Estimation of Models with Correlated Measurement Errors from Panel Data

Single-indicator multiwave models provide one way to estimate the error variance of survey items. Two influential papers in the early 1970s (Wiley and Wiley 1970; Wiley and Wiley 1974) presented variations of such models for three waves of data. The first assumes that the only measurement error present is random (RE model). The second allows for correlated errors (CE model). The RE model has frequently been applied with useful results. The CE model, on the contrary, has rarely been used and tends to produce anomalous results. CE estimates based on only three waves of data are shown to be generally so sensitive to sampling error that they are uninformative. The standard errors of the CE model improve substantially when panels of four or more waves are used. This improvement, however, is contingent on the appropriateness of extending the rigid assumptions underlying the three-wave CE model to longer panels.