trivers12


Does Trivers-Willard apply to people?

This notebook contains a "one-day paper", my attempt to pose a research question, answer it, and publish the results in one work day.

Copyright 2016 Allen B. Downey

MIT License: https://opensource.org/licenses/MIT


In [1]:
from __future__ import print_function, division

import thinkstats2
import thinkplot

import pandas as pd
import numpy as np

import statsmodels.formula.api as smf

%matplotlib inline

Trivers-Willard

According to Wikipedia, the Trivers-Willard hypothesis:

"...suggests that female mammals are able to adjust offspring sex ratio in response to their maternal condition. For example, it may predict greater parental investment in males by parents in 'good conditions' and greater investment in females by parents in 'poor conditions' (relative to parents in good condition)."

For humans, the hypothesis suggests that people with relatively high social status might be more likely to have boys. Some studies have shown evidence for this hypothesis, but based on my very casual survey, it is not persuasive.

To test whether the T-W hypothesis holds up in humans, I downloaded birth data for the nearly 4 million babies born in the U.S. in 2014.

I selected variables that seemed likely to be related to social status and used logistic regression to identify variables associated with sex ratio.

Summary of results

  1. Running regression with one variable at a time, many of the variables have a statistically significant effect on sex ratio, with the sign of the effect generally in the direction predicted by T-W.

  2. However, many of the variables are also correlated with race. If we control for either the mother's race or the father's race, or both, most other variables have no additional predictive power.

  3. Contrary to other reports, the age of the parents seems to have no predictive power.

  4. Strangely, the variable that shows the strongest and most consistent relationship with sex ratio is the number of prenatal visits. Although it seems obvious that prenatal visits are a proxy for quality of health care and general socioeconomic status, the sign of the effect is opposite what T-W predicts; that is, more prenatal visits is a strong predictor of lower sex ratio (more girls).

Following convention, I report sex ratio in terms of boys per 100 girls. The overall sex ratio at birth is about 105; that is, 105 boys are born for every 100 girls.

Data cleaning

Here's how I loaded the data:


In [2]:
names = ['year', 'mager9', 'restatus', 'mbrace', 'mhisp_r',
        'mar_p', 'dmar', 'meduc', 'fagerrec11', 'fbrace', 'fhisp_r', 'feduc', 
        'lbo_rec', 'previs_rec', 'wic', 'height', 'bmi_r', 'pay_rec', 'sex']
colspecs = [(15, 18),
            (93, 93),
            (138, 138),
            (143, 143),
            (148, 148),
            (152, 152),
            (153, 153),
            (155, 155),
            (186, 187),
            (191, 191),
            (195, 195),
            (197, 197),
            (212, 212),
            (272, 273),
            (281, 281),
            (555, 556),
            (533, 533),
            (413, 413),
            (436, 436),
           ]

colspecs = [(start-1, end) for start, end in colspecs]

In [3]:
df = None

In [4]:
filename = 'Nat2012PublicUS.r20131217.gz'
#df = pd.read_fwf(filename, compression='gzip', header=None, names=names, colspecs=colspecs)
#df.head()


Out[4]:
year mager9 restatus mbrace mhisp_r mar_p dmar meduc fagerrec11 fbrace fhisp_r feduc lbo_rec previs_rec wic height bmi_r pay_rec sex
0 2012 6 1 1 0 NaN 1 NaN 5 1 0 NaN 2 6 NaN NaN NaN NaN M
1 2012 3 1 3 0 NaN 2 NaN 4 3 0 NaN 2 5 NaN NaN NaN NaN F
2 2012 2 1 2 0 NaN 2 NaN 3 2 0 NaN 1 7 NaN NaN NaN NaN M
3 2012 3 1 1 0 NaN 1 NaN 3 1 0 NaN 9 7 NaN NaN NaN NaN M
4 2012 4 1 4 0 NaN 1 NaN 4 1 0 NaN 3 7 NaN NaN NaN NaN F

In [5]:
# store the dataframe for faster loading

#store = pd.HDFStore('store.h5')
#store['births2013'] = df
#store.close()


/home/downey/anaconda2/lib/python2.7/site-packages/IPython/core/interactiveshell.py:3066: PerformanceWarning: 
your performance may suffer as PyTables will pickle object types that it cannot
map directly to c-types [inferred_type->mixed,key->block2_values] [items->['mar_p', 'wic', 'sex']]

  exec(code_obj, self.user_global_ns, self.user_ns)

In [6]:
# load the dataframe

store = pd.HDFStore('store.h5')
df = store['births2013']
store.close()

In [6]:
def series_to_ratio(series):
    """Takes a boolean series and computes sex ratio.
    """
    boys = np.mean(series)
    return np.round(100 * boys / (1-boys)).astype(int)

I have to recode sex as 0 or 1 to make logit happy.


In [7]:
df['boy'] = (df.sex=='M').astype(int)
df.boy.value_counts().sort_index()


Out[7]:
0    1935228
1    2025568
Name: boy, dtype: int64

All births are from 2014.


In [8]:
df.year.value_counts().sort_index()


Out[8]:
2012    3960796
Name: year, dtype: int64

Mother's age:


In [9]:
df.mager9.value_counts().sort_index()


Out[9]:
1       3676
2     305837
3     918221
4    1126139
5    1015784
6     473533
7     109807
8       7187
9        612
Name: mager9, dtype: int64

In [10]:
var = 'mager9'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[10]:
boy
mager9
1 112
2 106
3 104
4 105
5 105
6 105
7 105
8 100
9 112

In [11]:
df.mager9.isnull().mean()


Out[11]:
0.0

In [12]:
df['youngm'] = df.mager9<=2
df['oldm'] = df.mager9>=7
df.youngm.mean(), df.oldm.mean()


Out[12]:
(0.078144140723228367, 0.029692516352773535)

Residence status (1=resident)


In [13]:
df.restatus.value_counts().sort_index()


Out[13]:
1    2874513
2     993222
3      85106
4       7955
Name: restatus, dtype: int64

In [14]:
var = 'restatus'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[14]:
boy
restatus
1 105
2 105
3 105
4 108

Mother's race (1=White, 2=Black, 3=American Indian or Alaskan Native, 4=Asian or Pacific Islander)


In [15]:
df.mbrace.value_counts().sort_index()


Out[15]:
1    3007229
2     634411
3      46105
4     273051
Name: mbrace, dtype: int64

In [16]:
var = 'mbrace'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[16]:
boy
mbrace
1 105
2 103
3 104
4 106

Mother's Hispanic origin (0=Non-Hispanic)


In [17]:
df.mhisp_r.replace([9], np.nan, inplace=True)
df.mhisp_r.value_counts().sort_index()


Out[17]:
0    3015510
1     562250
2      67192
3      17400
4     131955
5     135597
Name: mhisp_r, dtype: int64

In [18]:
def copy_null(df, oldvar, newvar):
    df.loc[df[oldvar].isnull(), newvar] = np.nan

In [19]:
df['mhisp'] = df.mhisp_r > 0
copy_null(df, 'mhisp_r', 'mhisp')
df.mhisp.isnull().mean(), df.mhisp.mean()


Out[19]:
(0.0077994423343186571, 0.23267591269405055)

In [20]:
var = 'mhisp'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[20]:
boy
mhisp
0 105
1 104

Marital status (1=Married)


In [21]:
df.dmar.value_counts().sort_index()


Out[21]:
1    2349102
2    1611694
Name: dmar, dtype: int64

In [22]:
var = 'dmar'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[22]:
boy
dmar
1 105
2 104

Paternity acknowledged, if unmarried (Y=yes, N=no, X=not applicable, U=unknown).

I recode X (not applicable because married) as Y (paternity acknowledged).


In [23]:
df.mar_p.replace(['U'], np.nan, inplace=True)
df.mar_p.replace(['X'], 'Y', inplace=True)
df.mar_p.value_counts().sort_index()


Out[23]:
N     430123
Y    3058398
Name: mar_p, dtype: int64

In [24]:
var = 'mar_p'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[24]:
boy
mar_p
N 103
Y 105

Mother's education level


In [25]:
df.meduc.replace([9], np.nan, inplace=True)
df.meduc.value_counts().sort_index()


Out[25]:
1    144045
2    443007
3    858548
4    732444
5    266066
6    644497
7    282351
8     81074
Name: meduc, dtype: int64

In [26]:
var = 'meduc'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[26]:
boy
meduc
1 103
2 104
3 105
4 105
5 105
6 105
7 105
8 107

In [27]:
df['lowed'] = df.meduc <= 2
copy_null(df, 'meduc', 'lowed')
df.lowed.isnull().mean(), df.lowed.mean()


Out[27]:
(0.12844993784077746, 0.17005983722051243)

Father's age, in 10 ranges


In [28]:
df.fagerrec11.replace([11], np.nan, inplace=True)
df.fagerrec11.value_counts().sort_index()


Out[28]:
1        422
2     104428
3     527157
4     871442
5     977564
6     591733
7     257619
8      84016
9      26361
10     11389
Name: fagerrec11, dtype: int64

In [29]:
var = 'fagerrec11'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[29]:
boy
fagerrec11
1 101
2 106
3 105
4 105
5 105
6 105
7 105
8 104
9 104
10 107

In [30]:
df['youngf'] = df.fagerrec11<=2
copy_null(df, 'fagerrec11', 'youngf')
df.youngf.isnull().mean(), df.youngf.mean()


Out[30]:
(0.12842494286502007, 0.03037254379975731)

In [31]:
df['oldf'] = df.fagerrec11>=8
copy_null(df, 'fagerrec11', 'oldf')
df.oldf.isnull().mean(), df.oldf.mean()


Out[31]:
(0.12842494286502007, 0.03527270546801382)

Father's race


In [32]:
df.fbrace.replace([9], np.nan, inplace=True)
df.fbrace.value_counts().sort_index()


Out[32]:
1    2475018
2     469930
3      35175
4     227463
Name: fbrace, dtype: int64

In [33]:
var = 'fbrace'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[33]:
boy
fbrace
1 105
2 103
3 105
4 107

Father's Hispanic origin (0=non-hispanic, other values indicate country of origin)


In [34]:
df.fhisp_r.replace([9], np.nan, inplace=True)
df.fhisp_r.value_counts().sort_index()


Out[34]:
0    2603738
1     500926
2      57417
3      16953
4     105376
5     116056
Name: fhisp_r, dtype: int64

In [35]:
df['fhisp'] = df.fhisp_r > 0
copy_null(df, 'fhisp_r', 'fhisp')
df.fhisp.isnull().mean(), df.fhisp.mean()


Out[35]:
(0.14146903804184816, 0.23429965187124352)

In [36]:
var = 'fhisp'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[36]:
boy
fhisp
0 105
1 104

Father's education level


In [37]:
df.feduc.replace([9], np.nan, inplace=True)
df.feduc.value_counts().sort_index()


Out[37]:
1    142003
2    336801
3    852923
4    574580
5    201888
6    544487
7    210268
8     97452
Name: feduc, dtype: int64

In [38]:
var = 'feduc'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[38]:
boy
feduc
1 103
2 105
3 105
4 105
5 105
6 105
7 106
8 105

Live birth order.


In [39]:
df.lbo_rec.replace([9], np.nan, inplace=True)
df.lbo_rec.value_counts().sort_index()


Out[39]:
1    1574534
2    1248053
3     651817
4     276179
5     106197
6      43907
7      19899
8      20268
Name: lbo_rec, dtype: int64

In [40]:
var = 'lbo_rec'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[40]:
boy
lbo_rec
1 105
2 105
3 104
4 103
5 104
6 101
7 106
8 103

In [41]:
df['highbo'] = df.lbo_rec >= 5
copy_null(df, 'lbo_rec', 'highbo')
df.highbo.isnull().mean(), df.highbo.mean()


Out[41]:
(0.0050348465308488492, 0.04828166686713083)

Number of prenatal visits, in 11 ranges


In [42]:
df.previs_rec.replace([12], np.nan, inplace=True)
df.previs_rec.value_counts().sort_index()


Out[42]:
1       53862
2       39409
3       90791
4      191909
5      361056
6      809787
7     1023277
8      659674
9      385390
10      98941
11     124582
Name: previs_rec, dtype: int64

In [43]:
df.previs_rec.mean()
df['previs'] = df.previs_rec - 7

In [44]:
var = 'previs'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[44]:
boy
previs
-6 106
-5 107
-4 107
-3 108
-2 107
-1 106
0 105
1 103
2 102
3 100
4 102

In [45]:
df['no_previs'] = df.previs_rec <= 1
copy_null(df, 'previs_rec', 'no_previs')
df.no_previs.isnull().mean(), df.no_previs.mean()


Out[45]:
(0.030831681308504656, 0.014031393099395157)

Whether the mother is eligible for food stamps


In [46]:
df.wic.replace(['U'], np.nan, inplace=True)
df.wic.value_counts().sort_index()


Out[46]:
N    1820030
Y    1591601
Name: wic, dtype: int64

In [47]:
var = 'wic'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[47]:
boy
wic
N 105
Y 104

Mother's height in inches


In [48]:
df.height.replace([99], np.nan, inplace=True)
df.height.value_counts().sort_index()


Out[48]:
30        14
31         3
32         2
34         1
36        17
37         5
38         9
39         4
40        13
41        18
42         8
43         8
44         6
45        15
46         9
47        21
48       732
49       505
50       335
51       414
52       480
53      1384
54      1434
55      2561
56      6587
57     17396
58     19343
59     71557
60    190472
61    240815
62    424926
63    442238
64    505897
65    404563
66    390878
67    303110
68    174629
69    116518
70     56687
71     30085
72     14269
73      4971
74      2381
75       895
76       526
77       584
78      1011
Name: height, dtype: int64

In [49]:
df['mshort'] = df.height<60
copy_null(df, 'height', 'mshort')
df.mshort.isnull().mean(), df.mshort.mean()


Out[49]:
(0.13443257365438666, 0.03584275286903034)

In [50]:
df['mtall'] = df.height>=70
copy_null(df, 'height', 'mtall')
df.mtall.isnull().mean(), df.mtall.mean()


Out[50]:
(0.13443257365438666, 0.03249652309458583)

In [51]:
var = 'mshort'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[51]:
boy
mshort
0 105
1 103

In [52]:
var = 'mtall'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[52]:
boy
mtall
0 105
1 104

Mother's BMI in 6 ranges


In [53]:
df.bmi_r.replace([9], np.nan, inplace=True)
df.bmi_r.value_counts().sort_index()


Out[53]:
1     129937
2    1573715
3     849357
4     442695
5     206615
6     141411
Name: bmi_r, dtype: int64

In [54]:
var = 'bmi_r'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[54]:
boy
bmi_r
1 104
2 105
3 105
4 104
5 104
6 104

In [55]:
df['obese'] = df.bmi_r >= 4
copy_null(df, 'bmi_r', 'obese')
df.obese.isnull().mean(), df.obese.mean()


Out[55]:
(0.15579343142136076, 0.23647872286338908)

Payment method (1=Medicaid, 2=Private insurance, 3=Self pay, 4=Other)


In [56]:
df.pay_rec.replace([9], np.nan, inplace=True)
df.pay_rec.value_counts().sort_index()


Out[56]:
1    1497162
2    1628336
3     147475
4     174821
Name: pay_rec, dtype: int64

In [57]:
var = 'pay_rec'
df[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[57]:
boy
pay_rec
1 104
2 105
3 105
4 105

Sex of baby


In [58]:
df.sex.value_counts().sort_index()


Out[58]:
F    1935228
M    2025568
Name: sex, dtype: int64

Regression models

Here are some functions I'll use to interpret the results of logistic regression


In [59]:
def logodds_to_ratio(logodds):
    """Convert from log odds to probability."""
    odds = np.exp(logodds)
    return 100 * odds

def summarize(results):
    """Summarize parameters in terms of birth ratio."""
    inter_or = results.params['Intercept']
    inter_rat = logodds_to_ratio(inter_or)
    
    for value, lor in results.params.iteritems():
        if value=='Intercept':
            continue
        
        rat = logodds_to_ratio(inter_or + lor)
        code = '*' if results.pvalues[value] < 0.05 else ' '
        
        print('%-20s   %0.1f   %0.1f' % (value, inter_rat, rat), code)

Now I'll run models with each variable, one at a time.

Mother's age seems to have no predictive value:


In [60]:
model = smf.logit('boy ~ mager9', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692887
         Iterations 3
mager9                 104.9   104.8  
Out[60]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3960796
Model: Logit Df Residuals: 3960794
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.778e-08
Time: 14:54:16 Log-Likelihood: -2.7444e+06
converged: True LL-Null: -2.7444e+06
LLR p-value: 0.5733
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0475 0.004 13.358 0.000 0.041 0.055
mager9 -0.0005 0.001 -0.563 0.573 -0.002 0.001

The estimated ratios for young mothers is higher, and the ratio for older mothers is lower, but neither is statistically significant.


In [61]:
model = smf.logit('boy ~ youngm + oldm', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692886
         Iterations 3
youngm[T.True]         104.6   105.6 *
oldm[T.True]           104.6   104.4  
Out[61]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3960796
Model: Logit Df Residuals: 3960793
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.205e-06
Time: 14:54:22 Log-Likelihood: -2.7444e+06
converged: True LL-Null: -2.7444e+06
LLR p-value: 0.03667
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0449 0.001 42.231 0.000 0.043 0.047
youngm[T.True] 0.0095 0.004 2.529 0.011 0.002 0.017
oldm[T.True] -0.0020 0.006 -0.334 0.739 -0.014 0.010

Neither does residence status


In [62]:
model = smf.logit('boy ~ C(restatus)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692887
         Iterations 3
C(restatus)[T.2]       104.6   104.7  
C(restatus)[T.3]       104.6   105.4  
C(restatus)[T.4]       104.6   108.2  
Out[62]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3960796
Model: Logit Df Residuals: 3960792
Method: MLE Df Model: 3
Date: Wed, 18 May 2016 Pseudo R-squ.: 6.393e-07
Time: 14:54:48 Log-Likelihood: -2.7444e+06
converged: True LL-Null: -2.7444e+06
LLR p-value: 0.3196
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0452 0.001 38.300 0.000 0.043 0.048
C(restatus)[T.2] 0.0008 0.002 0.338 0.735 -0.004 0.005
C(restatus)[T.3] 0.0078 0.007 1.126 0.260 -0.006 0.021
C(restatus)[T.4] 0.0335 0.022 1.493 0.136 -0.011 0.078

Mother's race seems to have predictive value. Relative to whites, black and Native American mothers have more girls; Asians have more boys.


In [63]:
model = smf.logit('boy ~ C(mbrace)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692881
         Iterations 3
C(mbrace)[T.2]         104.8   103.3 *
C(mbrace)[T.3]         104.8   104.0  
C(mbrace)[T.4]         104.8   106.3 *
Out[63]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3960796
Model: Logit Df Residuals: 3960792
Method: MLE Df Model: 3
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.640e-06
Time: 14:55:15 Log-Likelihood: -2.7444e+06
converged: True LL-Null: -2.7444e+06
LLR p-value: 2.829e-10
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0471 0.001 40.838 0.000 0.045 0.049
C(mbrace)[T.2] -0.0149 0.003 -5.382 0.000 -0.020 -0.009
C(mbrace)[T.3] -0.0075 0.009 -0.799 0.424 -0.026 0.011
C(mbrace)[T.4] 0.0143 0.004 3.567 0.000 0.006 0.022

Hispanic mothers have more girls.


In [64]:
model = smf.logit('boy ~ mhisp', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692884
         Iterations 3
mhisp                  105.0   103.6 *
Out[64]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3929904
Model: Logit Df Residuals: 3929902
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.225e-06
Time: 14:55:20 Log-Likelihood: -2.7230e+06
converged: True LL-Null: -2.7230e+06
LLR p-value: 9.580e-08
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0485 0.001 42.133 0.000 0.046 0.051
mhisp -0.0127 0.002 -5.335 0.000 -0.017 -0.008

If the mother is married or unmarried but paternity is acknowledged, the sex ratio is higher (more boys)


In [65]:
model = smf.logit('boy ~ C(mar_p)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692875
         Iterations 3
C(mar_p)[T.Y]          103.4   104.9 *
Out[65]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3488521
Model: Logit Df Residuals: 3488519
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 4.062e-06
Time: 14:55:45 Log-Likelihood: -2.4171e+06
converged: True LL-Null: -2.4171e+06
LLR p-value: 9.370e-06
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0338 0.003 11.071 0.000 0.028 0.040
C(mar_p)[T.Y] 0.0144 0.003 4.431 0.000 0.008 0.021

Being unmarried predicts more girls.


In [66]:
model = smf.logit('boy ~ C(dmar)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692885
         Iterations 3
C(dmar)[T.2]           105.0   104.2 *
Out[66]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3960796
Model: Logit Df Residuals: 3960794
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 2.561e-06
Time: 14:56:11 Log-Likelihood: -2.7444e+06
converged: True LL-Null: -2.7444e+06
LLR p-value: 0.0001776
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0487 0.001 37.345 0.000 0.046 0.051
C(dmar)[T.2] -0.0077 0.002 -3.749 0.000 -0.012 -0.004

Each level of mother's education predicts a small increase in the probability of a boy.


In [67]:
model = smf.logit('boy ~ meduc', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692874
         Iterations 3
meduc                  103.4   103.7 *
Out[67]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3452032
Model: Logit Df Residuals: 3452030
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.742e-06
Time: 14:56:15 Log-Likelihood: -2.3918e+06
converged: True LL-Null: -2.3918e+06
LLR p-value: 1.599e-07
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0330 0.003 11.862 0.000 0.028 0.038
meduc 0.0032 0.001 5.241 0.000 0.002 0.004

In [68]:
model = smf.logit('boy ~ lowed', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692875
         Iterations 3
lowed                  105.0   103.7 *
Out[68]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3452032
Model: Logit Df Residuals: 3452030
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 3.472e-06
Time: 14:56:19 Log-Likelihood: -2.3918e+06
converged: True LL-Null: -2.3918e+06
LLR p-value: 4.594e-05
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0484 0.001 40.975 0.000 0.046 0.051
lowed -0.0117 0.003 -4.075 0.000 -0.017 -0.006

Older fathers are slightly more likely to have girls (but this apparent effect could be due to chance).


In [69]:
model = smf.logit('boy ~ fagerrec11', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692865
         Iterations 3
fagerrec11             105.5   105.3  
Out[69]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3452131
Model: Logit Df Residuals: 3452129
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.250e-07
Time: 14:56:23 Log-Likelihood: -2.3919e+06
converged: True LL-Null: -2.3919e+06
LLR p-value: 0.1130
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0533 0.004 13.960 0.000 0.046 0.061
fagerrec11 -0.0012 0.001 -1.585 0.113 -0.003 0.000

In [70]:
model = smf.logit('boy ~ youngf + oldf', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692865
         Iterations 3
youngf                 104.9   105.8  
oldf                   104.9   104.2  
Out[70]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3452131
Model: Logit Df Residuals: 3452128
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 7.160e-07
Time: 14:56:28 Log-Likelihood: -2.3919e+06
converged: True LL-Null: -2.3919e+06
LLR p-value: 0.1804
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0474 0.001 42.574 0.000 0.045 0.050
youngf 0.0088 0.006 1.405 0.160 -0.003 0.021
oldf -0.0068 0.006 -1.156 0.248 -0.018 0.005

Predictions based on father's race are similar to those based on mother's race: more girls for black and Native American fathers; more boys for Asian fathers.


In [71]:
model = smf.logit('boy ~ C(fbrace)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692850
         Iterations 3
C(fbrace)[T.2.0]       105.0   103.4 *
C(fbrace)[T.3.0]       105.0   104.7  
C(fbrace)[T.4.0]       105.0   107.1 *
Out[71]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3207586
Model: Logit Df Residuals: 3207582
Method: MLE Df Model: 3
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.138e-05
Time: 14:56:53 Log-Likelihood: -2.2224e+06
converged: True LL-Null: -2.2224e+06
LLR p-value: 6.021e-11
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0492 0.001 38.677 0.000 0.047 0.052
C(fbrace)[T.2.0] -0.0161 0.003 -5.070 0.000 -0.022 -0.010
C(fbrace)[T.3.0] -0.0035 0.011 -0.328 0.743 -0.025 0.018
C(fbrace)[T.4.0] 0.0191 0.004 4.360 0.000 0.011 0.028

If the father is Hispanic, that predicts more girls.


In [72]:
model = smf.logit('boy ~ fhisp', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692864
         Iterations 3
fhisp                  105.2   103.6 *
Out[72]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3400466
Model: Logit Df Residuals: 3400464
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.006e-06
Time: 14:56:57 Log-Likelihood: -2.3561e+06
converged: True LL-Null: -2.3561e+06
LLR p-value: 8.137e-10
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0508 0.001 41.012 0.000 0.048 0.053
fhisp -0.0157 0.003 -6.142 0.000 -0.021 -0.011

Father's education level might predict more boys, but the apparent effect could be due to chance.


In [73]:
model = smf.logit('boy ~ feduc', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692855
         Iterations 3
feduc                  103.9   104.1 *
Out[73]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2960402
Model: Logit Df Residuals: 2960400
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 3.476e-06
Time: 14:57:00 Log-Likelihood: -2.0511e+06
converged: True LL-Null: -2.0511e+06
LLR p-value: 0.0001591
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0379 0.003 12.866 0.000 0.032 0.044
feduc 0.0025 0.001 3.776 0.000 0.001 0.004

Babies with high birth order are slightly more likely to be girls.


In [74]:
model = smf.logit('boy ~ lbo_rec', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692885
         Iterations 3
lbo_rec                105.5   105.1 *
Out[74]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3940854
Model: Logit Df Residuals: 3940852
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 4.164e-06
Time: 14:57:05 Log-Likelihood: -2.7306e+06
converged: True LL-Null: -2.7306e+06
LLR p-value: 1.855e-06
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0536 0.002 27.348 0.000 0.050 0.057
lbo_rec -0.0038 0.001 -4.769 0.000 -0.005 -0.002

In [75]:
model = smf.logit('boy ~ highbo', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692887
         Iterations 3
highbo                 104.7   103.6 *
Out[75]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3940854
Model: Logit Df Residuals: 3940852
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.626e-07
Time: 14:57:10 Log-Likelihood: -2.7306e+06
converged: True LL-Null: -2.7306e+06
LLR p-value: 0.02997
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0460 0.001 44.570 0.000 0.044 0.048
highbo -0.0102 0.005 -2.171 0.030 -0.019 -0.001

Strangely, prenatal visits are associated with an increased probability of girls.


In [76]:
model = smf.logit('boy ~ previs', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692859
         Iterations 3
previs                 104.5   103.6 *
Out[76]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3838678
Model: Logit Df Residuals: 3838676
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 4.565e-05
Time: 14:57:15 Log-Likelihood: -2.6597e+06
converged: True LL-Null: -2.6598e+06
LLR p-value: 9.364e-55
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0436 0.001 42.437 0.000 0.042 0.046
previs -0.0086 0.001 -15.583 0.000 -0.010 -0.007

The effect seems to be non-linear at zero, so I'm adding a boolean for no prenatal visits.


In [77]:
model = smf.logit('boy ~ no_previs + previs', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692856
         Iterations 3
no_previs              104.5   99.7 *
previs                 104.5   103.5 *
Out[77]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3838678
Model: Logit Df Residuals: 3838675
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.047e-05
Time: 14:57:21 Log-Likelihood: -2.6597e+06
converged: True LL-Null: -2.6598e+06
LLR p-value: 5.053e-59
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0440 0.001 42.713 0.000 0.042 0.046
no_previs -0.0473 0.009 -5.061 0.000 -0.066 -0.029
previs -0.0097 0.001 -16.347 0.000 -0.011 -0.009

If the mother qualifies for food stamps, she is more likely to have a girl.


In [78]:
model = smf.logit('boy ~ wic', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692878
         Iterations 3
wic[T.Y]               105.2   104.2 *
Out[78]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3411631
Model: Logit Df Residuals: 3411629
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 3.607e-06
Time: 14:57:47 Log-Likelihood: -2.3638e+06
converged: True LL-Null: -2.3639e+06
LLR p-value: 3.635e-05
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0504 0.001 33.979 0.000 0.047 0.053
wic[T.Y] -0.0090 0.002 -4.130 0.000 -0.013 -0.005

Mother's height seems to have no predictive value.


In [79]:
model = smf.logit('boy ~ height', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692877
         Iterations 3
height                 99.3   99.3 *
Out[79]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3428336
Model: Logit Df Residuals: 3428334
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.043e-06
Time: 14:57:51 Log-Likelihood: -2.3754e+06
converged: True LL-Null: -2.3754e+06
LLR p-value: 0.02598
coef std err z P>|z| [95.0% Conf. Int.]
Intercept -0.0075 0.024 -0.309 0.757 -0.055 0.040
height 0.0008 0.000 2.226 0.026 0.000 0.002

In [80]:
model = smf.logit('boy ~ mtall + mshort', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692876
         Iterations 3
mtall                  104.8   104.0  
mshort                 104.8   103.3 *
Out[80]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3428336
Model: Logit Df Residuals: 3428333
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.593e-06
Time: 14:57:55 Log-Likelihood: -2.3754e+06
converged: True LL-Null: -2.3754e+06
LLR p-value: 0.02272
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0472 0.001 42.200 0.000 0.045 0.049
mtall -0.0076 0.006 -1.249 0.212 -0.020 0.004
mshort -0.0145 0.006 -2.494 0.013 -0.026 -0.003

Mother's with higher BMI are more likely to have girls.


In [81]:
model = smf.logit('boy ~ bmi_r', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692879
         Iterations 3
bmi_r                  105.4   105.1 *
Out[81]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3343730
Model: Logit Df Residuals: 3343728
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.109e-06
Time: 14:57:59 Log-Likelihood: -2.3168e+06
converged: True LL-Null: -2.3168e+06
LLR p-value: 0.02338
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0523 0.003 18.191 0.000 0.047 0.058
bmi_r -0.0021 0.001 -2.267 0.023 -0.004 -0.000

In [82]:
model = smf.logit('boy ~ obese', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692878
         Iterations 3
obese                  104.9   104.1 *
Out[82]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3343730
Model: Logit Df Residuals: 3343728
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.833e-06
Time: 14:58:03 Log-Likelihood: -2.3168e+06
converged: True LL-Null: -2.3168e+06
LLR p-value: 0.003567
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0481 0.001 38.389 0.000 0.046 0.051
obese -0.0075 0.003 -2.914 0.004 -0.013 -0.002

If payment was made by Medicaid, the baby is more likely to be a girl. Private insurance, self-payment, and other payment method are associated with more boys.


In [83]:
model = smf.logit('boy ~ C(pay_rec)', data=df)    
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692877
         Iterations 3
C(pay_rec)[T.2.0]      104.4   105.1 *
C(pay_rec)[T.3.0]      104.4   105.3  
C(pay_rec)[T.4.0]      104.4   104.7  
Out[83]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3447794
Model: Logit Df Residuals: 3447790
Method: MLE Df Model: 3
Date: Wed, 18 May 2016 Pseudo R-squ.: 2.074e-06
Time: 14:58:29 Log-Likelihood: -2.3889e+06
converged: True LL-Null: -2.3889e+06
LLR p-value: 0.01934
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0427 0.002 26.107 0.000 0.039 0.046
C(pay_rec)[T.2.0] 0.0067 0.002 2.944 0.003 0.002 0.011
C(pay_rec)[T.3.0] 0.0094 0.005 1.720 0.085 -0.001 0.020
C(pay_rec)[T.4.0] 0.0033 0.005 0.645 0.519 -0.007 0.013

Adding controls

However, none of the previous results should be taken too seriously. We only tested one variable at a time, and many of these apparent effects disappear when we add control variables.

In particular, if we control for father's race and Hispanic origin, the mother's race has no additional predictive value.


In [84]:
formula = ('boy ~ C(fbrace) + fhisp + C(mbrace) + mhisp')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692846
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.3 *
C(fbrace)[T.3.0]       105.5   104.1  
C(fbrace)[T.4.0]       105.5   107.0  
C(mbrace)[T.2]         105.5   105.7  
C(mbrace)[T.3]         105.5   106.9  
C(mbrace)[T.4]         105.5   105.6  
fhisp                  105.5   104.1 *
mhisp                  105.5   105.0  
Out[84]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3184121
Model: Logit Df Residuals: 3184112
Method: MLE Df Model: 8
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.935e-05
Time: 14:59:16 Log-Likelihood: -2.2061e+06
converged: True LL-Null: -2.2061e+06
LLR p-value: 3.988e-15
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0531 0.001 35.736 0.000 0.050 0.056
C(fbrace)[T.2.0] -0.0211 0.006 -3.688 0.000 -0.032 -0.010
C(fbrace)[T.3.0] -0.0125 0.013 -1.002 0.316 -0.037 0.012
C(fbrace)[T.4.0] 0.0142 0.007 1.936 0.053 -0.000 0.029
C(mbrace)[T.2] 0.0022 0.006 0.367 0.714 -0.010 0.014
C(mbrace)[T.3] 0.0140 0.013 1.076 0.282 -0.012 0.040
C(mbrace)[T.4] 0.0013 0.007 0.186 0.853 -0.012 0.015
fhisp -0.0132 0.004 -2.951 0.003 -0.022 -0.004
mhisp -0.0046 0.004 -1.045 0.296 -0.013 0.004

In fact, once we control for father's race and Hispanic origin, almost every other variable becomes statistically insignificant, including acknowledged paternity.


In [85]:
formula = ('boy ~ C(fbrace) + fhisp + mar_p')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692837
         Iterations 3
C(fbrace)[T.2.0]       105.1   103.0 *
C(fbrace)[T.3.0]       105.1   104.0  
C(fbrace)[T.4.0]       105.1   106.6 *
mar_p[T.Y]             105.1   105.6  
fhisp                  105.1   103.3 *
Out[85]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2798315
Model: Logit Df Residuals: 2798309
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.968e-05
Time: 15:00:03 Log-Likelihood: -1.9388e+06
converged: True LL-Null: -1.9388e+06
LLR p-value: 4.935e-15
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0497 0.014 3.433 0.001 0.021 0.078
C(fbrace)[T.2.0] -0.0201 0.003 -5.761 0.000 -0.027 -0.013
C(fbrace)[T.3.0] -0.0104 0.012 -0.858 0.391 -0.034 0.013
C(fbrace)[T.4.0] 0.0144 0.005 3.013 0.003 0.005 0.024
mar_p[T.Y] 0.0045 0.014 0.310 0.757 -0.024 0.033
fhisp -0.0177 0.003 -5.694 0.000 -0.024 -0.012

Being married still predicts more boys.


In [86]:
formula = ('boy ~ C(fbrace) + fhisp + dmar')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692846
         Iterations 3
C(fbrace)[T.2.0]       104.9   102.7 *
C(fbrace)[T.3.0]       104.9   104.1  
C(fbrace)[T.4.0]       104.9   106.6 *
fhisp                  104.9   103.0 *
dmar                   104.9   105.3  
Out[86]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3188403
Model: Logit Df Residuals: 3188397
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.937e-05
Time: 15:00:29 Log-Likelihood: -2.2091e+06
converged: True LL-Null: -2.2091e+06
LLR p-value: 5.665e-17
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0478 0.003 13.880 0.000 0.041 0.055
C(fbrace)[T.2.0] -0.0209 0.003 -6.174 0.000 -0.028 -0.014
C(fbrace)[T.3.0] -0.0079 0.011 -0.728 0.467 -0.029 0.013
C(fbrace)[T.4.0] 0.0159 0.004 3.589 0.000 0.007 0.025
fhisp -0.0177 0.003 -5.947 0.000 -0.024 -0.012
dmar 0.0043 0.003 1.667 0.096 -0.001 0.009

The effect of education disappears.


In [87]:
formula = ('boy ~ C(fbrace) + fhisp + lowed')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692836
         Iterations 3
C(fbrace)[T.2.0]       105.6   103.6 *
C(fbrace)[T.3.0]       105.6   104.6  
C(fbrace)[T.4.0]       105.6   107.1 *
fhisp                  105.6   103.9 *
lowed                  105.6   105.0  
Out[87]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2777435
Model: Logit Df Residuals: 2777429
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.992e-05
Time: 15:00:55 Log-Likelihood: -1.9243e+06
converged: True LL-Null: -1.9243e+06
LLR p-value: 4.189e-15
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0546 0.002 34.777 0.000 0.052 0.058
C(fbrace)[T.2.0] -0.0198 0.004 -5.634 0.000 -0.027 -0.013
C(fbrace)[T.3.0] -0.0100 0.012 -0.823 0.410 -0.034 0.014
C(fbrace)[T.4.0] 0.0141 0.005 2.925 0.003 0.005 0.024
fhisp -0.0163 0.003 -4.999 0.000 -0.023 -0.010
lowed -0.0055 0.004 -1.471 0.141 -0.013 0.002

The effect of birth order disappears.


In [88]:
formula = ('boy ~ C(fbrace) + fhisp + highbo')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692847
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.5 *
C(fbrace)[T.3.0]       105.5   104.7  
C(fbrace)[T.4.0]       105.5   107.1 *
fhisp                  105.5   103.8 *
highbo                 105.5   104.8  
Out[88]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3175026
Model: Logit Df Residuals: 3175020
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.881e-05
Time: 15:01:20 Log-Likelihood: -2.1998e+06
converged: True LL-Null: -2.1998e+06
LLR p-value: 2.209e-16
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0531 0.001 36.240 0.000 0.050 0.056
C(fbrace)[T.2.0] -0.0192 0.003 -5.879 0.000 -0.026 -0.013
C(fbrace)[T.3.0] -0.0074 0.011 -0.683 0.495 -0.029 0.014
C(fbrace)[T.4.0] 0.0154 0.004 3.457 0.001 0.007 0.024
fhisp -0.0163 0.003 -5.586 0.000 -0.022 -0.011
highbo -0.0062 0.005 -1.127 0.260 -0.017 0.005

WIC is no longer associated with more girls.


In [89]:
formula = ('boy ~ C(fbrace) + fhisp + wic')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692838
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.4 *
C(fbrace)[T.3.0]       105.5   104.7  
C(fbrace)[T.4.0]       105.5   107.1 *
wic[T.Y]               105.5   105.6  
fhisp                  105.5   103.6 *
Out[89]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2735525
Model: Logit Df Residuals: 2735519
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 2.029e-05
Time: 15:02:07 Log-Likelihood: -1.8953e+06
converged: True LL-Null: -1.8953e+06
LLR p-value: 3.710e-15
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0539 0.002 31.172 0.000 0.050 0.057
C(fbrace)[T.2.0] -0.0209 0.004 -5.723 0.000 -0.028 -0.014
C(fbrace)[T.3.0] -0.0078 0.012 -0.636 0.525 -0.032 0.016
C(fbrace)[T.4.0] 0.0148 0.005 3.044 0.002 0.005 0.024
wic[T.Y] 0.0007 0.003 0.264 0.792 -0.004 0.006
fhisp -0.0181 0.003 -5.484 0.000 -0.025 -0.012

The effect of obesity disappears.


In [90]:
formula = ('boy ~ C(fbrace) + fhisp + obese')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692838
         Iterations 3
C(fbrace)[T.2.0]       105.7   103.5 *
C(fbrace)[T.3.0]       105.7   104.2  
C(fbrace)[T.4.0]       105.7   107.2 *
fhisp                  105.7   103.9 *
obese                  105.7   105.1  
Out[90]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2686167
Model: Logit Df Residuals: 2686161
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 2.202e-05
Time: 15:02:31 Log-Likelihood: -1.8611e+06
converged: True LL-Null: -1.8611e+06
LLR p-value: 3.274e-16
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0552 0.002 32.697 0.000 0.052 0.059
C(fbrace)[T.2.0] -0.0210 0.004 -5.842 0.000 -0.028 -0.014
C(fbrace)[T.3.0] -0.0137 0.012 -1.109 0.267 -0.038 0.011
C(fbrace)[T.4.0] 0.0145 0.005 2.949 0.003 0.005 0.024
fhisp -0.0174 0.003 -5.490 0.000 -0.024 -0.011
obese -0.0052 0.003 -1.770 0.077 -0.011 0.001

The effect of payment method is diminished, but self-payment is still associated with more boys.


In [91]:
formula = ('boy ~ C(fbrace) + fhisp + C(pay_rec)')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692835
         Iterations 3
C(fbrace)[T.2.0]       105.9   103.6 *
C(fbrace)[T.3.0]       105.9   104.7  
C(fbrace)[T.4.0]       105.9   107.4 *
C(pay_rec)[T.2.0]      105.9   105.3  
C(pay_rec)[T.3.0]      105.9   107.0  
C(pay_rec)[T.4.0]      105.9   105.7  
fhisp                  105.9   103.8 *
Out[91]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2763347
Model: Logit Df Residuals: 2763339
Method: MLE Df Model: 7
Date: Wed, 18 May 2016 Pseudo R-squ.: 2.100e-05
Time: 15:03:17 Log-Likelihood: -1.9145e+06
converged: True LL-Null: -1.9146e+06
LLR p-value: 1.132e-14
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0571 0.002 22.914 0.000 0.052 0.062
C(fbrace)[T.2.0] -0.0214 0.004 -5.920 0.000 -0.028 -0.014
C(fbrace)[T.3.0] -0.0113 0.012 -0.915 0.360 -0.035 0.013
C(fbrace)[T.4.0] 0.0142 0.005 2.955 0.003 0.005 0.024
C(pay_rec)[T.2.0] -0.0050 0.003 -1.839 0.066 -0.010 0.000
C(pay_rec)[T.3.0] 0.0103 0.007 1.580 0.114 -0.002 0.023
C(pay_rec)[T.4.0] -0.0016 0.006 -0.274 0.784 -0.013 0.010
fhisp -0.0193 0.003 -5.917 0.000 -0.026 -0.013

But the effect of prenatal visits is still a strong predictor of more girls.


In [92]:
formula = ('boy ~ C(fbrace) + fhisp + previs')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692809
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.0 *
C(fbrace)[T.3.0]       105.5   104.1  
C(fbrace)[T.4.0]       105.5   107.0 *
fhisp                  105.5   103.4 *
previs                 105.5   104.4 *
Out[92]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3097584
Model: Logit Df Residuals: 3097578
Method: MLE Df Model: 5
Date: Wed, 18 May 2016 Pseudo R-squ.: 7.830e-05
Time: 15:03:43 Log-Likelihood: -2.1460e+06
converged: True LL-Null: -2.1462e+06
LLR p-value: 1.719e-70
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0532 0.001 36.168 0.000 0.050 0.056
C(fbrace)[T.2.0] -0.0237 0.003 -7.129 0.000 -0.030 -0.017
C(fbrace)[T.3.0] -0.0129 0.011 -1.170 0.242 -0.035 0.009
C(fbrace)[T.4.0] 0.0141 0.005 3.112 0.002 0.005 0.023
fhisp -0.0193 0.003 -6.533 0.000 -0.025 -0.014
previs -0.0103 0.001 -16.043 0.000 -0.012 -0.009

And the effect is even stronger if we add a boolean to capture the nonlinearity at 0 visits.


In [93]:
formula = ('boy ~ C(fbrace) + fhisp + previs + no_previs')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692805
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.1 *
C(fbrace)[T.3.0]       105.5   104.1  
C(fbrace)[T.4.0]       105.5   107.0 *
fhisp                  105.5   103.5 *
previs                 105.5   104.3 *
no_previs              105.5   99.6 *
Out[93]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3097584
Model: Logit Df Residuals: 3097577
Method: MLE Df Model: 6
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.320e-05
Time: 15:04:09 Log-Likelihood: -2.1460e+06
converged: True LL-Null: -2.1462e+06
LLR p-value: 4.542e-74
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0536 0.001 36.382 0.000 0.051 0.057
C(fbrace)[T.2.0] -0.0235 0.003 -7.087 0.000 -0.030 -0.017
C(fbrace)[T.3.0] -0.0131 0.011 -1.188 0.235 -0.035 0.009
C(fbrace)[T.4.0] 0.0139 0.005 3.070 0.002 0.005 0.023
fhisp -0.0191 0.003 -6.468 0.000 -0.025 -0.013
previs -0.0113 0.001 -16.666 0.000 -0.013 -0.010
no_previs -0.0573 0.012 -4.587 0.000 -0.082 -0.033

More controls

Now if we control for father's race and Hispanic origin as well as number of prenatal visits, the effect of marriage disappears.


In [94]:
formula = ('boy ~ C(fbrace) + fhisp + previs + dmar')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692808
         Iterations 3
C(fbrace)[T.2.0]       105.2   102.6 *
C(fbrace)[T.3.0]       105.2   103.8  
C(fbrace)[T.4.0]       105.2   106.7 *
fhisp                  105.2   103.1 *
previs                 105.2   104.1 *
dmar                   105.2   105.4  
Out[94]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3097584
Model: Logit Df Residuals: 3097577
Method: MLE Df Model: 6
Date: Wed, 18 May 2016 Pseudo R-squ.: 7.846e-05
Time: 15:04:35 Log-Likelihood: -2.1460e+06
converged: True LL-Null: -2.1462e+06
LLR p-value: 1.058e-69
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0506 0.004 14.449 0.000 0.044 0.057
C(fbrace)[T.2.0] -0.0245 0.003 -7.072 0.000 -0.031 -0.018
C(fbrace)[T.3.0] -0.0136 0.011 -1.227 0.220 -0.035 0.008
C(fbrace)[T.4.0] 0.0142 0.005 3.151 0.002 0.005 0.023
fhisp -0.0198 0.003 -6.561 0.000 -0.026 -0.014
previs -0.0103 0.001 -15.969 0.000 -0.012 -0.009
dmar 0.0022 0.003 0.828 0.408 -0.003 0.007

The effect of payment method disappears.


In [95]:
formula = ('boy ~ C(fbrace) + fhisp + previs + C(pay_rec)')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692799
         Iterations 3
C(fbrace)[T.2.0]       105.7   103.1 *
C(fbrace)[T.3.0]       105.7   104.0  
C(fbrace)[T.4.0]       105.7   107.0 *
C(pay_rec)[T.2.0]      105.7   105.6  
C(pay_rec)[T.3.0]      105.7   105.7  
C(pay_rec)[T.4.0]      105.7   105.3  
fhisp                  105.7   103.6 *
previs                 105.7   104.6 *
Out[95]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2679860
Model: Logit Df Residuals: 2679851
Method: MLE Df Model: 8
Date: Wed, 18 May 2016 Pseudo R-squ.: 7.905e-05
Time: 15:05:21 Log-Likelihood: -1.8566e+06
converged: True LL-Null: -1.8568e+06
LLR p-value: 9.714e-59
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0553 0.003 21.819 0.000 0.050 0.060
C(fbrace)[T.2.0] -0.0248 0.004 -6.723 0.000 -0.032 -0.018
C(fbrace)[T.3.0] -0.0166 0.012 -1.326 0.185 -0.041 0.008
C(fbrace)[T.4.0] 0.0128 0.005 2.610 0.009 0.003 0.022
C(pay_rec)[T.2.0] -0.0012 0.003 -0.436 0.663 -0.007 0.004
C(pay_rec)[T.3.0] 3.729e-05 0.007 0.006 0.996 -0.013 0.013
C(pay_rec)[T.4.0] -0.0035 0.006 -0.589 0.556 -0.015 0.008
fhisp -0.0203 0.003 -6.114 0.000 -0.027 -0.014
previs -0.0103 0.001 -14.715 0.000 -0.012 -0.009

Here's a version with the addition of a boolean for no prenatal visits.


In [96]:
formula = ('boy ~ C(fbrace) + fhisp + previs + no_previs')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692805
         Iterations 3
C(fbrace)[T.2.0]       105.5   103.1 *
C(fbrace)[T.3.0]       105.5   104.1  
C(fbrace)[T.4.0]       105.5   107.0 *
fhisp                  105.5   103.5 *
previs                 105.5   104.3 *
no_previs              105.5   99.6 *
Out[96]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3097584
Model: Logit Df Residuals: 3097577
Method: MLE Df Model: 6
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.320e-05
Time: 15:05:46 Log-Likelihood: -2.1460e+06
converged: True LL-Null: -2.1462e+06
LLR p-value: 4.542e-74
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0536 0.001 36.382 0.000 0.051 0.057
C(fbrace)[T.2.0] -0.0235 0.003 -7.087 0.000 -0.030 -0.017
C(fbrace)[T.3.0] -0.0131 0.011 -1.188 0.235 -0.035 0.009
C(fbrace)[T.4.0] 0.0139 0.005 3.070 0.002 0.005 0.023
fhisp -0.0191 0.003 -6.468 0.000 -0.025 -0.013
previs -0.0113 0.001 -16.666 0.000 -0.013 -0.010
no_previs -0.0573 0.012 -4.587 0.000 -0.082 -0.033

Now, surprisingly, the mother's age has a small effect.


In [97]:
formula = ('boy ~ C(fbrace) + fhisp + previs + no_previs + mager9')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692805
         Iterations 3
C(fbrace)[T.2.0]       106.2   103.7 *
C(fbrace)[T.3.0]       106.2   104.8  
C(fbrace)[T.4.0]       106.2   107.8 *
fhisp                  106.2   104.2 *
previs                 106.2   105.0 *
no_previs              106.2   100.3 *
mager9                 106.2   106.1  
Out[97]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3097584
Model: Logit Df Residuals: 3097576
Method: MLE Df Model: 7
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.378e-05
Time: 15:06:13 Log-Likelihood: -2.1460e+06
converged: True LL-Null: -2.1462e+06
LLR p-value: 1.081e-73
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0603 0.004 13.417 0.000 0.051 0.069
C(fbrace)[T.2.0] -0.0241 0.003 -7.209 0.000 -0.031 -0.018
C(fbrace)[T.3.0] -0.0139 0.011 -1.255 0.209 -0.036 0.008
C(fbrace)[T.4.0] 0.0144 0.005 3.176 0.001 0.006 0.023
fhisp -0.0196 0.003 -6.592 0.000 -0.025 -0.014
previs -0.0113 0.001 -16.525 0.000 -0.013 -0.010
no_previs -0.0571 0.012 -4.578 0.000 -0.082 -0.033
mager9 -0.0015 0.001 -1.573 0.116 -0.003 0.000

So does the father's age. But both age effects are small and borderline significant.


In [98]:
formula = ('boy ~ C(fbrace) + fhisp + previs + no_previs + fagerrec11')
model = smf.logit(formula, data=df)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692804
         Iterations 3
C(fbrace)[T.2.0]       106.4   103.8 *
C(fbrace)[T.3.0]       106.4   105.0  
C(fbrace)[T.4.0]       106.4   107.9 *
fhisp                  106.4   104.3 *
previs                 106.4   105.2 *
no_previs              106.4   100.4 *
fagerrec11             106.4   106.2 *
Out[98]:
Logit Regression Results
Dep. Variable: boy No. Observations: 3088740
Model: Logit Df Residuals: 3088732
Method: MLE Df Model: 7
Date: Wed, 18 May 2016 Pseudo R-squ.: 8.510e-05
Time: 15:06:39 Log-Likelihood: -2.1399e+06
converged: True LL-Null: -2.1401e+06
LLR p-value: 1.099e-74
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0620 0.004 14.546 0.000 0.054 0.070
C(fbrace)[T.2.0] -0.0243 0.003 -7.284 0.000 -0.031 -0.018
C(fbrace)[T.3.0] -0.0137 0.011 -1.236 0.217 -0.035 0.008
C(fbrace)[T.4.0] 0.0143 0.005 3.143 0.002 0.005 0.023
fhisp -0.0197 0.003 -6.622 0.000 -0.026 -0.014
previs -0.0113 0.001 -16.639 0.000 -0.013 -0.010
no_previs -0.0581 0.013 -4.637 0.000 -0.083 -0.034
fagerrec11 -0.0017 0.001 -2.082 0.037 -0.003 -0.000

What's up with prenatal visits?

The predictive power of prenatal visits is still surprising to me. To make sure we're controlled for race, I'll select cases where both parents are white:


In [99]:
white = df[(df.mbrace==1) & (df.fbrace==1)]
len(white)


Out[99]:
2381977

And compute sex ratios for each level of previs


In [100]:
var = 'previs'
white[[var, 'boy']].groupby(var).aggregate(series_to_ratio)


Out[100]:
boy
previs
-6 106
-5 110
-4 108
-3 109
-2 108
-1 107
0 105
1 103
2 102
3 100
4 103

The effect holds up. People with fewer than average prenatal visits are substantially more likely to have boys.


In [101]:
formula = ('boy ~ previs + no_previs')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692804
         Iterations 3
previs                 105.1   103.8 *
no_previs              105.1   98.9 *
Out[101]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2320227
Model: Logit Df Residuals: 2320224
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 6.584e-05
Time: 15:06:43 Log-Likelihood: -1.6075e+06
converged: True LL-Null: -1.6076e+06
LLR p-value: 1.073e-46
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0493 0.001 37.359 0.000 0.047 0.052
previs -0.0116 0.001 -14.535 0.000 -0.013 -0.010
no_previs -0.0608 0.015 -3.966 0.000 -0.091 -0.031

In [102]:
inter = results.params['Intercept']
slope = results.params['previs']
inter, slope


Out[102]:
(0.04929183382635937, -0.011584489975776435)

In [103]:
previs = np.arange(-5, 5)
logodds = inter + slope * previs
odds = np.exp(logodds)
odds * 100


Out[103]:
array([ 111.31727637,  110.03516315,  108.76781686,  107.51506742,
        106.2767467 ,  105.05268853,  103.84272863,  102.64670462,
        101.46445599,  100.29582409])

In [104]:
formula = ('boy ~ dmar')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692845
         Iterations 3
dmar                   105.2   105.1  
Out[104]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2381977
Model: Logit Df Residuals: 2381975
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 3.675e-08
Time: 15:06:46 Log-Likelihood: -1.6503e+06
converged: True LL-Null: -1.6503e+06
LLR p-value: 0.7276
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0505 0.004 12.847 0.000 0.043 0.058
dmar -0.0010 0.003 -0.348 0.728 -0.007 0.005

In [105]:
formula = ('boy ~ lowed')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692830
         Iterations 3
lowed                  105.3   103.9 *
Out[105]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2089901
Model: Logit Df Residuals: 2089899
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 4.146e-06
Time: 15:06:48 Log-Likelihood: -1.4479e+06
converged: True LL-Null: -1.4480e+06
LLR p-value: 0.0005303
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0520 0.001 35.035 0.000 0.049 0.055
lowed -0.0142 0.004 -3.465 0.001 -0.022 -0.006

In [106]:
formula = ('boy ~ highbo')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692845
         Iterations 3
highbo                 105.1   104.1  
Out[106]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2373894
Model: Logit Df Residuals: 2373892
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 6.498e-07
Time: 15:06:50 Log-Likelihood: -1.6447e+06
converged: True LL-Null: -1.6447e+06
LLR p-value: 0.1437
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0496 0.001 37.359 0.000 0.047 0.052
highbo -0.0095 0.006 -1.462 0.144 -0.022 0.003

In [107]:
formula = ('boy ~ wic')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692836
         Iterations 3
wic[T.Y]               105.3   104.8  
Out[107]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2059437
Model: Logit Df Residuals: 2059435
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 1.267e-06
Time: 15:07:06 Log-Likelihood: -1.4269e+06
converged: True LL-Null: -1.4269e+06
LLR p-value: 0.05720
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0519 0.002 29.448 0.000 0.048 0.055
wic[T.Y] -0.0055 0.003 -1.902 0.057 -0.011 0.000

In [108]:
formula = ('boy ~ obese')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692834
         Iterations 3
obese                  105.2   104.8  
Out[108]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2029161
Model: Logit Df Residuals: 2029159
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 4.153e-07
Time: 15:07:08 Log-Likelihood: -1.4059e+06
converged: True LL-Null: -1.4059e+06
LLR p-value: 0.2798
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0509 0.002 31.979 0.000 0.048 0.054
obese -0.0037 0.003 -1.081 0.280 -0.010 0.003

In [109]:
formula = ('boy ~ C(pay_rec)')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692834
         Iterations 3
C(pay_rec)[T.2.0]      105.0   105.2  
C(pay_rec)[T.3.0]      105.0   105.8  
C(pay_rec)[T.4.0]      105.0   104.8  
Out[109]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2077652
Model: Logit Df Residuals: 2077648
Method: MLE Df Model: 3
Date: Wed, 18 May 2016 Pseudo R-squ.: 5.425e-07
Time: 15:07:23 Log-Likelihood: -1.4395e+06
converged: True LL-Null: -1.4395e+06
LLR p-value: 0.6681
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0486 0.002 20.446 0.000 0.044 0.053
C(pay_rec)[T.2.0] 0.0021 0.003 0.684 0.494 -0.004 0.008
C(pay_rec)[T.3.0] 0.0076 0.007 1.036 0.300 -0.007 0.022
C(pay_rec)[T.4.0] -0.0020 0.007 -0.296 0.767 -0.015 0.011

In [110]:
formula = ('boy ~ mager9')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692845
         Iterations 3
mager9                 105.8   105.6  
Out[110]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2381977
Model: Logit Df Residuals: 2381975
Method: MLE Df Model: 1
Date: Wed, 18 May 2016 Pseudo R-squ.: 6.201e-07
Time: 15:07:27 Log-Likelihood: -1.6503e+06
converged: True LL-Null: -1.6503e+06
LLR p-value: 0.1525
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0559 0.005 11.397 0.000 0.046 0.066
mager9 -0.0016 0.001 -1.431 0.153 -0.004 0.001

In [111]:
formula = ('boy ~ youngm + oldm')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692844
         Iterations 3
youngm[T.True]         105.0   106.0  
oldm[T.True]           105.0   104.9  
Out[111]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2381977
Model: Logit Df Residuals: 2381974
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 9.503e-07
Time: 15:07:30 Log-Likelihood: -1.6503e+06
converged: True LL-Null: -1.6503e+06
LLR p-value: 0.2084
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0486 0.001 35.884 0.000 0.046 0.051
youngm[T.True] 0.0101 0.006 1.766 0.077 -0.001 0.021
oldm[T.True] -0.0004 0.008 -0.055 0.956 -0.015 0.014

In [112]:
formula = ('boy ~ youngf + oldf')
model = smf.logit(formula, data=white)
results = model.fit()
summarize(results)
results.summary()


Optimization terminated successfully.
         Current function value: 0.692843
         Iterations 3
youngf                 105.1   105.6  
oldf                   105.1   104.0  
Out[112]:
Logit Regression Results
Dep. Variable: boy No. Observations: 2376438
Model: Logit Df Residuals: 2376435
Method: MLE Df Model: 2
Date: Wed, 18 May 2016 Pseudo R-squ.: 7.327e-07
Time: 15:07:34 Log-Likelihood: -1.6465e+06
converged: True LL-Null: -1.6465e+06
LLR p-value: 0.2993
coef std err z P>|z| [95.0% Conf. Int.]
Intercept 0.0495 0.001 37.030 0.000 0.047 0.052
youngf 0.0053 0.008 0.652 0.514 -0.011 0.021
oldf -0.0107 0.008 -1.390 0.164 -0.026 0.004

In [ ]:


In [ ]: