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

A Guide to Small Area Estimation - Version 1.1 05/05/2006
Spatial Relationships
Spatial relationships in the data can be harnessed in much the same way that time series
relationships can be. Thus, if we hypothesize that different units bear some relationship
to each other that depends upon the distance and direction between them, units can
then be pooled together to give a greater effective sample size for each small area
estimate. This approach also has the benefit of reducing the impact of the odd unit value
that is discordant with its neighbouring values. Spatial methods are commonly used in
the contexts of health, disease, agricultural or environmental data but may be quite
applicable to other specific topics.
As in the case of time series relationships, borrowing strength through spatial
relationships adds additional complexity to the small area estimation and should only be
contemplated where statistical expertise is available.
Multivariate Relationships
In a univariate model the response or target variable is a single variable. In this manual
the models referred to are univariate models. So using the example of disability type
(physical, sensory, intellectual, psychological/psychiatric, head injury/acquired brain
damage), a separate univariate model is fitted to each of the disability types. In a
multivariate model, the target variable is a vector of these variables and the model is
fitted to these variables simultaneously.
A multivariate approach may be more efficient in terms of producing more accurate
predictions if there are strong correlations between the constituent variables. For
example, physical impairment may have a strong correlation with sensory impairment. A
multivariate approach that takes advantage of this additional information should be
more robust and give more accurate estimates. However, multivariate models add
additional complexity to small area estimation and should only be contemplated where
statistical expertise is available.
3.2 Basic Conditions for Success
The first step in undertaking a small area exercise is to determine the quality of the
direct estimates and the auxiliary data at the small area level. The variable of interest is
often drawn from a sample survey, which can not provide estimates at a fine level due to
small sample size in each small area and correspondingly high Relative Standard Errors
(RSE's). Auxiliary data can be obtained from many sources including administrative
datasets, survey variables and census counts. Table 3.1 outlines some issues that will
help in determining whether the basic conditions for producing quality small area
estimates are being met.
Australian Bureau of Statistics 18