Iterative proportional fitting is an algorithm used is many different fields such as economics or social sciences, to alter results in such a way that aggregates along one or several dimensions match known marginals (or aggregates along these same dimensions).
The algorithm exists in 2 versions:
The algorithm recognizes the input variable type and and uses the appropriate version to solve the problem. To install the package:
For more information and examples, please visit:
wikipedia page on ipf <https://en.wikipedia.org/wiki/Iterative_proportional_fitting>_slides explaining the methodology and links to specific examples <http://www.demog.berkeley.edu/~eddieh/IPFDescription/AKDOLWDIPFTWOD.pdf>_If you want to test the package, clone the repo and from the main folder, run:
The project is similar to the ipfp package available for R and tests have been run to ensure same results.
Input Variables:
original: numpy darray matrix or dataframe to perform the ipfn on.
aggregates: list of numpy array or darray or pandas dataframe/series. The aggregates are the same as the marginals. They are the target values that we want along one or several axis when aggregating along one or several axes.
dimensions: list of lists with integers if working with numpy objects, or column names if working with pandas objects. Preserved dimensions along which we sum to get the corresponding aggregates.
convergence_rate: if there are many aggregates/marginal, it could be useful to loosen the convergence criterion.
max_iteration: Integer. Maximum number of iterations allowed.
verbose: integer 0, 1 or 2. Each case number includes the outputs of the previous case numbers.
0: Updated matrix returned.
1: Flag with the output status (0 for failure and 1 for success).
2: dataframe with iteration numbers and convergence rate information at all steps.
rate_tolerance: float value. If above 0.0, like 0.001, the algorithm will stop once the difference between the conv_rate variable of 2 consecutive iterations is below that specified value.
To illustrate Iterative Proportional Fitting, Wikipedia uses an example here <https://en.wikipedia.org/wiki/Iterative_proportional_fitting#Example>_
Below is that example solved with IPFN::
import numpy as np
from ipfn import ipfn
m = [[40, 30, 20, 10], [35, 50, 100, 75], [30, 80, 70, 120], [20, 30, 40, 50]]
m = np.array(m)
xip = np.array([150, 300, 400, 150])
xpj = np.array([200, 300, 400, 100])
aggregates = [xip, xpj]
dimensions = [[0], [1]]
IPF = ipfn.ipfn(m, aggregates, dimensions, convergence_rate=1e-6)
m = IPF.iteration()
print(m)Please, follow the example below to run the package. Several additional examples in addition to the one listed below, are listed in the ipfn.py script. This example is taken from <http://www.demog.berkeley.edu/~eddieh/IPFDescription/AKDOLWDIPFTHREED.pdf>_
First, let us define a matrix of N=3 dimensions, the matrix being of specific size 243 and populate that matrix with some values ::
from ipfn import ipfn
import numpy as np
import pandas as pd
m = np.zeros((2,4,3))
m[0,0,0] = 1
m[0,0,1] = 2
m[0,0,2] = 1
m[0,1,0] = 3
m[0,1,1] = 5
m[0,1,2] = 5
m[0,2,0] = 6
m[0,2,1] = 2
m[0,2,2] = 2
m[0,3,0] = 1
m[0,3,1] = 7
m[0,3,2] = 2
m[1,0,0] = 5
m[1,0,1] = 4
m[1,0,2] = 2
m[1,1,0] = 5
m[1,1,1] = 5
m[1,1,2] = 5
m[1,2,0] = 3
m[1,2,1] = 8
m[1,2,2] = 7
m[1,3,0] = 2
m[1,3,1] = 7
m[1,3,2] = 6Now, let us define some marginals::
xipp = np.array([52, 48]) xpjp = np.array([20, 30, 35, 15]) xppk = np.array([35, 40, 25]) xijp = np.array([[9, 17, 19, 7], [11, 13, 16, 8]]) xpjk = np.array([[7, 9, 4], [8, 12, 10], [15, 12, 8], [5, 7, 3]])
I used the letter p to denote the dimension(s) being summed over
For this specific example, they all have to be less than N=3 dimensions and be consistent with the dimensions of contingency table m. For example, the marginal along the first dimension will be made of 2 elements. We want the sum of elements in m for dimensions 2 and 3 to equal the marginal::
m[0,:,:].sum() == xipp[0]
m[1,:,:].sum() == xipp[1]Define the aggregates list and the corresponding list of dimension to indicate the algorithm which dimension(s) to sum over for each aggregate::
aggregates = [xipp, xpjp, xppk, xijp, xpjk]
dimensions = [[0], [1], [2], [0, 1], [1, 2]]Finally, run the algorithm::
IPF = ipfn.ipfn(m, aggregates, dimensions)
m = IPF.iteration()
print(xijp[0,0])
print(m[0, 0, :].sum())In the same fashion, we can run a similar example, but using a dataframe::
from ipfn import ipfn
import numpy as np
import pandas as pd
m = np.array([1., 2., 1., 3., 5., 5., 6., 2., 2., 1., 7., 2.,
5., 4., 2., 5., 5., 5., 3., 8., 7., 2., 7., 6.], )
dma_l = [501, 501, 501, 501, 501, 501, 501, 501, 501, 501, 501, 501,
502, 502, 502, 502, 502, 502, 502, 502, 502, 502, 502, 502]
size_l = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4,
1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]
age_l = ['20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45',
'20-25','30-35','40-45']
df = pd.DataFrame()
df['dma'] = dma_l
df['size'] = size_l
df['age'] = age_l
df['total'] = m
xipp = df.groupby('dma')['total'].sum()
xpjp = df.groupby('size')['total'].sum()
xppk = df.groupby('age')['total'].sum()
xijp = df.groupby(['dma', 'size'])['total'].sum()
xpjk = df.groupby(['size', 'age'])['total'].sum()
# xppk = df.groupby('age')['total'].sum()
xipp.loc[501] = 52
xipp.loc[502] = 48
xpjp.loc[1] = 20
xpjp.loc[2] = 30
xpjp.loc[3] = 35
xpjp.loc[4] = 15
xppk.loc['20-25'] = 35
xppk.loc['30-35'] = 40
xppk.loc['40-45'] = 25
xijp.loc[501] = [9, 17, 19, 7]
xijp.loc[502] = [11, 13, 16, 8]
xpjk.loc[1] = [7, 9, 4]
xpjk.loc[2] = [8, 12, 10]
xpjk.loc[3] = [15, 12, 8]
xpjk.loc[4] = [5, 7, 3]
aggregates = [xipp, xpjp, xppk, xijp, xpjk]
dimensions = [['dma'], ['size'], ['age'], ['dma', 'size'], ['size', 'age']]
IPF = ipfn.ipfn(df, aggregates, dimensions)
df = IPF.iteration()
print(df)
print(df.groupby('size')['total'].sum(), xpjp)To call the algorithm in a program, execute::
from ipfn import ipfn