Step 1: Calculate living arrangement propensities from Census
2021 living arrangement propensities were calculated for each five-year age group (0–4, 5–9, …, 85 and over). The propensity is the Census counts of people (for each age group) in that living arrangement type, divided by the total Census count for each age group. There are 15 living arrangement types, as shown in summary tables in 'Types of Living Arrangements'.
Living arrangement propensities were calculated using a large proportion (92% in 2021) of the Census count of Australian usual residents. Categories of people included in the 2021 Census counts but excluded from the calculation of living arrangement propensities were:
- imputed records
- people coded to 'other non-classifiable' relationship in household
- visitors in the private dwelling in which they were enumerated, who were usually resident elsewhere in Australia
- people enumerated in non-private dwellings who were usually resident elsewhere in Australia.
People included in the projected population but not included in the living arrangement calculation were proportionally distributed across the living arrangement types. This assumes that these people have the same living arrangement distribution as those included in the calculation of the propensities.
Distributing by this method is likely to lead to an underestimation of lone person households. It is less likely that a lone person household will be enumerated at home on Census night because there are fewer people in the household. This bias is addressed in part by replacing Census counts of lone person households with lone person household estimates in the propensity calculations.
Census-based living arrangement propensities in the base year (2021) are reconciled to align with the estimate of households published in National, state and territory population for both total households and lone-person households. These estimates are based on Census counts but have been adjusted to account for person and dwelling undercount, dwelling misclassification and residents temporarily overseas on Census night.
The difference between the total numbers of households and lone-person households was proportionally distributed to group and family households. The number of families and then persons by living arrangement were derived from the scaled household estimates, using the method outlined in step 4 in reverse. For example, to obtain the number of persons in a group household, the ‘reconciled’ number of group households was multiplied by the average size of group households in the 2021 Census.
The 2021 reconciled counts by living arrangement were proportionally distributed across the five-year age groups according to the 2021 living arrangement propensities (as described in paragraph 1 of Step 1). The distribution was constrained to sum to 30 June 2021 ERP (by age) and the reconciled totals for each living arrangement.
Reconciled base year living arrangement propensities are used in step 2 as the basis for the projected propensities.