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Paul Biemer, UNC and RTI Bac Tran, US Census Bureau Jane Zavisca, University of Arizona SAMSI Conference, 11/10/2005 Latent Class Analysis of Rotation Group Bias: The Case of Unemployment

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Overview Motivation: To understand measurement error in the official unemployment rate Method: Latent Class Analysis: measurement error as classification error Distinction from previous research: Focus on measurement error mechanisms, as opposed to correcting marginal estimates. Ultimate goal: To improve survey design.

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The Official Unemployment Rate In Labor Force { Source: The Current Population Survey, 2004

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The Official Unemployment Rate Categories Employed: worked at least one hour in previous week, or temporarily absent from job. Unemployed: not employed and actively looking for work (unprompted categories), or temporarily laid off. Not in Labor Force (NILF): All others.

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Evidence for Measurement Error in Labor Force Status (LFS) in the CPS 1.Re-interview inconsistency 2.Rotation group bias

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Re-interview Inconsistency 1% random sample of original sample of 50,000 households is re-interviewed monthly (without replacement). Re-interview occurs in same week as the original interview. Inconsistent responses suggest measurement error.

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Re-interview Inconsistency (2001-2003) 8.9% of cases are inconsistently classified.

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Unemployment Inconsistency (2001-2003)

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Rotation Group Design

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Rotation Group Bias (2002 Full CPS)

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What Could Cause Rotation Group Bias? Non-response bias: rotation groups may represent different populations. Differences in interview setting telephone vs. face-to-face proxy vs. self Time in sample effect Improved understanding of questionnaire Embarrassment at admitting prolonged unemployment Interview changes behavior

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Latent Class Analysis to Test Hypotheses Sources of Rotation Group Bias Non-response bias (different populations): Does latent employment status vary by rotation group? Measurement error: Does rotation group influence error rates? Differences in setting: Does interview mode (telephone vs. face-to-face) initial interview influence error rates? Does interview mode account for apparent rotation group effects on error rates? Social pressure: Gender influences latent employment status Does gender also influence error rates? Does the effect of rotation group vary by gender?

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Correlation between Month-in-Sample and Interview Mode

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Re-interview Data Set N = 24,297 (un-weighted data) X = True Labor Force Status (Latent Variable) A = Observed Labor Force Status at Inititial Interview B = Observed Labor Force Status as Time 2 (Reinterview)

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Basic Latent Class Model X A B X, A|X, B|X Shorthand: (with usual constraints for identifiability)

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Grouping Variable X A B S, X|S, A|X, B|X S

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External Variable influencing Classification Error X A B SM, X|S, A|XM, B|XM SM

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Grouping versus External Variables X A B SM, X|S, A|XMS {AXM AXS}, B|XMS {BXM BXS} SM

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Covariates S = Gender Men: 47% Women: 52% M = Month in Sample 1 or 5: 28% 2-4, 6-8: 72% T = Interview Mode (Initial Interview) Telephone: 72% In Person: 18%

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Statistical Power & Identifiability Issues Large total N, but relatively small N for unemployed. More variables means more identifiable models, but also diminishing cell counts and boundary solutions.

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Principles of Model Construction Always include X|S A|X B|X Assume 3 latent classes & S as grouping variable Fit classification table of A*B*M*T*S. Vary following effects M as grouping variable M &/or T affecting classification error for A & B T affecting A but not B S affecting A & B when identifiable based on other restrictions (including interaction of M & S)

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Principles of Model Construction Try equality constraints Equal influence of M & or S on error rate for A & B. Error rate for T at time A = error rate at time B (when T does not affect B).

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Principles of Model Selection Limit search to theoretically plausible models. Limit search to identifiable models. Overall model fit P-value of likelihood ratio test vs. saturated model >.01 Dissimilarity index <.05 Model selection among those meeting above criteria: Bayesian information criterion (BIC) Likelihood ratio test for nested models Check substantive interpretation within set of possible best models.

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Best-Fitting Models

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Estimated Unemployment Rate Model 1 (similar to other top models) UE = 4.9% Observed M.I.S. 1 & 5 UE = 6.0% Observed M.I.S. 2-4, 6-8 UE = 4.7%

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Conditional Probabilities for Employment Status

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Conditional Probabilities for A|TX & B|TX

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Conditional Probabilities for A|MX & B|MX

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Summary Findings Change in structural model (treating month-in- sample as grouping variable) does not change the preferred measurement model. Models fit nearly as well without M as grouping variable; casts doubt on non-response bias hypothesis. M-I-S bias is not just a function of interview mode. Covariate effects (esp. S) on response error should be examined further in model with more df; need another grouping variable.

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Unresolved Issues Ambiguous results for model selection Most interested in fit of unemployment classification, but this is overwhelmed in measures of overall fit Software limitations: clustering, local & boundary solutions, standard errors not consistently output

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Future Research Agenda Try finer coding of month-in-sample Develop models for other variables: age, race, proxy vs. self Pool more years of data Develop hypotheses & interpretation based on review of: experimental work analyses of non-response related models including Markov latent class models of employment status transitions

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Rotation Group Bias (2001-2003, reinterview data)

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