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A Guide to Small Area Estimation - Version 1.1 05/05/2006 3.3 Choice of Small Area Within the ABS, the choice of small areas generally aligns with pre-specified boundaries as defined by the Australian Standard Geographical Classification (ASGC). Each area within Australia is broken up into Census Collection Districts (CDs) within Statistical Local Areas (SLAs) within Statistical Subdivisions (SSDs) within Statistical Divisions (SDs) within states. If possible, it is generally advisable to use ASGC classifications as they provide a consistent and integrated framework with a readily available set of concordances. However, other agencies often have different boundaries for their administrative areas. These boundaries generally line up with council boundaries which again line up with SLAs. Another common boundary is the postcode which can be related to a CD, although only approximately. A new geographical unit, called the meshblock, will be introduced in the 2006 population census for output purposes. The meshblock is considerably smaller than the CD, and with the help of the Geocoded National Address File (G-NAF) will improve the accuracy with which locations are coded to other ASGC classifications. In Section 2 we saw how it is important to find out from users the broadest area that will meet their small area requirements in order to improve the reliability of the modelled estimates. Figure 3.2 depicts the different choices that must be made to get reasonable estimates. Figure 3.2: Choosing the Appropriate Small Area Australian Bureau of Statistics 20
A Guide to Small Area Estimation - Version 1.1 05/05/2006 As discussed in Section 3.2 under "Auxiliary Data", a choice exists as to the level at which small area models should be applied. In practice, users may require small area data at different levels of aggregation and it may be expedient to fit the model at the finest level, produce small area estimates at that level and let users aggregate those estimates up to the required levels of aggregation. However it is important to realise that this may run the risk of incurring what is known as the atomistic fallacy (PAHO, 2003). The atomistic fallacy occurs when trying to draw inferences about units defined at a higher level of aggregation from a model fitted at a lower level of aggregation. Relationships between lower levels of aggregated units may not be the same as those between higher level aggregated units. Hence if another model was fitted at the higher level, the estimated model parameters and the predictions may be quite different to those for the model fitted at the lower level. A similar fallacy, called the ecological fallacy, may occur in the reverse situation of fitting a model at a broad regional level and assuming that the inferences drawn can be readily applied to small areas within those regions. Wherever possible it is advisable to make model inferences (that is predicted estimates and their associated measures of accuracy) at the small area level required by users. Where small area estimates are to be aggregated the extent of the aggregation should be kept to a minimum. If small area estimates are produced at the LGA level, aggregation to user defined regions consisting of only a few LGAs may be acceptable but aggregation of many LGA estimates should be met with caution. In choosing the most appropriate small area to use, consideration needs to be given to the sample size in each small area. This needs to be sufficient so that the model can produce appropriately reliable estimates. The size of the sample will depend on the strengths of the cross-sectional relationships or other areas for borrowing strength. If these are quite strong then perhaps as few as ten or twenty will be sufficient. In the absence of strong relationships in the data, a larger sample size of perhaps a couple of hundred units may be required in each small area. The sample sizes referred to here should be interpreted as a very rough guide as, apart from model strength, the required sample size will also depend upon the variation of units within each small area. The number of small areas is also important especially if units are clustered within small areas. Generally having more small areas will help improve the goodness of fit of the small area model. Consideration should also be given to the geographical distribution of the sample through each small area. In ABS household surveys clustering is used in the sample design to help reduce costs, with the result that in remote areas all of the sampled dwellings in a small area may have been selected from one or more small towns and none from throughout the vast rural expanse. This is likely to result in bias if the characteristics of people in those towns are different to those in the remote rural areas. The allocation of the sample across small areas will often reflect the relative frequency with which the characteristic or variable of interest occurs in the population. In the case of a common sub-population such as the number of persons employed or the number of persons with a disability then local government area (LGA) may be a suitable choice of small area. For rare characteristics such as indigenous status or a particular type of illness then larger areas may be required to give reasonable estimates. For this, the Statistical Subdivision (SSD) or broader regions may be required. Of course the decision on which level of geography to choose for the small area will Australian Bureau of Statistics 21
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