Using SPSS raking algorithm handling population and sample differences

1. WEIGHTING OF DATA
Robert Radicsa (riradics@ncsu.edu), Sudipta Dasmohapatrab (sdasmoh@ncsu.edu), Steve Kelley c (sskelley@ncsu.edu),
a Graduate Research Assistant, b Associate Prof., c Department Head, Department of Forest Biomaterials, College of Natural Resources
Data Collection Method
Abstract
Data collected from consumer samples in the IBSS
project was adjusted (weighted) to make inferences
to the population in the states of NC and TN. This
paper presents information from the lessons learned
during the process of weighting of the data when
using multiple variables to account for differences
between a selected sample and the population.
Goal of Weighting and Raking
Battaglia, M., Hoaglin, D., & Frankel, M. (2013). Practical considerations in raking survey data.
http://magmods.wordpress.com/2011/03/23/magmods-questionnaire-3/
Weighting with More Variables; Raking
Battaglia, M., Hoaglin, D., & Frankel, M. (2013). Practical considerations in raking survey data.
Basic Algorithm
Limitations
Weighting with One Variable -Gender
Weighting with Two Variables – Gender,
Ethnicity
• Survey instrument
• Sampling: Randomly selected consumer
email addresses from third party
consumer database
• Data collection: Fall 2013 in NC and TN
•Pilot test: 34 consumers
•Cover Letter
• Completed Surveys:
• 586 in total
• 376 in NC and 210 in TN
• Response rate=2%
respondents % NC Census TN Census
n 376 9,848,000 209 6,496,000
Gender
Male 54.0 48.7 45.5 48.8
Female 46.0 51.3 54.5 51.2
Education
College 4 or 4+ 66.7 26.8 31.0 23.5
Ethnicity
White/Caucasian 79.0 71.9 88.5 79
Black/African-American 10.1 22.0 6.7 17
Age
18-24 9.6 10.0 10.3 2.1
25-44 26.5 43.1 26.8 26.6
45-64 26.9 24.9 26.2 52.1
65+ 13.3 1.0 12.4 17.8
Sample and Population
Demography Data
Sample data do not have the same demographics
proportions as the population data have.
Weighting and raking improve the relation between
the sample and the population by fine tuning the
sampling weights of the cases. At the end of the
process the marginal totals of the adjusted weights
on different characteristics are equal to the totals of
the population on the similar characteristics.
NC Census Weight
n 376 9,848,000 Census% / Sample%
Gender
Male 54 48.7 0.90
Female 46 51.3 1.12
• All male respondents get 0.90 weight for statistic analyses.
• All female respondents get 1.12 weight for statistic analyses.
NC Census Weight
n 376 9,848,000 Census% / Sample%
Gender
Male 54 48.7 0.90
Female 46 51.3 1.12
Ethnicity
White/Caucasian 79 71.9 0.91
Black/African-
American 10.1 22 2.18
Others 10.9 6.1 0.56
All respondents get two weights.
Issue: Gender proportions are not represented according to
the census because of these two multiplications.
Raking is the method of the iterative
proportional fitting.
Raking adjusts a set of data so that its
marginal totals match specified control totals
on a specified set of variables.
Raking is analogy of the process of leveling
the soil in a garden by alternately working
with a rake in two perpendicular directions.
• Lack of convergence or slow convergence.
• Large weights > 30, few respondents
represents large proportion of the
population.
• Small weights < 0.01 large proportion of the
sample represents small proportion of the
population.
The basic raking algorithm in terms of those individual weights, wi, i = 1, 2, ..., n. For an
unweighted (i.e., equally weighted) sample, one can simply take the initial weights to be wi = 1
for each i. In a cross-classification that has J rows and K columns, we denote the sum of the wi
in cell (j,k) by wjk. To indicate further summation, we replace a subscript by a + sign. Thus, the
initial row totals and column totals of the sample weights are w j+ and w+k respectively.
Analogously, we denote the corresponding population control totals by T j+ and T+k .
(1) for the sum of the modified weights in cell (j,k) at the end of step 1. If we begin by matching
the control totals for the rows, T j+, the initial steps of the algorithm are
mjk(0) = wjk (j = 1,...,J; k=1,...,K)
mjk(1) = mjk(0) ( T j+ / mj+(0) )
mjk(2) = mjk(1) ( T +k / m+k(1) )
The adjustment factors, T j+ /m j+(0) and T+k / m+k
(1), are actually applied to the individual weights, which we could denote by mi (2), for example.
In the iterative process an iteration rakes both rows and columns. For iteration s ( s = 0, 1, ...) we
may write
mjk(2s+1) = mjk(2s) ( T j+ / mj+(2s) )
mjk(2s+2) = mjk(2s+1) ( T +k / m+k(2s+1) )
Raking can also adjust a set of data to control totals on three or more variables.