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

A Guide to Small Area Estimation - Version 1.1 05/05/2006
then be added to the corresponding sample totals to form small area estimates. A
potential disadvantage of this approach is that the small area sub-group level model may
be less efficient than a unit level model.
Auxiliary data may be available at area-level or person/unit level or a combination of
both. However, in practice due to confidentiality or security reasons, data from
government administrative sources are more likely to be available at some aggregated
level. The choice between a unit/person level or area level model will depend on the
level at which data for the variable of interest and explanatory variables are available as
well as the efficiency of the small area estimates generated. For example, if data for
the target variable and the auxiliary variables are only available at the area level, fitting
an area level model will be the only option. However if unit level data is available for
all variables, either an area level or unit level model is an option. It is also possible to
fit a model in which the target variable is at the unit level but some auxiliary variables
are at the unit level while others are at area level. Further discussion on the choice of
small area model is provided in Section 4.2 below.
In practice, the efficiency of predicted small area estimates may be improved by
including some auxiliary variables as small area averages. Such covariates are referred to
as contextual effects and may be included as an additional covariate even if the variable
already appears in the model as a unit level auxiliary variable. Contextual effects allow
differences in the area level characteristics in which a person lives to be accounted for in
the model. For example, high income earners living in low income areas may have quite
different characteristics to people on similarly high incomes living in high income areas,
and it may be important to take account of this in the model.
We now give an example of the data sources and auxiliary variables that were considered
for the disability empirical study. The target variable was whether or not a person has a
disability. The auxiliary data was drawn from the survey, a census as well as
administrative data sources and comprised:
- Survey of Disability, Ageing and Carers (SDAC) (ABS, 1998)
- Census of Population and Housing, 2001 (ABS)
- Socio-Economic Indexes For Areas (SEIFA) (ABS)
- Disability Support Pension (DSP) data from Centrelink
Given these sources of data, the following auxiliary variables were considered:
- proportion of people in the small area receiving the DSP,
- age and sex, income, household structure (from SDAC)
- Socio- Economic Indexes For Area (SEIFA) score for the small area,
- Indicator of remoteness
Some of these variables were only available at the area level while those sourced from
SDAC/Census, for example, age, sex and income, were available at the person level.
These SDAC variables were chosen subject to the requirement that these variables were
similarly defined and available from the census.
Another key issue relating to auxiliary data concerns the case where survey data cannot
be matched to auxiliary data sources. In order to make predictions for each small area,
auxiliary variables obtained from the survey must correspond closely with similar data
items available for the rest of the population. If this is not the case then model
predictions may be significantly biased. For example in the empirical study of small area
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