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Measurement Error

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Measurement Error

e

M

- Survey record differs from its true value
- Sampling error: arise from the random sampling variation when n of units measured instead of N units.
- Measurement error
(Systematic error, nonsampling error)

- Not decrease with the overall sample size.
- Decrease with the repeated measurement.
- Possible sources of measurement error in survey data
- Interviewer
- Coder

Normal Dist’n

- In presence of measurement error with mean zero, the estimator of mean and total remain unbiased or consistent.
- For more complex parameters, the nice feature may not hold.
- Fuller (1995) points out that the usual estimators for dist’n func., quantiles, regression coef. are biased.

- Assuming non-zero constant measurement error mean, the usual estimators of mean, total, proportion are also biased.
- Furthermore, assuming correlated errors between individuals with the same interviewer, the usual estimator of standard errors are also biased.

- If estimates of the measurement error variances are available, it is possible to obtain bias-adjusted estimators.
- Repeated measurement of sub-samples
- Allocate resources at design stage to make repeated observations on a sub-sample.
- Hartley and Rao (1978) and Hartley and Biemer (1978) provided interview and coder assignment conditions that permit the estimation of sampling and measurement error.

- Measurement error variance model.

- Earliest examination of measurement error in the survey focuses on evaluating the impact of interviewers on the data.
- There is correlation among measured values collected by the same interviewer.
- Hansen, Hurwitz and Bershad model shows

- ANOVA model can be specified to estimate interviewer variability.
- Model is appropriate for continuous responses.
- For binary response, the result underestimate the intra-interview variability.

- Full, W.A. Estimation in the presence of measurement error.
- Scott, A. and Davis, P.. Estimating interviewer effects fro survey responses.
- Hartley, H.O. and Biemer, P.. The estimation of nonsampling variances in current surveys.
- Hartley, H.O. and Rao, J.N.K. The estimation of nonsampling variance components in sample surveys.
- Measurement errors in surveys. Paul Biermer, et al.

Binary Data and Interviewer Effects

An Example

- Often use binary variables
- Interested in proportion parameters
- Very specialized studies
- Few reviewers (highly skilled)
- Very expensive to train
- Large case loads

- Interviewer variability is usually ignored because it affects binary data less than continuous data

- Studying ‘adverse events’ in New Zealand hospitals
- 2-stage design
- PPS sample of hospitals
- Systematic sample of 575 medical records drawn from each hospital for 1998 admissions

- Average case load per reviewer is 300 (problem!)
- Typical of such studies
- Interest in proportion of hospital admissions associated with an adverse event

- Random Effects Model
- Hospital Effect
- Interviewer Effect
- Respondent Effect
- Assume an underlying continuous variable initially and then extend to the binary case

- : Normally Distributed
- : Normally Distributed
- : Logisticly Distributed
- All these effects are assumed to be uncorrelated with all other effects

- Represents the inflation in variance due to the interviewer and cluster effects (i.e. inflation when there are not independent observations)
- This is assuming small interviewer and PSU effects

- = 0.04
- = 0.002
- = 687
- Design Effect = 29.0
- So the variability is increased by a multiplicative factor of 29!

- With high case loads, even small interviewer variability can have high impact on estimates of population means and proportions
- Binary data poses special challenges and more research needs to be done when the PSU and interviewer correlations are not small