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

A Guide to Small Area Estimation - Version 1.1 05/05/2006
Synthetic models work well when all relevant auxiliary variables that help
predict the response variable are available, accurate and can be included in the
model. However in practice this is more the exception than the rule.
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Random Effects Regressions Models
When fitting a synthetic model, the residuals should look like "white noise",
however in practice they often display significant between area variation which
indicates that there is some other systematic variation in the response variable
between different small areas that is not being accounted for by the auxiliary
variables. This implies that the synthetic model is missing certain auxiliary
variables, the values of which would, had they been available, better help
predict differences between small areas.
This problem can be addressed by incorporating a random effect into the
model. This is done by treating the constant or intercept term in the model as
a fixed constant plus a random component known as the random effect. The
interpretation of this is that each small area is assigned an intercept term in the
model which is allowed to vary, around some overall constant value, from one
small area to another. This is usually sufficient to take account of between area
variation, however it is possible to include a random effect in a parameter
coefficient rather than the intercept term. Doing this further adds to the level
of complexity and is not covered in this manual.
For models fitted to small area level data, the inclusion of random effects may
give a distinct advantage over the synthetic model approach, possibly leading
to estimates with higher precision and robustness. In the case of linear models,
random effects model can theoretically be shown to give small area estimates
that reflect the best trade-off between the accuracy of the direct estimate and
the uncertainty associated with the synthetic model. So for a small area that
happens to have a low sampling error (eg because of a large sample size, say)
relative to the total error (sum of sampling error of the direct estimate and
synthetic model error), a random effects model will give more weight to the
direct estimate for that small area. On the other hand, for a small area with
high sampling error, more weight will be given to the model based estimate as
this will be more reliable.
While being more complex than synthetic models, random effects models can
be estimated using a variety of statistical techniques. However due to their
technical nature, this manual will not go into any further detail about how to
apply random effects models. A more detailed treatment will be given in the
forthcoming technical manual.
Australian Bureau of Statistics 27