Page 81 - Contributed Paper Session (CPS) - Volume 2

CPS1437 Thanyani M.
Bar-Gera et al. (2009) introduced the entropy maximisation method to
estimate household survey weights to match the exogenously given
distributions of the population, including both households and persons. Bar-
Gera et al. (2009) also presents a Relaxed Formulation to deal with cases when
constraints are not feasible and convergence is not achieved. The goal through
this optimisation procedure is to find a weight for each household so that the
distributions of characteristics in the weighted sample match the exogenously
given distribution in the population, for both household characteristics as well
as person characteristics.
The process to accurately handle the procedure is iterative to find weight
which is as close as possible to the target distribution. There are obvious
situations where the constraints are not met. In sample surveys some samples
from the sample may be too small to an extent that distributions do not match
right away. In those instances the calibration classes may need to be redefined
by creating broader and comparable classes between sample data and
auxiliary data.
Further proposed method by Bar-Gera et al. (2009) is that of relaxing the
constraints while maintaining the distribution. Relaxed formulation can be
used to estimate weights when the constraints are infeasible such that
distributions of the population characteristics are satisfied to within
reasonable limits. There may be cases where a perfect match between the
weighted sums and the exogenous distributions of population characteristics
cannot be found because of infeasibility in the constraints. The issues of
infeasibility can be addressed by using the relaxed convex optimisation.
Different artificially chosen objective functions are likely to lead to many
different solutions. The solutions found by the Simplex method, while
satisfying the conditions on marginal distributions, are corner solutions and
potentially unsuitable as survey weights. The weights estimated will be a
combination of zero weights and non-zero weights. The number of non-zero
weights in any corner solution will be equal (at most) to the number of
constraints, meaning that the weight of most households will be zero. This
kind of weighting scheme may be undesirable for survey weighting even
though they satisfy the marginal distributions. Linear programming theory can
also be used to analyse the conditions under which the problem is infeasible.

3. Result
Survey estimates results
The final survey weights were constructed using regression estimation to
calibrate survey estimates to the known population counts at the national-
level by cross-classification of age, gender and race, and the population counts
at the individual metros and non-metros within the provinces by two age
groups (0-14, and 15 years and over). The computer program StatMx

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