3.3: Interactions

In [1]:

    

from __future__ import print_function, division
%matplotlib inline

import matplotlib
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# use matplotlib style sheet
plt.style.use('ggplot')

# import statsmodels for R-style regression
import statsmodels.formula.api as smf


    

In [2]:

    

kidiq  = pd.read_stata("../../ARM_Data/child.iq/kidiq.dta")
kidiq.head()


    

    
Out[2]:






  

    

      

      
kid_score
      
mom_hs
      
mom_iq
      
mom_work
      
mom_age
    
  
  

    

      
0
      
65
      
1
      
121.117529
      
4
      
27
    
    

      
1
      
98
      
1
      
89.361882
      
4
      
25
    
    

      
2
      
85
      
1
      
115.443165
      
4
      
27
    
    

      
3
      
83
      
1
      
99.449639
      
3
      
25
    
    

      
4
      
115
      
1
      
92.745710
      
4
      
27
    
  

In [3]:

    

fit = smf.ols('kid_score ~ mom_hs + mom_iq + mom_hs:mom_iq', data=kidiq).fit()
print(fit.summary())


    

    




                            OLS Regression Results                            
==============================================================================
Dep. Variable:              kid_score   R-squared:                       0.230
Model:                            OLS   Adj. R-squared:                  0.225
Method:                 Least Squares   F-statistic:                     42.84
Date:                Wed, 29 Jul 2015   Prob (F-statistic):           3.07e-24
Time:                        15:25:10   Log-Likelihood:                -1867.5
No. Observations:                 434   AIC:                             3743.
Df Residuals:                     430   BIC:                             3759.
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [95.0% Conf. Int.]
---------------------------------------------------------------------------------
Intercept       -11.4820     13.758     -0.835      0.404       -38.523    15.559
mom_hs           51.2682     15.338      3.343      0.001        21.122    81.414
mom_iq            0.9689      0.148      6.531      0.000         0.677     1.260
mom_hs:mom_iq    -0.4843      0.162     -2.985      0.003        -0.803    -0.165
==============================================================================
Omnibus:                        8.014   Durbin-Watson:                   1.660
Prob(Omnibus):                  0.018   Jarque-Bera (JB):                8.258
Skew:                          -0.333   Prob(JB):                       0.0161
Kurtosis:                       2.887   Cond. No.                     3.10e+03
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.1e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

In [4]:

    

fig, ax = plt.subplots(figsize=(8, 6))
# set for x-range used below
iq_linspace = np.linspace(50, 145, 50)

# default color cycle
colors = plt.rcParams['axes.color_cycle']

# mom_hs == 0
hs0 = (kidiq['mom_hs'] == 0)
plt.scatter(kidiq[hs0]['mom_iq'], kidiq[hs0]['kid_score'],
            s=60, alpha=0.5, c=colors[0])
# mom_hs == 1
hs1 = (kidiq['mom_hs'] == 1)
plt.scatter(kidiq[hs1]['mom_iq'], kidiq[hs1]['kid_score'],
            s=60, alpha=0.5, c=colors[1])

# add fits
# mom_hs == 1
plt.plot(iq_linspace, fit.params[0] + fit.params[1] * 1. + 
         (fit.params[2] + fit.params[3])* iq_linspace,
         lw=3, c=colors[0])
# mom_hs == 0
plt.plot(iq_linspace, fit.params[0] + fit.params[2] * iq_linspace,
         lw=3, c=colors[1])

plt.ylim([10, 145])
plt.xlim([50, 145])
plt.xlabel("Mother IQ score")
plt.ylabel("Child test score")


    

    
Out[4]:





<matplotlib.text.Text at 0x7fe7e44692d0>






    

In [5]:

    

fig, ax = plt.subplots(figsize=(8, 6))
# create x-axis point to zero
iq_linspace = np.linspace(0., kidiq['mom_iq'].max(), 50)

# default color cycle
colors = plt.rcParams['axes.color_cycle']

# mom_hs == 0
hs0 = (kidiq['mom_hs'] == 0)
plt.scatter(kidiq[hs0]['mom_iq'], kidiq[hs0]['kid_score'],
            s=60, alpha=0.5, c=colors[0])
# mom_hs == 1
hs1 = (kidiq['mom_hs'] == 1)
plt.scatter(kidiq[hs1]['mom_iq'], kidiq[hs1]['kid_score'],
            s=60, alpha=0.5, c=colors[1])

# add fits
# mom_hs == 1
plt.plot(iq_linspace, fit.params[0] + fit.params[1] * 1. + 
         (fit.params[2] + fit.params[3])* iq_linspace,
         lw=3, c=colors[0])
# mom_hs == 0
plt.plot(iq_linspace, fit.params[0] + fit.params[2] * iq_linspace,
         lw=3, c=colors[1])

plt.ylim([-5, 145])
plt.xlim([-5, 145])
plt.xlabel("Mother IQ score")
plt.ylabel("Child test score")


    

    
Out[5]:





<matplotlib.text.Text at 0x7fe7e427efd0>