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ESTIMATION Overview of weighting for the PES Weighting is the process of adjusting results from a sample survey to infer results for the total in-scope population. The weight can be considered an indication of how many population units are represented by the sample unit. Essentially, the PES weighting methodology produces an estimate of the number of people who should have been counted in the Census. Weights are given to people that were counted in the Census and to people that were missed in the Census. The sum of weights (i.e. the people who were counted plus the people who should have been counted but were not) becomes the estimate of all people that should have been counted. Weighting begins with the initial dwelling weight, which is essentially equal to the inverse of the probability that a dwelling was selected in the PES sample. Then dwelling weighting adjustments are made to compensate for the different rates of non-response in different dwelling types and areas of Australia. Person weighting adjustments are then applied to allow for undercoverage and non-response in the PES. Larger adjustments are made for categories of people (such as young adult males) who are harder to contact and interview successfully in the PES. Dwelling weights in the PES Each dwelling in the PES sample is given a 'dwelling weight', so that the PES sample represents all private dwellings in Australia. The PES sample is designed to ensure each private dwelling in a state or territory has a fixed and non-zero probability of selection. The inverse of this probability is the dwelling's selection weight. In practice, certain types of dwellings are more likely to be missed in the PES. Adjustment for this is made according to a dwelling's post-stratum, where dwellings are assigned to a particular post-stratum based on the following variables:
These initial weights apply to all dwellings in the PES sample, even those that did not result in a PES response. Responding dwellings in the PES are further weighted up to represent non-responding dwellings which are deemed to be occupied. For example, suppose that the PES selected 22 dwellings in a post-stratum, each with a probability of 0.2, and that 18 of them were counted in the Census. The selection weight for each dwelling is 5 (i.e. 1 divided by 0.2) with the total selection weight of the dwellings counted in the Census being 90 (i.e. 18 multiplied by 5). If 99 dwellings were counted in the Census, the initial dwelling weight for all these dwellings becomes 5 multiplied by 99/90, which is equal to 5.5. Furthermore, if 5 of the selected dwellings fail to respond in the PES, then the cumulative weight of these dwellings will be redistributed to the other dwellings in the sample in order for the sample to reflect the independently estimated distribution of the population. In this case, the weight for the 17 responding dwellings becomes 7.1 (i.e. 5.5 multiplied by 22/17). Person weighting In estimation, the weights of persons responding in PES are adjusted so that when summed across those persons counted in the Census the totals correspond to the actual Census counts within a number of benchmark categories. The benchmark categories are based on personal characteristics including age, sex, state/territory, country of birth and Indigenous status. Estimates of the number of people who should have been counted in the Census based on the dwelling weights would only represent the population of people who were in private dwellings at the time of PES. That is, they would underestimate the private dwelling population at the time of the Census because some people in private dwellings on Census night will be in non-private dwellings, overseas, or may even be deceased at PES time. Such estimates would also not represent people living in non-private dwellings. To represent all in-scope people on Census night requires adjusting the dwelling weights to give a person weight. The initial person weight adjustments are chosen to ensure that the PES estimates of people counted in private dwellings (other than late return or imputed dwellings) in a set of benchmark categories match the actual Census counts for these categories. The variables used to form these benchmark categories are region, sex, age (by 16 age groups), country of birth, marital status, Indigenous status, and whether sampled in an ICF dwelling. The weight adjustment applied to a person depends only on the information reported in the PES. As a final step in weight adjustment, the initial person weights are adjusted so that the PES estimates represent people in non-private dwellings as well as private dwellings. This final step uses region, age and sex only, as information on other items is not reliable for non-private dwellings. Intuitively, a 'good' set of weights for the PES should ensure that if the PES were used to estimate the actual Census count, the PES would get the 'right' answer. The above step makes sure that this happens. Technically this is also a desirable property for a set of PES weights to have, since there is a very strong relationship between the actual Census count, and the count that the Census should have made. For example, consider the benchmark category consisting of ACT males aged 25 to 29 years in Census dwellings (that were not imputed or late returns). Suppose there are 120 of these records in the sample, 100 of whom were counted in the Census and 20 who were not. Also suppose the dwelling weights for each were 10, with a Census total of 2000. The dwelling weight will therefore be increased to give a person weight of 20, so that the 100 records will add up to the Census count of 2000. However, the 20 records that were not counted will also have an equivalent weight of 20, giving us an estimate of 400 people in this category who were missed in the Census. In 2011, the ABS will again use the Prediction Regression (PREG) estimator, which was developed and used in 2006 as an estimator that extends the Dual System Estimator approach to account for overlapping benchmark categories and the situation where people give different responses between PES and Census. A detailed description of the PREG estimator can be found in Research Paper: An Estimating Equation Approach to Census Coverage Adjustment, May 2007 (cat. no. 1351.0.55.019). Estimating the number of people in Census late return and imputed dwellings For some people who have not returned a Census form, contact from the ABS following selection in the PES acts as a reminder and possible motivator to return a completed Census form. These late returns, if not identified, would result in the PES sample having a higher proportion of Census response than in the overall population. To protect against this, all Census forms received after the start of PES field work are deemed 'late'. For the purpose of PES estimation, the dwellings from which these forms are received are treated as though they had not been contacted in the Census and are classified to the 'non-contact sector' of the Census. Comparability of sub-state undercount estimates over time Estimates of net undercount below the state level are important to the production of sub-state population estimates and the evaluation of Census coverage on a more localised basis. In 2006, these sub-state estimates incorporated a capital city and balance of state/territory split, which will again be included for the 2011 results. The comparability of these estimates over time will be affected by the transition from the ASGC to ASGS. While the sub-state split is similar, it is not directly comparable.
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