SAE Manual Sections 1 to 4_1 (May 06).pdf - National Statistical ...

A Guide to Small Area Estimation - Version 1.1 05/05/2006
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Calibration Estimator
To produce calibration estimators, the original survey weights (usually the
inverse probabilities of inclusion in the sample) are replaced with new
"calibrated" weights that are in some sense as close as possible to the original
weights, but are calibrated on some auxiliary variable available for the
population (Chambers, 2005). The small area estimate for this auxiliary
variable, calculated using the calibrated weights, will agree with the known
population totals. A simple example of calibration is where population age by
gender demographic totals are known for each small area. The survey weights
are then adjusted so that estimates of population count by age and gender,
agree with the known population counts.
There are a couple of points to note about the calibration estimator. Firstly it is
a straightforward method to put into production because the resulting
adjusted (calibrated) weights can be stored on the survey file and used to
produce estimates at the desired level of aggregation. Secondly the auxiliary
variables should be chosen with care and should relate to variables we wish to
produce estimates for. If the calibrated weights are used to produce estimates
for variables that aren’t related to the auxiliary variable(s) used in determining
the calibrated weights, the resulting estimates may be biased. In general
calibrated estimates possess good design-based properties. Government
statisticians have historically preferred the design-based to the model-based
approach as the resulting estimates are not subject to the consequences of
model mis-specification.
4.1.2 Regression Methods
Where a higher level of accuracy is required for small area estimates, an alternative is to
use regression or model-based approaches, however these methods require a higher
level of statistical expertise to implement and interpret results. A wide variety of
different regression techniques are available, but for the purposes of this manual, they
are divided into two main categories: synthetic and random effects regression models.
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Synthetic Regression Models
Synthetic regression models make use of available auxiliary data to
mathematically express a deterministic relationship between those auxiliary
variables and the target (response) variable we are trying to predict in each
small area. Synthetic models assume that all the systematic variability in the
response variable is explained by the variability in the values of the auxiliary
variables. The remaining variability, which is referred to as the "random noise"
or "stochastic variation", is represented by the difference between the
predicted value for the response variable under the model and the value
observed from the data. These differences are called random errors, residuals
or disturbances.
In the case of small area models, synthetic models assume that the same
deterministic relationship between the variable of interest and the auxiliary
variables, holds across a range of small areas, say for example within a state.
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