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A Latent Class Callback Model for Survey Nonresponse

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Latent class model (LCM) ... Introduces a latent variable X where X = 1, if HCNR and X = 2, ... The Latent Class Model can be employed to reduce total ... – PowerPoint PPT presentation

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Title: A Latent Class Callback Model for Survey Nonresponse


1
A Latent Class Call-back Model for Survey
Nonresponse
  • Paul P. Biemer
  • RTI International and UNC-CH
  • Michael W. Link
  • Centers for Disease Control and Prevention

2
Outline
  • Motivation for the study
  • Early cooperator effects (ECE) in the Behavior
    Risk Factor Surveillance System (BRFSS)
  • Call-back models
  • Manifest and latent
  • Model extensions
  • Application to the BRFSS
  • Results
  • Summary and conclusions

3
Terms and definitions
  • Cooperators units that will eventually respond
    at some request or call-back
  • Non-cooperators (also called hardcore
    nonrespondents) units that will not respond to
    any call-back

4
Terms and definitions (contd)
  • Early cooperator Cooperators that respond at
    early calls (say, 5 or less)
  • Later cooperators Cooperators that respond at
    later calls (say, 6 or more)
  • Early cooperator effect (ECE) expected
    difference in estimates based on early vs. early
    later cooperators (say, )

5
Response rates as a function of number of call
attempts
Number of call attempts
6
Illustration 1- Have you ever been told by a
doctor, nurse or other health professional that
you had asthma?
Small ECE maximum of 5 calls is adequate
7
Illustration 2- During the past 12 months, have
you had a flu shot?
Larger ECE max of 5 call attempts may be
biasing Could consider other definitions of
early cooperator.
8
Why study ECE?
  • Effort (and costs) could be saved if ECE is small
  • If ECE is not small, adjustments may be applied
    to reduce it
  • May need to adjust for HCNRs, not only later
    cooperators

9
What adjustments can be applied to reduce the ECE?
  • Nonresponse adjustments
  • Requires characteristics of nonrespondents
  • Lack of information a limitation for some surveys
  • Post-stratification adjustments
  • Requires known target population totals within
    adjustment cells
  • Variables limited to those available externally
  • Call-back model adjustments
  • Assumes response propensity is function of level
    of effort required to obtain a response and
    grouping variables
  • Related work of Drew and Fuller (1980), Politz
    and Simmons (1949), others

10
ECE in the BRFSS
  • Survey details
  • One of the largest RDD surveys in the world
  • Estimates the prevalence of risk behaviors and
    preventive health practices
  • Monthly, state-based, cross-sectional survey
  • Target population is adults in telephone hhs
  • Data source 2004 survey with 300,000
    interviews

11
ECE in the BRFSS (contd)
  • Early cooperator defined as responding with 5
    fewer call attempts
  • Examined differences in
  • demographic characteristics
  • 10 selected health characteristics overall and by
    demographic domain
  • ECE estimated by
  • Data weighted by base weights only

12
Typical Values of ECE
13
Typical Values of ECE (contd)
14
Summary of the Results
  • Early cooperators are different from later
    cooperators on many dimensions
  • For most characteristics ECE is relatively small
  • Less than 3 percentage points at aggregate level
  • Rarely more than 3 points for domains
  • For some characteristics, ECE may be important
  • Other definitions of ECE also considered

15
Hardcore Nonresponse Bias
  • Hardcore Nonrespondents Units that will not
    respond under the current survey protocol no
    matter the number of call-backs
  • ECE does not include the bias due to hardcore
    nonrespondents
  • Total nonresponse bias Bias due to cooperators
    who did not respond bias due to hardcore
    nonrespondents
  • Adjusting for ECE may not remove bias due to HCNR

16
Call-back Models for Adjusting for ECE and HCNR
Bias
  • General idea
  • Estimate the response propensity for subgroups of
    the population
  • Response propensity is modeled as a function
    level of effort (LOE) to obtain a response
  • Two models are considered
  • Manifest model (MM) Ignores HCNR
  • Latent class model (LCM) Includes HCNR
  • Includes a latent indicator variable to represent
    the HCNRs in the population
  • Why latent?

17
Illustration for 5 Call-backs
1 interview 2 noninterview 3 noncontact
18
Illustration for 5 Call-backs
1 interview 2 noninterview 3 noncontact
19
Potential Advantages over Post-Stratification
  • Post-stratification adjustments (PSAs) depend
    upon the availability of external benchmarks or
    auxiliary data
  • Selection of control variables is quite limited
  • Target populations also quite limited
  • Adjust for ignorable nonresponse only

20
Potential Advantages over Post-Stratification
  • Call-back model can rely only on internal
    variables
  • Weighting classes can be defined for any
    variables collected in the survey
  • Can be applied for any target population
  • Greater ability to selected variables that are
    highly correlated with response propensity
  • Adjust for ignorable and nonignorable
    nonresponse

21
Modeling Framework
  • Simple random sampling
  • Survey eligibility is known for all sample
    members
  • No right censoring
  • (i.e., all noncontacts received maximum LOE)
  • Extensions to relax these assumptions are
    described in the paper

22
Incorporating the Model-based Weights
  • Unadjusted estimator of the mean

Based on the sample distribution
Adjusted estimator of the mean
Estimated from the model
23
Two Models for Estimating
  • MM (Manifest Model)
  • Assumes all nonrespondents would eventually
    respond at some LOE (i.e., all nonrespondents
    have a positive probability of response)
  • LCM (Latent class model)
  • Incorporates 0 probability of response for the
    hardcore nonrespondents (HNCRs)

24
Technical Details
25
Notation
Levels of effort (LOE)
Outcome of LOE l where 1interview, 2
noninterview, 3noncontact
LOE associated with state S1 or 2
Grouping variable (weighting class variable)
26
Notation
Probability person in group g is interviewed at
LOE l
Probability person in group g is noninterviewed
at LOE l
Probability person in group g is never contacted
Number of sample persons in group g interviewed
at LOE l
Number of sample persons noninterviewed at LOE l
Number of sample persons never contacted after L
(max LOE) attempts
27
General Idea Outcome Patterns for 5 Call-backs
  • Cooperator HCNR
  • 11111 0
  • 31111 0
  • 33111 0
  • 33311 0
  • 33331 0
  • 22222
  • 32222
  • 33222
  • 33322
  • 33332
  • 33333

28
Likelihood for the Manifest Model
  • This model is appropriate when
  • Every sample member has a positive probability of
    responding at some LOE, or
  • Adjustment for ECE only is desired

29
Likelihood for the Latent Class Model
Introduces a latent variable X where X 1, if
HCNR and X 2, if otherwise Appropriate when
some sample members have a 0 probability of
responding and adjustment for total nonresponse
(Later Cooperators HCNRs) is desired
30
Model Restrictions
The key assumptions regard the form of the
probabilities
, and
where
and
31
Model Restrictions (contd)
Manifest Model
(i)
, say, for l 3,...,L for Llt10
and (ii)
i.e., no HCNR,s and response probabilities are
equal for LOE 3,..., 9. The probabilities for
LOEs 1, 2 and 10 (if present in the model) were
not restricted
Latent Class Model
  • is replaced by ...
  • (i')

to represent the HCNR group in the model.
32
Results
33
Four Estimators were Considered
  • Unadjusted estimator
  • Estimator using MM estimates of
  • Estimator using LCM estimates of
  • Estimator using CPS estimates of
  • i.e., usual PSA estimator
  • treated as the gold standard

34
Comparison of the ECE for a Maximum Five
Callbacks Strategy Before and After MM Adjustment
35
Differences between PSA and Unadjusted and
Adjusted Estimates for a Maximum Five Callbacks
36
Estimating the Potential Bias Reduction
  • BRFSS data do not exhibit very large nonresponse
    biases
  • Therefore, consider a variable, Y, that has
    maximum nonresponse bias given the BRFSS
    nonresponse rates
  • To do this, we form
  • Yg BRFSS response rate for group g
  • Compute the relative difference between
    unadjusted and adjusted estimates and the PSA
    estimate of the mean of Y

37
A Measure of Potential Bias Reduction
  • Define the relative difference operator for any
    maximum LOE, L as

Gold standard estimator
38
Absolute Relative Differences (RDL) for
Unadjusted and Adjusted Estimators as a Function
of Number of Call-backs
39
Conclusions
  • ECE for 5 call-backs is generally small, but can
    be moderately high for some characteristics
  • The Manifest Model can be employed to reduce ECE
  • The Latent Class Model can be employed to reduce
    total nonresponse bias (Later Cooperators HCNR
    bias)
  • Future research should focus on
  • Variable selection
  • Comparisons of MSEs of the estimators
  • Small/medium size sample properties
  • Integration with other post-survey weight
    adjustments
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