Estimating Population Totals using Imperfect Register Data and a Survey Subject to Nonignorable. Dr. James Chipperfield

Transcription

1 Estimating Population Totals using Imperfect Register Data and a Survey Subject to Nonignorable Non-response Dr. James Chipperfield

2 Outline Registers Sampling Example 1- Population Counts Example 2- Simulation Way forward

3 Registers- Characteristics Are relatively cheap May have poor coverage (over- and under-coverage) of our population of interest May contain errors (e.g. duplicates) May be inaccurate (out-of-date) May contain information that is inconsistent between registers or with surveys

4 Registers- Example Personal Income Tax (PIT) Medicare (PBS, MBS) Mortality Migrant Settlements Census Social Security

5 Registers- Notation Population set U of people indexed by j. R registers collect information only about U Register r collects x j(r) = (x j1(r),, x jk(r),, x jk(r) ) for all j, where x jk(r) is person j s kth covariate on register r. If person j has no record on register r then x j(r) = (0,, 0). When no register-to-register linkage we do not observe x j = (x j(1), x j(2),.., x j(r) ) but we can calculate X = j x j. X may or may not be useful in its own right. The registers are not a perfect. People who earn less than about $18,000 are not required to submit a 2016/7 Tax Return.

6 Sample Target population total is T = t j j Selects a sample, s, of people from U. Let I j = 1 if person j is selected in the sample. Sample people indexed by i = 1,.., n are selected with probability w i 1 Sample collects t i and covariates z i (which may contain t i ) Non-response to the survey may depend upon z (nonignorable non-response) After linking the survey separately to each register, we obtain x i, the value of x, for all i = 1,.., n. (e.g. if person i has no record on any register then x i = (0,, 0).)

7 Sample- Estimates Consider T = i s w i (t i x i T α) + X T α. Generalised REGression (GREG) estimator: T α GREG = i s w i x i x 1 i w i x T i s i t i. Instrumental Regression estimator (IR): α IREG = w i z i x i T i s 1 w i z i t i i s

8 Sample- Estimates(2) GREG is motivated by the model t j = x j T α + e j E(e j x j )=0 (1) Under non-response, validity of GREG requires t x = t x, I = 1 t x = 0 = t x = 0, I = 1, which means that sample non-response is completely ignorable in the population for which x = 0 (i.e. not on any register). Not plausible.

9 Sample- Estimates (3) A motivating model for Instrumental Regression is t j = z j T θ + ε 1j (2) x j = z j T γ + ε 2j, where E(ε 1j z j )=0, E(ε 2j z j )=0, Cov(ε 1j, ε 2j z j ) 0, α IREG = γ 1 θ Assume in the population that t z = t z, I = 1 (3) x z = x z, I = 1 If t z, non-response is non-ignorable.

10 Example 1- Estimating Australian Population Size X= Census, Survey=Post Enumeration Survey x Census person-present counts by Indigenous and Torres Strait Islanders (ATSI) status and the cross-classification of region, sex and age groups z same as x but obtained from PES on a usual residents basis X= Medicare, Survey=Post enumeration Survey Population Size estimates are too high due to over-coverage (i.e. we cannot identify register records that do not belong to U).

11 Example 2- Registers Register 1: Age Group, Capital City and Sex Covers 80% of people aged years and cover 95% of people otherwise Capital City is correct for 80% of people in the year age otherwise correct for 95% Register 2: Aboriginal and Torres Strait Islanders (ATSI) status Covers 60% of the ATSI population and covers 90% of the remaining population. Status is correct for only 80% of the ATSI population and 95% of the remaining population. Register 3: Covers 95% of people with Income greater than $20,000. Here z and x are the same characteristics but collected by the survey and register, respectively.

12 Example 2- Sample Table 1: Marginal Reductions (from 100%) in Response Rate by Characteristics (z) in Five Scenarios Scenario Age Range = (20 to 30 years) Aboriginal and Torres Strait Islander Income is less than $20,000 No Yes No Yes No Yes

13 Example 2- Bias of Instrumental Regression Scenario Income <$20,000 Income >$20,000 Living in the Capital City? Living in the Capital City? No No Yes

14 Way forward? Population estimates from only Registers Over-Coverage on Australian Registers. Select sample of register records? Record linkage errors Critical that linkage errors are negligible (c.f overcoverage) Q: Can some incorrect links not cause bias? Sample Design: target people with SQDs Plan to target indigenous dwellings Data Management Framework.