid']
except:
    resid = interM_lm32.get_influence().summary_frame()['standard_resid']

plt.figure(figsize=(6,6))
for values, group in factor_groups:
    i,j = values
    idx = group.index
    plt.scatter(X[idx], resid[idx], marker=symbols[j], color=colors[i-1],
            s=144, edgecolors='black')
plt.xlabel('X[~[32]]');
plt.ylabel('standardized resids');

"""
Explanation: Replot the residuals
End of explanation
"""


lm_final = ols('S ~ X + C(E)*C(M)', data = salary_table.drop([drop_idx])).fit()
mf = lm_final.model.data.orig_exog
lstyle = ['-','--']

plt.figure(figsize=(6,6))
for values, group in factor_groups:
    i,j = values
    idx = group.index
    plt.scatter(X[idx], S[idx], marker=symbols[j], color=colors[i-1],
                s=144, edgecolors='black')
    # drop NA because there is no idx 32 in the final model
    plt.plot(mf.X[idx].dropna(), lm_final.fittedvalues[idx].dropna(),
            ls=lstyle[j], color=colors[i-1])
plt.xlabel('Experience');
plt.ylabel('Salary');

"""
Explanation: Plot the fitted values
End of explanation
"""


U = S - X * interX_lm32.params['X']

plt.figure(figsize=(6,6))
interaction_plot(E, M, U, colors=['red','blue'], markers=['^','D'],
        markersize=10, ax=plt.gca())

"""
Explanation: From our first look at the data, the difference between Master's and PhD in the management group is different than in the non-management group. This is an interaction between the two qualitative variables management,M and education,E. We can visualize this by first removing the effect of experience, then plotting the means within each of the 6 groups using interaction.plot.
End of explanation
"""


try:
    jobtest_table = pd.read_table('jobtest.table')
except:  # don't have data already
    url = 'http://stats191.stanford.edu/data/jobtest.table'
    jobtest_table = pd.read_table(url)

factor_group = jobtest_table.groupby(['ETHN'])

fig, ax = plt.subplots(figsize=(6,6))
colors = ['purple', 'green']
markers = ['o', 'v']
for factor, group in factor_group:
    ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],
                marker=markers[factor], s=12**2)
ax.set_xlabel('TEST');
ax.set_ylabel('JPERF');

min_lm = ols('JPERF ~ TEST', data=jobtest_table).fit()
print(min_lm.summary())

fig, ax = plt.subplots(figsize=(6,6));
for factor, group in factor_group:
    ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],
                marker=markers[factor], s=12**2)

ax.set_xlabel('TEST')
ax.set_ylabel('JPERF')
fig = abline_plot(model_results = min_lm, ax=ax)

min_lm2 = ols('JPERF ~ TEST + TEST:ETHN',
        data=jobtest_table).fit()

print(min_lm2.summary())

fig, ax = plt.subplots(figsize=(6,6));
for factor, group in factor_group:
    ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],
                marker=markers[factor], s=12**2)

fig = abline_plot(intercept = min_lm2.params['Intercept'],
                 slope = min_lm2.params['TEST'], ax=ax, color='purple');
fig = abline_plot(intercept = min_lm2.params['Intercept'],
        slope = min_lm2.params['TEST'] + min_lm2.params['TEST:ETHN'],
        ax=ax, color='green');

min_lm3 = ols('JPERF ~ TEST + ETHN', data = jobtest_table).fit()
print(min_lm3.summary())

fig, ax = plt.subplots(figsize=(6,6));
for factor, group in factor_group:
    ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],
                marker=markers[factor], s=12**2)

fig = abline_plot(intercept = min_lm3.params['Intercept'],
                 slope = min_lm3.params['TEST'], ax=ax, color='purple');
fig = abline_plot(intercept = min_lm3.params['Intercept'] + min_lm3.params['ETHN'],
        slope = min_lm3.params['TEST'], ax=ax, color='green');

min_lm4 = ols('JPERF ~ TEST * ETHN', data = jobtest_table).fit()
print(min_lm4.summary())

fig, ax = plt.subplots(figsize=(8,6));
for factor, group in factor_group:
    ax.scatter(group['TEST'], group['JPERF'], color=colors[factor],
                marker=markers[factor], s=12**2)

fig = abline_plot(intercept = min_lm4.params['Intercept'],
                 slope = min_lm4.params['TEST'], ax=ax, color='purple');
fig = abline_plot(intercept = min_lm4.params['Intercept'] + min_lm4.params['ETHN'],
        slope = min_lm4.params['TEST'] + min_lm4.params['TEST:ETHN'],
        ax=ax, color='green');

# is there any effect of ETHN on slope or intercept?
table5 = anova_lm(min_lm, min_lm4)
print(table5)

# is there any effect of ETHN on intercept
table6 = anova_lm(min_lm, min_lm3)
print(table6)

# is there any effect of ETHN on slope
table7 = anova_lm(min_lm, min_lm2)
print(table7)

# is it just the slope or both?
table8 = anova_lm(min_lm2, min_lm4)
print(table8)

"""
Explanation: Minority Employment Data
End of explanation
"""


try:
    rehab_table = pd.read_csv('rehab.table')
except:
    url = 'http://stats191.stanford.edu/data/rehab.csv'
    rehab_table = pd.read_table(url, delimiter=",")
    rehab_table.to_csv('rehab.table')

fig, ax = plt.subplots(figsize=(8,6))
fig = rehab_table.boxplot('Time', 'Fitness', ax=ax, grid=False)

rehab_lm = ols('Time ~ C(Fitness)', data=rehab_table).fit()
table9 = anova_lm(rehab_lm)
print(table9)

print(rehab_lm.model.data.orig_exog)

print(rehab_lm.summary())

"""
Explanation: One-way ANOVA
End of explanation
"""


try:
    kidney_table = pd.read_table('./kidney.table')
except:
    url = 'http://stats191.stanford.edu/data/kidney.table'
    kidney_table = pd.read_table(url, delimiter=" *")

"""
Explanation: Two-way ANOVA
End of explanation
"""


kidney_table.groupby(['Weight', 'Duration']).size()

"""
Explanation: Explore the dataset
End of explanation
"""


kt = kidney_table
plt.figure(figsize=(8,6))
fig = interaction_plot(kt['Weight'], kt['Duration'], np.log(kt['Days']+1),
        colors=['red', 'blue'], markers=['D','^'], ms=10, ax=plt.gca())

"""
Explanation: Balanced panel
End of explanation
"""


kidney_lm = ols('np.log(Days+1) ~ C(Duration) * C(Weight)', data=kt).fit()

table10 = anova_lm(kidney_lm)

print(anova_lm(ols('np.log(Days+1) ~ C(Duration) + C(Weight)',
                data=kt).fit(), kidney_lm))
print(anova_lm(ols('np.log(Days+1) ~ C(Duration)', data=kt).fit(),
               ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)',
                   data=kt).fit()))
print(anova_lm(ols('np.log(Days+1) ~ C(Weight)', data=kt).fit(),
               ols('np.log(Days+1) ~ C(Duration) + C(Weight, Sum)',
                   data=kt).fit()))

"""
Explanation: You have things available in the calling namespace available in the formula evaluation namespace
End of explanation
"""


sum_lm = ols('np.log(Days+1) ~ C(Duration, Sum) * C(Weight, Sum)',
            data=kt).fit()

print(anova_lm(sum_lm))
print(anova_lm(sum_lm, typ=2))
print(anova_lm(sum_lm, typ=3))

nosum_lm = ols('np.log(Days+1) ~ C(Duration, Treatment) * C(Weight, Treatment)',
            data=kt).fit()
print(anova_lm(nosum_lm))
print(anova_lm(nosum_lm, typ=2))
print(anova_lm(nosum_lm, typ=3))

"""
Explanation: Sum of squares
Illustrates the use of different types of sums of squares (I,II,II)
 and how the Sum contrast can be used to produce the same output between
 the 3.
Types I and II are equivalent under a balanced design.
Don't use Type III with non-orthogonal contrast - ie., Treatment
End of explanation
"""


