Practical Considerations in Raking Survey Data

weights of the n individual respondents. Thus, the basic raking algorithm is described in terms of
those individual weights, w, i = 1,2,..., n.
For an unweighted (i.e., equally weighted) sample, one
i
can simply take the initial weights to be w = 1 for each i.
i
In a cross-classification that has J rows and K columns, denote the sum of the
wi
in cell ( j, k)
by
w . jk
To indicate further summation, replace a subscript by a + sign. Thus, the initial row totals
and column totals of the sample weights are
w
j +
and
corresponding population control totals by T +
and .
j
T + k
w + k
, respectively. Analogously, denote the
The iterative raking algorithm produces modified weights, whose sums are denoted by a suitably
subscripted m with a parenthesized superscript for the number of the step. Thus, in the twovariable
cross-classification
m (1) jk
denotes the sum of the modified weights in cell (j,k) at the end
of Step 1. If one begins by matching the control totals for the rows,
algorithm are
T
j +
, the initial steps of the
m
(0)
jk
= w
(j = 1,...,J; k=1,...,K)
jk
m = m ( T / m )
(for each k within each j)
(1) (0) (0)
jk jk j+ j+
m = m ( T / m )
(for each j within each k)
(2) (1) (1)
jk jk + k + k
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