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

A Guide to Small Area Estimation - Version 1.1 05/05/2006
for some small areas or units. Such differences, therefore, call for a more general/flexible
specification of the models to capture the area-specific (person-specific) factors after
taking account of the auxiliary variables - and hence the random effects models. Thus,
the choice between random effects models versus synthetic models could be made on
the basis of one or more of the following factors:
i.
ii.
iii.
iv.
v.
prior knowledge of small areas or units vis-a-vis the auxiliary data gained from
experience or through discussions with subject matter specialists,
users/stakeholders, etc. (for example, we may not have a lot of faith in our auxiliary
variables /the synthetic model).
from statistical outcomes based on the models. A close assessment or evaluation of
the small area estimates/predictions from comparative synthetic and random effects
models and see whether they meet expectations.
on the basis of statistical/econometric tests (a battery of diagnostic and statistical
tests) on the adequacy of the models.
when one wants small areas with large samples to be less affected by the model
because the direct estimates for such areas can be expected to be quite reliable in
their own right. The random effects model allows for a suitable trade-off between the
reliability of the direct estimates and reliability of model estimates.
when one wants to apply the model to areas with no sample in them (out of sample
areas). Random effects models allow for greater flexibility in applying the model to
make predictions for areas other than those to which it was fitted.
Clearly, once the random effects models are chosen they require a higher level of
statistical skill and some familiarity with specialised software. It is also true that more
complex models may not necessarily provide better results. This is particularly true if
sufficiently strong relationships in the data, from which to borrow strength, are simply
not present in the data. One should be aware that results from simple models may be as
good as those from complex ones. In other words, as will be discussed later in this
section, the gains in efficiency of estimates from using more complex models need to be
assessed.
An important aspect of the modeling process which may also have significant bearing on
the complexity and quality of the analysis is whether the variable of interest involves a
univariate or multivariate analytical framework. Here we are specifically referring
whether the variable of interest is a univariate or multivariate form. For example, in the
disability study, if our variable of interest is simply to predict whether a person has an
impairment or not (i.e., 1= person has a disability and 0= person has no disability)
regardless of the type of impairment then this is within a univariate framework. On the
other hand, a breakdown of the variable of interest by type of impairment (e.g., physical,
mental, sensory etc.) would involve a multivariate framework. The real issue here is that
while a univariate analysis is simpler to undertake, a multivariate analysis provides an
opportunity to exploit additional information on the correlations that exist between the
various types of impairment and hence improve the reliability of estimates.
Australian Bureau of Statistics 32