In this exercise, reproduce some of the findings from What Makes Houston the Next Great American City? | Travel | Smithsonian, specifically the calculation represented in
whose caption is
To assess the parity of the four major U.S. ethnic and racial groups, Rice University researchers used a scale called the Entropy Index. It ranges from 0 (a population has just one group) to 1 (all groups are equivalent). Edging New York for the most balanced diversity, Houston had an Entropy Index of 0.874 (orange bar).
The research report by Smithsonian Magazine is Houston Region Grows More Racially/Ethnically Diverse, With Small Declines in Segregation: A Joint Report Analyzing Census Data from 1990, 2000, and 2010 by the Kinder Institute for Urban Research & the Hobby Center for the Study of Texas.
In the report, you'll find the following quotes:
How does Houston’s racial/ethnic diversity compare to the racial/ethnic diversity of other large metropolitan areas? The Houston metropolitan area is the most racially/ethnically diverse.
....
Houston is one of the most racially/ethnically diverse metropolitan areas in the nation as well. *It is the most diverse of the 10 largest U.S. metropolitan areas.* [emphasis mine] Unlike the other large metropolitan areas, all four major racial/ethnic groups have substantial representation in Houston with Latinos and Anglos occupying roughly equal shares of the population.
....
Houston has the highest entropy score of the 10 largest metropolitan areas, 0.874. New York is a close second with a score of 0.872.
....
Your task is:
Tabulate all the metropolian/micropolitan statistical areas. Remember that you have to group various entities that show up separately in the Census API but which belong to the same area. You should find 942 metropolitan/micropolitan statistical areas in the 2010 Census.
Calculate the normalized Shannon index (entropy5) using the categories of White, Black, Hispanic, Asian, and Other as outlined in the Day_07_G_Calculating_Diversity notebook
Calculate the normalized Shannon index (entropy4) by not considering the Other category. In other words, assume that the the total population is the sum of White, Black, Hispanic, and Asian.
Figure out how exactly the entropy score was calculated in the report from Rice University. Since you'll find that the entropy score reported matches neither entropy5 nor entropy4, you'll need to play around with the entropy calculation to figure how to use 4 categories to get the score for Houston to come out to "0.874" and that for NYC to be "0.872". [I think I've done so and get 0.873618 and
0.872729 respectively.]
Add a calculation of the Gini-Simpson diversity index using the five categories of White, Black, Hispanic, Asian, and Other.
Note where the Bay Area stands in terms of the diversity index.
For bonus points:
Deliverable:
msas_df.HAVE FUN: ASK QUESTIONS AND WORK TOGETHER
Below is testing code to help make sure you are on the right track. A key assumption made here is that you will end up with a Pandas DataFrame called msas_df, indexed by the FIPS code of a metropolitan/micropolitan area (e.g., Houston's code is 26420) and with the the following columns:
You should have 942 rows, one for each MSA. You can compare your results for entropy5, entropy_rice with mine.
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# FILL IN WITH YOUR CODE
from __future__ import division
%pylab --no-import-all inline
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import numpy as np
import matplotlib.pyplot as plt
from pandas import DataFrame, Series, Index
import pandas as pd
from itertools import islice
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import census
import us
import settings
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c = census.Census(key=settings.CENSUS_KEY)
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def msas(variables="NAME"):
for state in us.STATES:
geo = {'for':'metropolitan statistical area/micropolitan statistical area:*',
'in':'state:{state_fips}'.format(state_fips=state.fips)
}
for msa in c.sf1.get(variables, geo=geo):
yield msa
def states(variables='NAME'):
geo={'for':'state:*'}
states_fips = set([state.fips for state in us.states.STATES])
# need to filter out non-states
for r in c.sf1.get(variables, geo=geo):
if r['state'] in states_fips:
yield r
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def convert_P005_to_int(df):
# do conversion in place
df[list(P005_vars)] = df[list(P005_vars)].astype('int')
return df
def convert_to_rdotmap(row):
"""takes the P005 variables and maps to a series with White, Black, Asian, Hispanic, Other
Total and Name"""
return pd.Series({'MSAS': row['metropolitan statistical area/micropolitan statistical area'],
'Total':row['P0050001'],
'White':row['P0050003'],
'Black':row['P0050004'],
'Asian':row['P0050006'],
'Hispanic':row['P0050010'],
'Other': row['P0050005'] + row['P0050007'] + row['P0050008'] + row['P0050009'],
'Name': row['NAME']
}, index=['MSAS','Name', 'Total', 'White', 'Black', 'Hispanic', 'Asian', 'Other'])
def normalize(s):
"""take a Series and divide each item by the sum so that the new series adds up to 1.0"""
total = np.sum(s)
return s.astype('float') / total
def entropy(series):
"""Normalized Shannon Index"""
# a series in which all the entries are equal should result in normalized entropy of 1.0
# eliminate 0s
series1 = series[series!=0]
# if len(series) < 2 (i.e., 0 or 1) then return 0
if len(series) > 1:
# calculate the maximum possible entropy for given length of input series
max_s = -np.log(1.0/len(series))
total = float(sum(series1))
p = series1.astype('float')/float(total)
return sum(-p*np.log(p))/max_s
else:
return 0.0
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def proportion_race(df):
races=["White","Black","Asian","Hispanic","Other"]
for i in races:
df["p_"+i] = df[[races[races.index(i)],"Total"]].apply(lambda x: x[0]/x[1],axis=1)
return df
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def rice_entropy(series):
if len(series)>4:
series=series[:4]
# print series
max_s = -np.log(1.0/len(series))
rice=-1*sum([i*np.log(i) for i in series])
return rice/max_s
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def gini_simpson(series):
return 1-sum([i**2 for i in series])
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def diversity(r):
"""Returns a DataFrame with the following columns
"""
df = DataFrame(r)
df = convert_P005_to_int(df)
# df.head()
# df[list(P005_vars)] = df[list(P005_vars)].astype('int')
df1 = df.apply(convert_to_rdotmap, axis=1)
# print df1.columns
df1=df1.groupby('MSAS').sum()
df1['entropy5'] = df1[['Asian','Black','Hispanic','White','Other']].apply(entropy,axis=1)
df1['entropy4'] = df1[['Asian','Black','Hispanic','White']].apply(entropy,axis=1)
df1=proportion_race(df1)
df1['entropy_rice'] = df1[['p_Asian','p_Black','p_Hispanic','p_White','p_Other']].apply(rice_entropy,axis=1)
df1['gini_simpson'] = df1[['p_Asian','p_Black','p_Hispanic','p_White','p_Other']].apply(gini_simpson,axis=1)
return df1
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def P005_range(n0,n1):
return tuple(('P005'+ "{i:04d}".format(i=i) for i in xrange(n0,n1)))
P005_vars = P005_range(1,18)
P005_vars_str = ",".join(P005_vars)
P005_vars_with_name = ['NAME'] + list(P005_vars)
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#Testing entropy_rice
houston=[0.396931,0.167970,0.064673,0.353032,0.017394]
# sum(houston[:4])
rice_entropy(houston)
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r=list(msas(P005_vars_with_name))
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msas_df=diversity(r)
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msas_df.sort_index(by='Total', ascending=False)[:10].sort_index(by='entropy_rice',
ascending=False)
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# Testing code
def to_unicode(vals):
return [unicode(v) for v in vals]
def test_msas_df(msas_df):
min_set_of_columns = set(['Asian','Black','Hispanic', 'Other', 'Total', 'White',
'entropy4', 'entropy5', 'entropy_rice', 'gini_simpson','p_Asian', 'p_Black',
'p_Hispanic', 'p_Other','p_White'])
assert min_set_of_columns & set(msas_df.columns) == min_set_of_columns
# https://www.census.gov/geo/maps-data/data/tallies/national_geo_tallies.html
# 366 metro areas
# 576 micropolitan areas
assert len(msas_df) == 942
# total number of people in metro/micro areas
assert msas_df.Total.sum() == 289261315
assert msas_df['White'].sum() == 180912856
assert msas_df['Other'].sum() == 8540181
# list of msas in descendng order by entropy_rice
# calculate the top 10 metros by population
top_10_metros = msas_df.sort_index(by='Total', ascending=False)[:10]
msa_codes_in_top_10_pop_sorted_by_entropy_rice = list(top_10_metros.sort_index(by='entropy_rice',
ascending=False).index)
assert to_unicode(msa_codes_in_top_10_pop_sorted_by_entropy_rice)== [u'26420', u'35620', u'47900', u'31100', u'19100',
u'33100', u'16980', u'12060', u'37980', u'14460']
top_10_metro = msas_df.sort_index(by='Total', ascending=False)[:10]
list(top_10_metro.sort_index(by='entropy_rice', ascending=False)['entropy5'])
np.testing.assert_allclose(top_10_metro.sort_index(by='entropy_rice', ascending=False)['entropy5'],
[0.79628076626851163, 0.80528601550164602, 0.80809418318973791, 0.7980698349711991,
0.75945930510650161, 0.74913610558765376, 0.73683277781032397, 0.72964862063970914,
0.64082509648457675, 0.55697288400004963])
np.testing.assert_allclose(top_10_metro.sort_index(by='entropy_rice', ascending=False)['entropy_rice'],
[0.87361766576115552,
0.87272877244078051,
0.85931803868749834,
0.85508015237749468,
0.82169723530719896,
0.81953527301129059,
0.80589423784325431,
0.78602596561378812,
0.68611350427640316,
0.56978827050565117])
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# you are on the right track if test_msas_df doesn't complain
test_msas_df(msas_df)
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# code to save your dataframe to a CSV
# upload the CSV to bCourses
# uncomment to run
msas_df.to_csv("msas_2010.csv", encoding="UTF-8")
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# load back the CSV and test again
df = DataFrame.from_csv("msas_2010.csv", encoding="UTF-8")
test_msas_df(df)
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