Accounting for the "Known Unknowns": Incorporating Uncertainty in Second-Stage Estimation

Recent political science research has seen a surge in interest in estimating latent variables (including ideal points of legislators and judges, political sophistication, and democratization) using item-response theory modeling and other factor-analytic techniques. These models offer several advantages over summated scales and other techniques, but one of these advantages—having an estimate of the uncertainty in our measurement of the latent variable—is often discarded when these estimates are used in second-stage models. Here I demonstrate a technique known as simulation-extrapolation estimation (SIMEX) for incorporating uncertainty into latent variable estimates. I then compare estimates using standard estimators such as ordered logit and binary probit to their SIMEX counterparts incorporating uncertainty. These results demonstrate the value of including known error variance in second-stage estimates without the added complication of using structural-equation model approaches. * This paper is based on preliminary research presented at the 2007 Meeting of the Society for Political Methodology, University Park, Pa.; I thank the participants in that meeting (particularly Michelle Dion, who also reviewed this manuscript) for their helpful feedback on this project.