Measurement error
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Measurement Error. e. M. Measurement Error. 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).

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Measurement Error

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Measurement error

Measurement Error


Measurement error1

e

M

Measurement Error

  • 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)


Measurement error

  • Not decrease with the overall sample size.

  • Decrease with the repeated measurement.

  • Possible sources of measurement error in survey data

    • Interviewer

    • Coder


Simplified model

Simplified Model

Normal Dist’n


Effect

Effect

  • 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.


Measurement error

  • 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.


Measurement error

  • 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.


Interviewer effect

Interviewer Effect

  • 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


Measurement error

  • 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.


References

References

  • 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

Binary Data and Interviewer Effects

An Example


Medical questionnaires

Medical Questionnaires

  • 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


New zealand quality of health care study

New Zealand Quality of Health Care Study

  • 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


Model

Model

  • Random Effects Model

  • Hospital Effect

  • Interviewer Effect

  • Respondent Effect

  • Assume an underlying continuous variable initially and then extend to the binary case


Assumptions

Assumptions

  • : Normally Distributed

  • : Normally Distributed

  • : Logisticly Distributed

  • All these effects are assumed to be uncorrelated with all other effects


Design effect

Design Effect

  • 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


Results

Results

  • = 0.04

  • = 0.002

  • = 687

  • Design Effect = 29.0

  • So the variability is increased by a multiplicative factor of 29!


Conclusions

Conclusions

  • 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


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