2080.5 - Information Paper: Australian Census Longitudinal Dataset, Methodology and Quality Assessment, 2006-2016 Quality Declaration 
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APPENDIX: WEIGHTING THE ACLD

INTRODUCTION

The process of weighting enables the data user to estimate the number of people in the whole population with particular characteristics based on the observations from a sample. To do this, a 'weight' is allocated to each sample unit. The value of the weight indicates how many population units are represented by the sample unit.

The ACLD is designed to measure change in Australian society over time. For the 2011 ACLD Panel, a longitudinal weight has been implemented which allows the weighted sample to represent all persons who were in scope of both of the 2011 and 2016 Censuses. As shown in Figure 1, this ‘longitudinal population’ is the overlap between the two Censuses (the shaded region). To estimate the size of this population, the 2016 Estimated Resident Population (ERP) was multiplied by the estimated probability that a person was in scope in 2011, calculated using the 2016 Census responses for the reported 5 year ago address. Further information on this approach can be found in the paper Chipperfield, Brown & Watson (2017).


FIGURE 1 - IN SCOPE POPULATION FOR THE AUSTRALIAN CENSUS LONGITUDINAL DATASET, 2011-2016

Venn diagram showing 2006 and 2011 samples, which mostly overlap. The part of the 2006 circle that does not overlap with 2011 is deaths and overseas departures. The part of the 2011 circle that does not overlap with 2006 is births and overseas arrivals.


This method for estimating the relevant overlapping 2011 and 2016 populations is an improvement over the method used in the original linkage of the 2006-2011 ACLD. The current approach overcomes the limitations of the previous approach which inaccurately accounted for:

  • people who were overseas arrivals after one Census and who subsequently left Australia (or died) before the following Census; and
  • people who left Australia after one Census and then returned to Australia before the following Census.


CALCULATING LONGITUDINAL WEIGHTS

Longitudinal weights were calculated for each 2011 Panel sample record that was linked to a 2016 Census record. No weights were calculated for the unlinked records. The longitudinal weight for a linked sample record in this release of the ACLD is a measure of how many people it represents in the 2011 and 2016 overlapping populations. The weights consist of three components. The first component reflects the probability of a record being selected in the 2011 Panel sample. The second component takes into account that some selected records are less likely to be linked than other selected records. The third component takes into account Census undercount (e.g. a person in an undercounted population is less likely to have a Census record and so is less likely to have a selected Census record) and ensures that the weights are consistent with population benchmarks. These three components lead to the final weight, calculated as:

Final weight = (Design weight) x (Missed link adjustment) x (Calibration to known population totals adjustment).

Design Weight

The records in the 2011 ACLD Panel sample were selected from the 2011 Census population using equal probability random selection. For a sample size of 5.7%, the design weight for all records of the ACLD is the inverse of the probability of selection, and is equal to 17.5.

Missed Link Adjustment

A missed link occurs when a 2011 sampled record has a corresponding 2016 Census record, but the link is not identified. As missed links are more likely to occur in certain population groups, not making this adjustment would mean that these population groups would be under-represented in the linked sample. The missed link adjustment weight is equal to the inverse of the estimated propensity to link. No attempt was made to correct for false links.

The propensity to link was estimated using a logistic regression model that was applied to the 2011 Panel sample with link status as the response variable. The logistic regression model describes a relationship between a 2011 sample record's propensity to link and its values for a range of 2011 Census variables such as Indigenous status, marital status, country of birth, language spoken at home and English proficiency, labour force participation and occupation, educational attainment, mobility (whether moved address in the preceding year) and remoteness. It was found that the estimated propensity to link varied considerably between records.

Two separate models were applied to the 2011 Panel sample. The first model was applied to people under the age of 15 years on 2011 Census night. This model excluded the variables that were not applicable to people under 15 years of age, such as marital status and labour force participation. The second model was applied to the remainder of the sample (persons aged 15 years or over in 2011).

The missed link adjustment carries the assumption that the ACLD contains no false links, while not assuming that all records in the 2011 sample have a corresponding 2016 Census record.

Odds ratios and accompanying Wald confidence intervals for the predictor variables for the first model (for persons aged under 15 years in 2011) are contained in Table A.1. A comparison group is selected for each characteristic, and the odds ratio for the other categories represents the ratio of the odds of being linked in contrast to the comparison group. For instance, Table A.1 shows the odds ratios by age group in 2011. Those persons aged under 15 years with English proficiency ‘Not at All’ were less likely to be linked than those with English proficiency ‘Very Well’ (the comparison group), but more likely than those with English proficiency ‘Not Well’. Conversely, the odds ratios for remoteness in 2011 show that persons aged under 15 years reporting 'Inner Regional' were more likely to be linked than those reporting 'Major City' (the comparison group).

TABLE A.1 - ODDS RATIOS FROM THE LOGISTIC REGRESSION MODEL, Persons aged under 15 years, 2011
95% CONFIDENCE LIMITS
Selected characteristics
Odds ratio
Low limit
Upper limit

AGE GROUP

0-7 years (comparison group)
1.000
. .
. .
8-13 years
1.013
1.000
1.026
14 years
1.011
0.989
1.033

COUNTRY OF BIRTH

Oceania and Antarctica (non-Indigenous persons) (comparison group)
1.000
. .
. .
Americas
0.577
0.525
0.635
Indigenous Australian
0.872
0.847
0.897
North Africa & Middle East
0.465
0.423
0.510
North-East Asia
0.526
0.483
0.572
North-West Europe
0.661
0.630
0.693
South-East Asia
0.569
0.533
0.606
Southern & Central Asia
0.620
0.582
0.660
Southern & Eastern Europe
0.425
0.360
0.501
Sub Saharan Africa
0.722
0.668
0.780
Missing(a)
0.773
0.710
0.841

LANGUAGE

English (comparison group)
1.000
. .
. .
Australian Indigenous
1.087
0.976
1.211
East Asian
0.992
0.954
1.032
East European
0.973
0.916
1.034
Other North European
0.967
0.891
1.050
South Asian
1.004
0.955
1.056
South East Asian
0.987
0.943
1.033
South European
0.977
0.934
1.021
South West and Central Asian
0.984
0.940
1.029
Other
0.805
0.754
0.859
Missing(a)
0.882
0.803
0.969

ENGLISH PROFICIENCY

Very Well (comparison group)
1.000
. .
. .
Well
0.777
0.743
0.812
Not Well
0.644
0.589
0.704
Not at All
0.806
0.658
0.987
Missing
0.939
0.841
1.049

MOBILITY

Same usual address one year ago (comparison group)
1.000
. .
. .
Different usual address one year ago
0.838
0.829
0.848

SCHOOL SECTOR

Government (comparison group)
1.000
. .
. .
Catholic
1.042
1.026
1.058
Other Non-Government
1.057
1.039
1.076
Missing/Other(b)
0.874
0.853
0.896

REMOTENESS

Major City (comparison group)
1.000
. .
. .
Inner Regional
1.021
1.006
1.036
Outer Regional
1.010
0.989
1.031
Remote
0.961
0.913
1.012
Very Remote
0.936
0.866
1.011
Other(c)
1.047
0.813
1.348

. . Not applicable
(a) Includes Supplementary codes
(b) Includes other school sector and pre-school

(c) Includes Migratory, Offshore and Shipping Zones and No usual address
Source: Australian Census Longitudinal Dataset

Odds ratios and accompanying Wald confidence intervals for the predictor variables in the second model (for persons aged 15 years or over in 2011) are contained in Table A.2. A wider variety of variables were available for this age group. In comparison to those persons aged under 15, persons aged 15 years or over with English proficiency ‘Not Well’ were less likely to be linked than those with English proficiency ‘Very Well’ (the comparison group), but more likely than those with English proficiency ‘Not At All’. Conversely, the odds ratios for age in 2011 show that persons reporting aged 65 and over were more likely to be linked than those reporting age 15-24 (the comparison group). This was similar for persons reporting 'Clerical and Administrative' and 'Sales Workers' for Occupation as they were more likely to be linked than those that were 'Not in the labour force' (the comparison group).

TABLE A.2 - ODDS RATIOS FROM LOGISTIC REGRESSION MODEL, persons aged 15 years or over, 2011

95% CONFIDENCE LIMITS
Selected characteristics
Odds ratio
Low limit
Upper limit

AGE GROUP

15-24 years (comparison group)
1.000
. .
. .
25-34 vs 15-24
0.841
0.832
0.850
35-44 vs 15-24
0.968
0.957
0.978
45-54 vs 15-24
1.008
0.997
1.020
55-64 vs 15-24
1.031
1.019
1.043
65+ vs 15-24
1.080
1.067
1.094

COUNTRY OF BIRTH

Oceania and Antarctica (non-Indigenous persons) (comparison group)
1.000
. .
. .
Americas
0.829
0.810
0.848
Indigenous Australian
0.955
0.939
0.971
North Africa & Middle East
0.951
0.928
0.976
North-East Asia
0.748
0.730
0.766
North-West Europe
0.951
0.943
0.959
South-East Asia
0.894
0.877
0.911
Southern & Central Asia
0.838
0.820
0.858
Southern & Eastern Europe
0.976
0.961
0.992
Sub Saharan Africa
0.930
0.912
0.949
Missing
0.884
0.867
0.900

LANGUAGE

English (comparison group)
1.000
. .
. .
Australian Indigenous
0.978
0.925
1.035
East Asian
1.004
0.983
1.026
East European
1.006
0.986
1.026
Other North European
0.926
0.902
0.950
South Asian
0.947
0.922
0.973
South East Asian
0.969
0.948
0.990
South European
0.953
0.940
0.967
South West and Central Asian
0.989
0.965
1.013
Missing
0.951
0.918
0.985
Other
0.836
0.813
0.860

ENGLISH PROFICIENCY

Very Well (comparison group)
1.000
. .
. .
Well
0.859
0.848
0.871
Not Well
0.826
0.811
0.840
Not at All
0.661
0.636
0.687
Not stated
0.950
0.912
0.990

MOBILITY

Same usual address one year ago (comparison group)
1.000
. .
. .
Different usual address one year ago
0.797
0.793
0.801
Remoteness
Major City (comparison group)
1.000
. .
. .
Inner Regional
1.005
0.999
1.011
Outer Regional
0.979
0.971
0.987
Remote
0.938
0.918
0.959
Very Remote
0.845
0.818
0.874
Other(b)
0.948
0.894
1.005

REGISTERED MARITAL STATUS

Married (comparison group)
1.000
. .
. .
Separated
0.951
0.938
0.964
Divorced
0.939
0.931
0.947
Widowed
0.991
0.980
1.002
Never Married
0.940
0.933
0.946

HIGHEST YEAR OF SCHOOL COMPLETED

Year 12 (comparison group)
1.000
. .
. .
Year 11
1.010
1.002
1.018
Year 10
0.996
0.989
1.003
Year 9 or below(a)
1.003
0.995
1.012
Not stated
0.990
0.974
1.007

LABOUR FORCE STATUS AND OCCUPATION

Not in the labour force (comparison group)
1.000
. .
. .
Unemployed
0.954
0.942
0.966
Employed
Professional
1.080
1.070
1.090
Manager
1.045
1.035
1.055
Technicians and trades
1.038
1.028
1.049
Community and personal service
1.056
1.045
1.067
Clerical and administrative
1.076
1.065
1.086
Sales workers
1.075
1.063
1.086
Machinery operators and drivers
1.016
1.003
1.030
Labourers
0.999
0.988
1.010
Employed, occupation not stated
0.865
0.843
0.887
Not stated
0.889
0.863
0.916

LEVEL OF NON-SCHOOL QUALIFICATION

No post-school qualification (comparison group)
1.000
. .
. .
Postgraduate Degree
0.969
0.958
0.982
Graduate Diploma and Graduate Certificate
1.028
1.012
1.045
Bachelor Degree
0.985
0.977
0.993
Advanced Diploma and Diploma
1.009
1.001
1.018
Certificate
1.021
1.015
1.028
Level of non-school qualification not stated or inadequately described
0.948
0.936
0.960

. . Not applicable
(a) Includes persons who did not go to school.

(b) Includes Migratory, Offshore and Shipping Zones and No usual address
Source: Australian Census Longitudinal Dataset, 2011-2016

Calibration to Longitudinal Population Totals

At this point in the process an intermediate weight had been calculated for each linked sample record that was equal to (Design weight) x (Missed link adjustment). This intermediate weight was then calibrated (or adjusted) so that the resulting weighted counts of the ACLD links would be equal to estimates of the longitudinal population size at the national and selected sub-national levels. The two sets of longitudinal population groups calibrated to were:
  1. state/territory, by sex, by ten year age group;
  2. Indigenous status by state/territory.

The size of these longitudinal population groups was estimated by multiplying the 2016 ERP for each group by the estimated proportion of 2016 Census responders for that group who reported being in scope of the 2011 Census, i.e. resident at an Australian address on 2011 Census night. These proportions were estimated for the cross-classification of the state/territory, age group, and sex (Table A.3) and separately for the cross-classification of state and Indigenous status (Table A.4) using the responses to the 2016 Census address five years ago question. For example, Table A.3 indicates that 96.7% of males in NSW aged 45-54 reported being in scope of the 2011 Census.

TABLE A.3. ESTIMATED PROPORTION OF 2016 CENSUS RESPONDENTS IN SCOPE OF THE 2011 CENSUS, By state/territory, sex and age

STATE/TERRITORY 2011 AND 2016
Age group (years)
Males
(no.)
Females
(no.)

NEW SOUTH WALES
5-14
0.949
0.949
15-24
0.889
0.883
25-34
0.835
0.823
35-44
0.918
0.925
45-54
0.967
0.967
55-64
0.979
0.974
65-74
0.984
0.983
75-84
0.991
0.991
85 or over
0.995
0.995

VICTORIA
5-14
0.938
0.938
15-24
0.864
0.858
25-34
0.842
0.824
35-44
0.917
0.921
45-54
0.964
0.965
55-64
0.978
0.973
65-74
0.984
0.984
75-84
0.992
0.992
85 or over
0.996
0.996

QUEENSLAND
5-14
0.948
0.948
15-24
0.920
0.910
25-34
0.881
0.864
35-44
0.937
0.935
45-54
0.968
0.968
55-64
0.980
0.979
65-74
0.985
0.986
75-84
0.992
0.992
85 or over
0.995
0.995

SOUTH AUSTRALIA
5-14
0.944
0.946
15-24
0.910
0.909
25-34
0.896
0.876
35-44
0.930
0.932
45-54
0.973
0.975
55-64
0.987
0.984
65-74
0.990
0.991
75-84
0.995
0.995
85 or over
0.998
0.998

WESTERN AUSTRALIA
5-14
0.915
0.916
15-24
0.893
0.893
25-34
0.840
0.817
35-44
0.895
0.898
45-54
0.948
0.952
55-64
0.975
0.972
65-74
0.983
0.983
75-84
0.991
0.990
85 or over
0.996
0.995

TASMANIA
5-14
0.976
0.974
15-24
0.952
0.949
25-34
0.928
0.922
35-44
0.965
0.965
45-54
0.985
0.985
55-64
0.992
0.993
65-74
0.993
0.995
75-84
0.996
0.996
85 or over
0.998
0.997

NORTHERN TERRITORY
5-14
0.941
0.939
15-24
0.928
0.920
25-34
0.873
0.842
35-44
0.912
0.917
45-54
0.955
0.962
55-64
0.972
0.970
65-74
0.981
0.985
75-84
0.987
0.985
85 or over
0.984
0.993

AUSTRALIAN CAPITAL TERRITORY
5-14
0.922
0.921
15-24
0.862
0.853
25-34
0.867
0.844
35-44
0.906
0.909
45-54
0.951
0.956
55-64
0.969
0.966
65-74
0.982
0.982
75-84
0.991
0.990
85 or over
0.998
0.997

Source: 2016 Estimated Resident Population


TABLE A.4. ESTIMATED PROPORTION OF 2016 CENSUS RESPONDENTS IN SCOPE OF THE 2011 CENSUS, By state/territory and Indigenous status
State/Territory
Aboriginal and Torres Strait Islander persons
(no.)
Other persons(a)
(no.)

New South Wales
0.996
0.927
Victoria
0.993
0.922
Queensland
0.996
0.941
South Australia
0.997
0.947
Western Australia
0.997
0.914
Tasmania
0.997
0.971
Northern Territory
0.999
0.894
Australian Capital Territory
0.988
0.914

(a) Includes non-Indigenous persons and persons who did not state an Indigenous status in 2016.
Source: 2016 Estimated Resident Population

At this point an intermediate weight was calculated for each linked sample record that was equal to (Design weight) x (Missed link adjustment). This intermediate weight was calibrated (or adjusted) so that the resulting weighted counts of the ACLD links would be equal to the estimated longitudinal population sizes in Table A.3 and A.4. The intermediate weights were calibrated using a 'raking' tool. This is a program which was developed to determine record level weights using iterative horizontal and vertical passes through the unit records until a satisfactory set of final weights are converged upon. Imposing bounds on the calibration adjustment was not necessary because extremely high or low final weights were not produced.

This calibration adjustment improves the accuracy of weighted estimates and it implicitly adjusts for the small proportion of people who were in scope for the 2011 Census but who did not complete a Census form in 2016.

Summary of weights

The mean weight for selected characteristics gives an indication of how much the final weight differs from the initial design weight (17.5) in order to address missed links and Census undercount. Table A.5 shows that the mean final weight for the linked records is 22.3 for females, and 23.2 for males. The largest weight was 83 and the smallest was 14.8. The mean weight was higher for Aboriginal and Torres Strait Islander persons (30.4) and for people in the Northern Territory (30.2).


TABLE A.5 - DESCRIPTIVE STATISTICS FOR WEIGHTS, by Selected Characteristics, 2016

Count (a)
Minimum Weight
Maximum Weight
Mean Weight
Standard Deviation
Median Weight

SEX
Male
450 054
14.8
83.1
23.2
4.9
22.0
Female
477 460
14.8
81.9
22.3
4.7
21.3

AGE
0-14
126 917
16.1
81.9
22.3
5.1
21.0
15-24
119 827
16.5
67.5
23.5
4.0
22.7
25-34
109 438
17.4
83.1
27.9
5.3
27.3
35-44
127 858
15.9
60.6
23.3
4.7
22.7
45-54
139 010
16.0
68.8
21.9
4.1
20.8
55-64
127 797
15.6
62.7
21.3
3.8
20.1
65-74
99 605
15.2
55.5
20.6
3.4
19.4
75-84
54 414
14.8
58.0
20.2
3.5
18.8
85 or over
22 651
14.8
56.2
21.2
3.9
19.8

INDIGENOUS STATUS
Aboriginal and/or Torres Strait Islander
23 059
18.9
83.1
30.4
6.0
29.9
Other (b)
904 457
14.8
81.9
22.5
4.6
21.5

STATE/TERRITORY OF USUAL RESIDENCE
New South Wales
296 695
15.5
81.9
22.7
4.9
21.6
Victoria
234 629
15.7
80.5
22.7
4.7
21.6
Queensland
185 576
15.7
81.2
23.0
4.6
22.2
South Australia
71 025
14.8
68.7
21.5
4.3
20.3
Western Australia
95 198
15.4
73.8
23.0
5.2
21.7
Tasmania
21 781
15.9
58.8
21.8
3.8
20.7
Northern Territory
6 929
17.1
83.1
30.2
8.0
28.7
Australian Capital Territory
15 583
15.2
60.0
22.0
4.6
21.1

a) Counts presented in the table have been perturbed.
b) Includes non-Indigenous persons and persons who did not state an Indigenous status in 2016.
Source: ABS, Australian Census Longitudinal Dataset.


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