Testing for measurement error in survey data analysis using paradata

SummaryParadata refers to survey variables which are not of direct interest themselves, but are related to the quality of data on survey variables which are of interest. We focus on a categorical paradata variable, which reflects the presence of measurement error in a variable of interest. We propose a quasi-score test of the hypothesis of no measurement error bias in the estimation of regression coefficients under models for paradata. We also propose a regression-based test, analogous to a simple test proposed by Fuller for instrumental variables. The methods developed can take account of a complex sampling design. In an application with data from the British Household Panel Survey, all tests provide clear evidence of measurement bias in the estimated coefficient of gross pay. In a simulation study, all tests have rejection rates close to the nominal level under the null hypothesis; the quasi-score tests display more power than the regression-based test. The size of the quasi-score test is shown to be robust to some forms of misspecification of the paradata model, both by a theoretical argument and in findings of the simulation study.