The Multiplicative Simulation-Extrapolation Approach

Abstract

We develop a new general approach for handling multiplicative measurement error in continuous covariates in linear and nonlinear regression models. We apply the Simulation-Extrapolation (SIMEX) approach, which is a simulation based method of estimating and reducing the bias due to additive measurement error, to the case of multiplicative measurement error. We do not apply a logarithmic transformation, so that the multiplicative measurement error model becomes an additive one, but we show how to modify the SIMEX approach, in order to use the multiplicative measurement error model as such. Multiplying the measurement error by additional measurement error allows us to infer in which way the estimation bias is affected by the increase of variance of the measurement error. In the extrapolation step, the estimated parameters are modelled as a function of the magnitude of the variance of the measurement error and extrapolated to the case of no measurement error. We apply our method to the case of data masking, in order to obtain parameter estimates of the true data generating process, if the data are multiplied by an additional measurement error. We produce Monte-Carlo evidence on how the reduction of data quality can be minimized by masking.