Current Population Survey Design and Methodology - Census Bureau

the other panel in the SR SECU or NSR pseudostratum (Fay,
Dippo, and Morganstein, 1984). Thus the full sample was
included in each replicate, but the matrix determined differing
weights for the half samples. These 48 replicates
were processed through all stages of the CPS weighting
through compositing. The estimated variance for the characteristic
of interest was computed by summing a squared
difference between each replicate estimate (Y ˆ r) and the full
sample estimate (Y ˆ 0) The complete formula 1 is
Var(Yˆ 0)= 4
48 � 48
r=1
(Y ˆ r � Y ˆ 0) 2 .
Due to costs and computer limitations, variance estimates
were calculated for only 13 months (January 1987 through
January 1988) and for about 600 estimates at the national
level. Replication estimates of variances at the subnational
level were not reliable because of the small number of
SECUs available (Lent, 1991). Based on the 13 months of
variance estimates, generalized sampling errors (explained
below) were calculated. (See Wolter 1985; or Fay 1984,
1989 for more details on half-sample replication for variance
estimation.)
METHOD FOR ESTIMATING VARIANCE FOR 1990
AND 2000 DESIGNS
The general goal of the current variance estimation methodology,
the method in use since July 1995, is to produce
consistent variances and covariances for each month over
the entire life of the design. Periodic maintenance reductions
in the sample size and the continuous addition of
new construction to the sample complicated the strategy
needed to achieve this goal. However, research has shown
that variance estimates are not adversely affected as long
as the cumulative effect of the reductions is less than 20
percent of the original sample size (Kostanich, 1996).
Assigning all future new construction sample to replicates
when the variance subsamples are originally defined provides
the basis for consistency over time in the variance
estimates.
The current approach to estimating the 1990 and 2000
design variances is called successive difference replication.
The theoretical basis for the successive difference
method was discussed by Wolter (1984) and extended by
Fay and Train (1995) to produce the successive difference
replication method used for the CPS. The following is a
description of the application of this method. Successive
1
Usually balanced half-sample replication uses replicate factors
of 2 and 0 with the formula,
Var(Yˆ 0)= 1 k
(Yˆ r � Yˆ 0) 2
k � r=1
where k is the number of replicates. The factor of 4 in our variance
estimator is the result of using replicate factors of 1.5 and
0.5.
USUs 2 (ultimate sampling units) formed from adjacent hit
strings (see Chapter 3) are paired in the order of their
selection to take advantage of the systematic nature of the
CPS within-PSU sampling scheme. Each USU usually occurs
in two consecutive pairs: for example, (USU1, USU2),
(USU2, USU3), (USU3, USU4), etc. A pair then is similar to a
SECU in the 1980 design variance methodology. For each
USU within a PSU, two pairs (or SECUs) of neighboring
USUs are defined based on the order of selection—one
with the USU selected before and one with the USU
selected after it. This procedure allows USUs adjacent in
the sort order to be assigned to the same SECU, thus better
reflecting the systematic sampling in the variance estimator.
Also, the large increase in the number of SECUs and
in the number of replicates (160 vs. 48) over the 1980
design increases the precision of the variance estimator.
Replicate Factors for Total Variance
Total variance is composed of two types of variance, the
variance due to sampling of housing units within PSUs
(within-PSU variance) and the variance due to the selection
of a subset of all NSR PSUs (between-PSU variance). Replicate
factors are calculated using a 160-by-160 3 Hadamard
orthogonal matrix. To produce estimates of total variance,
replicates are formed differently for SR and NSR samples.
Between-PSU variance cannot be estimated directly using
this methodology; it is the difference between the estimates
of total variance and within-PSU variance. NSR
strata are combined into pseudo- strata within each state,
and one NSR PSU from the pseudostratum is randomly
assigned to each panel of the replicate as in the 1980
design variance methodology. Replicate factors of 1.5 or
0.5 adjust the weights for the NSR panels. These factors
are assigned based on a single row from the Hadamard
matrix and are further adjusted to account for the unequal
sizes of the original strata within the pseudostratum
(Wolter, 1985). In most cases these pseudostrata consist of
a pair of strata except where an odd number of strata
within a state requires that a triplet be formed. In this
case, for the 1990 design, two rows from the Hadamard
matrix are assigned to the pseudostratum resulting in replicate
factors of about 0.5, 1.7, and 0.8; or 1.5, 0.3, and
1.2 for the three PSUs assuming roughly equal sizes of the
original strata. However, for the 2000 design, these factors
were further adjusted to account for the unequal
sizes of the original strata within the pseudostratum. All
USUs in a pseudostratum are assigned the same row number(s).
For an SR sample, two rows of the Hadamard matrix are
assigned to each pair of USUs creating replicate factors,
f r for r = 1,...,160
2 An ultimate sampling unit is usually a group of four neighboring
housing units.
3 Rows 1 and 81 have been dropped from the matrix.
14–2 Estimation of Variance Current Population Survey TP66
U.S. Bureau of Labor Statistics and U.S. Census Bureau