• An investigation into the effectiveness of simulation-extrapolation for correcting measurement error-induced bias in multilevel models

      Custer, Christopher (2015-04)
      This paper is an investigation into correcting the bias introduced by measurement errors into multilevel models. The proposed method for this correction is simulation-extrapolation (SIMEX). The paper begins with a detailed discussion of measurement error and its effects on parameter estimation. We then describe the simulation-extrapolation method and how it corrects for the bias introduced by the measurement error. Multilevel models and their corresponding parameters are also defined before performing a simulation. The simulation involves estimating the multilevel model parameters using our true explanatory variables, the observed measurement error variables, and two different SIMEX techniques. The estimates obtained from our true explanatory values were used as a baseline for comparing the effectiveness of the SIMEX method for correcting bias. From these results, we were able to determine that the SIMEX was very effective in correcting the bias in estimates of the fixed effects parameters and often provided estimates that were not significantly different than those from the estimates derived using the true explanatory variables. The simulation also suggested that the SIMEX approach was effective in correcting bias for the random slope variance estimates, but not for the random intercept variance estimates. Using the simulation results as a guideline, we then applied the SIMEX approach to an orthodontics dataset to illustrate the application of SIMEX to real data.