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

A Guide to Small Area Estimation - Version 1.1 05/05/2006
One of the more important prerequisites for the successful production of small area
estimates is the availability of accurate auxiliary data that is well correlated with the
target variable. By auxiliary data we mean one or more variables obtained from either
administrative data sources or a census that are included in the model as explanatory
variables. The auxiliary data should:
o
o
o
comprehensively cover the entire population scope for which small area estimates
are required. If an auxiliary data item is not available for the unselected part of the
population then small area predictions cannot be made and the affected data items
cannot be included in the model.
include reliable geographic information so that all units belonging to a small area can
be accurately identified, and
be contemporaneous with the target variable and other auxiliary data used in the
model
Model based small area estimates are produced by firstly fitting the model to the
sample data to estimate model parameters, which include the intercept and slope
parameters. The estimated model is then applied to the population auxiliary data to
produce the small area predicted estimates.
In the case of a purely area level model, the target variable and auxiliary variables are
all at the small area level, so it is relatively straightforward to produce small area
estimates as described above. However in the case of unit or person level models, the
second step referred to above is a little more complex as the model fitted to the
sampled units is generally applied to those population units not selected in the
sample. Small area estimates are compiled by taking the sum of the sample unit
values for the target variable (obtained from the survey data) and adding to it the sum
of the model predictions for the non-sampled units.
This approach naturally applies if the survey data can be reliably matched to the
auxiliary information using a hard matching identifier such as Medicare number or tax
file number. This is common practice in a number of European Union countries
where national identifiers exist. However due to privacy considerations and related
issues, this practice rarely occurs in Australia. Where it is not possible to distinguish
between sampled and non-sampled units on the auxiliary data sources, there are two
options available:
- apply the model fitted to the sample data to the entire population data file, or
- group population units within each small area (eg age by sex), fit a model to the
small area by sub-group level sample data and then apply this model to make
predictions for the non-sampled population in each small area sub-group.
The first approach suffers from the disadvantage that the prediction error for the small
area estimates will be increased slightly because target variable values for the sampled
units are predicted from the model, thereby contributing to total model error. It would
be more preferable, however to make use of the available survey response values which
are not subject to model error. If the sampling fraction is very small then this should not
be a major concern.
The second approach has the advantage that only population counts of the non-sampled
population in each small area sub-group are required to make predictions. The
predicted totals for the non-sampled population (at the small area sub-group level) can
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