Using a Mixture Latent Markov Model to Analyze Longitudinal U.S. Employment Data Involving Measurement Error

Latent Markov modeling is used as an alternative to the Current Population Survey (Census, 2002) reinterviewing methodology for estimating the measurement error in the recorded employment status. This alternative methodology, which is implemented in the syntax version the Latent GOLD program, turns out to be a promising new approach for estimating measurement error in longitudinal surveys. However, it is important to take into account unobserved heterogeneity in the initial-state and transition probabilities because the size of the measurement error is overestimated when unobserved heterogeneity is not taken into account. 1. Background and Statement of the Problem The Current Population Survey (CPS) is a national household survey conducted by the U.S. Census Bureau for the Bureau of Labor Statistics (Census, 2002). It is designed to generate monthly national estimates of labor force characteristics including employment status i.e, counts of: (E) employed, (U) unemployed, and (N) not in the labor force. For a variety of reasons, employment status questions in the CPS may not elicit true employment status. Thus, a respondent’s true employment status is unknown. The primary goal was to improve the methodology for estimating the magnitude and direction of measurement errors that exist in employment status elicited by the survey. Some years ago the U.S. Census Bureau started exploring the solution of utilizing a latent Markov (LM) structure to estimate the measurement error as a more cost effective and timely approach than its current reinterview methodology (Biemer and Bushery, 2000; Tran & Winters, 2003). Rather than incurring a monthly cost of reinterviewing a sample of respondents, the LM approach replaces the reinterview with the repeated measurements that are readily available at no additional cost as part of the longitudinal design. On the other hand, the use of repeated measures instead of a reinterview means that differences in a respondent’s state from one month to another may reflect either measurement error or a true transition from one state to another (e.g., from being employed to being unemployed). Thus, it is necessary to model both measurement and transitions simultaneously as part of the model. The main contribution of the current project is that it shows that it is important to use a mixture LM model instead of a standard LM model. Use of the latter may seriously overestimate the size of measurement error probabilities. Below we first introduce the standard LM model, as well as its mixture extension. Then, details are provided on the implementation of these models in the Latent GOLD software package. Subsequently, we describe the CPS data set This research project was supported by contract #50 YABC-2-66060 from the U.S. Census