Incorporating Nonresponse in a Markov Latent Class Measurement Error Model of Consumer Expenditure Brian Meekins, Clyde Tucker Bureau of Labor Statistics Paul Biemer RTI International Any opinions expressed in this paper are those of the authors and do not constitute policy of the Bureau of Labor Statistics

Uses repeated measurements from panel survey data to estimate classification error Used successfully in evaluation of labor force data (e.g., Biemer & Bushery, 2001 Tucker, Biemer, Meekins 2012) Does not require external validation data; estimates of error directly from panel data Applied to reports of expenditures in the CEIS Markov Latent Class Analysis

U.S. Consumer Expenditure Interview Survey (CEIS) ~ 6,000 CU’s/year CU’s interviewed every 3 months about prior 3 months expenditures 4 consecutive interviews on each CU New data: N=23,719 From to Unweighted analysis

ElectricityMen’s Clothing OnlyMinor Vehicle Repairs CableWomen’s Clothing OnlyVehicle Oil TrashMen’s AccessoriesMajor Vehicle Repairs GasWomen’s AccessoriesVehicle Other TVMen’s ShoesDental SportsWomen’s ShoesEyes FurnitureKid’s ApparelDrugs* Other HouseholdKid’s Clothing OnlyPets Kitchen AccessoriesKid’s Accessories Men’s ApparelKid’s Shoes Commodity Categories 4

1 st Order Markov Model 5 ZYX W Where

Definition of Indicator Variables Define for Interview 1, 1, if reported as a purchaser for the quarter 2, if reported as non-purchaser with similar definition for X, Y, Z for 2nd, 3rd, and 4th interviews W=

2 nd Order Markov Model 7 ZYX W

Mover-Stayer 8 ZYX W M 1, P(W=1) = P(X =1) = P(Y =1) = P(Z = 1) = 1 M = 2, P(W=1) = P( X =1) = P(Y =1) = P(Z = 1) = 0 3, P(W),P(X), P(Y), and P(Z) are unconstrained.

Measurement Error Model 9 ADCB ZYX W = = = =

Markov Latent Class Model Notation True expenditure status is a latent variable Latent Var. Indicator Var. Interview 1W A Interview 2X B Interview 3Y C Interview 4Z D

Definition of Latent Variables Where, 1, if one or more purchases of an item during the W=quarter (“purchaser”) 2, if no purchase (“non-purchaser”) with similar definition for X, Y, Z for 2nd, 3rd, and 4th interview

Markov or Mover-Stayer model assumptions Equal measurement error across all interviews No False Positives Model Assumptions

Model Selection Limitations on Lem forced estimation of separate pieces of the full model: ME & NR Multiple iterations to avoid local maxima Best refusal, noncontact, and measurement error variables were selected based on fit in these component models Using best variables constructed combined model

Estimates ME Model No covariates P(A=1|W=1) = P(B=1|X=1) = P(C=1|Y=1) = P(D=1|Z=1) =

Measurement Error Model 15 ADCB ZYX W = = = = Measurement Error Indicators

Measurement Error Model 16 ADCB ZYX W Measurement Error Indicators

ME Variables 1. Missing income data (CU) 2. Type and frequency of records used (interiew) 3. Length of interview (interview) 4. Ratio of expend. in last month to entire quarter (interview) 5. Combination of types of record and int length (interview) 6. Number of expenditure questions imputed/allocated (interview) 7. Completion mode (interview) 8. Family size (CU)

ME Model w/Covariates 18 ME Model w/ Covariates P(A=1|W=1)0.781 P(B=1|X=1)0.733 P(C=1|Y=1)0.696 P(D=1|Z=1)0.687

ME Model: Covariates 19 Income MissingP(A=1|W=1) Missing0.779 Not Missing0.796 ModeP(A=1|W=1) Telephone0.766 In person0.814 Record use/Int timeP(A=1|W=1) Short int/few records0.664 Medium int/med records0.779 Long int/lots of records0.982

Nonresponse Error Model 20 EHGF Noncontact Covariates 1 Reports All Qtr 2 Reports Some 3 Reports None M Refusal Covariates

Nonresponse Error Model 21 EHGF Noncontact Covariates 1 Latent.. likelihood c of Interview M Refusal Covariates

Noncontact Variables 1. Number of noncontact problems reported in CHI (interview) 2. Age (CU) 3. Owner/Renter (CU) 4. Urbanicity (CU)

Noncontact Estimates 23 WaveProb of Responding E1.000 F0.877 G0.823 H0.798

Noncontact Estimates 24 Noncontact Problems P(F=1) % Samp No mentions or 2 mentions Three or more P(F=1) % Samp Rents Owns

Noncontact Estimates 25 AgeP(F=1) % Samp < UrbanicityP(F=1) % Samp Urban Rural

Refusal Variables 1. Factor1 variables – Reluctance privacy concerns (CU) 2. Factor2 variables – Reluctance time concerns (CU) 3. Any reluctance mentioned (CU) 4. Conversion Refusal – only wave 1 available? (CU) 5. Region (CU) 26

Refusal Estimates 27 Refusal Reason Factor 2P(M=3) Worst % Samp Never mentioned Avg 1 per interview More Refusal Reason Factor 1P(M=3) Worst % Samp Mentioned Not mentioned

Refusal Estimates 28 RegionP(M=3) Worst % Samp Northeast Midwest South West Any Conversion RefusalP(M=3) Worst % Samp Yes No

29 EHGF Noncontact Covariates Refusal Covariates ADCB ZYX W = = = = Measurement Error Indicators 1 Reports All Qtr 2 Reports Some 3 Reports None M Combined ModelCombined Model

Estimates: Full Model Measurement Error (Item Nonresponse) P(A=1|W=1)0.781 P(B=1|X=1)0.758 P(C=1|Y=1)0.739 P(D=1|Z=1)0.745 Unit Nonresponse P(F=1|X=1)0.957 P(G=1|Y=1)0.953 P(H=1|Z=1)0.957

Missing Reports Of the estimated 1,939 missed reports  1,721 were a result of item nonresponse  218 were a result of unit nonresponse Reminder: nonresponse conditioned on first wave response 31

Discussion Can be conducted for each commodity category Models need further specification & adjustments, thorough evaluation of covariates Estimates can be used to inform:  Allocation of resources  Adjustment: relationship of NR and ME  Fatigue, conditioning, etc. 32

Contact Information Brian Meekins Office of Survey Methods Research U.S. Bureau of Labor Statistics

Objective Diagnositics Fit Statistics  L-square Dissimilarity Index BIC

Subjective Diagnostics True purchase pattern given estimated purchase pattern Mover-stayer classification by purchase pattern Accuracy rates by subgroup  Accuracy is the percent of true purchasers that reported purchasing that commodity