Known Unknowns and Unknown Knowns Incorporating Uncertainty in Second-Stage Estimation

Recent political science research has seen a resurgence in interest in estimating latent variables (including ideal points, political sophistication, and democratization) using item-response theory modeling and other factor-analytic techniques. Yet, despite these models offering advantages over summated scales other techniques, one key advantage-the estimation of the uncertainty of estimates of the latent variable-is often discarded in second-stage analysis, such as efforts to explain roll-call voting behavior or incorporating estimated knowledge into explanations of voter decision-making. Here I demonstrate a technique known as simulation-extrapolation estimation (SIMEX) for incorporating uncertainty into these estimates, and compare estimates using standard estimators such as ordinary least squares linear regression and maximum-likelihood probit regression to their SIMEX counterparts using latent-variable estimates with both low (estimates of legislator ideal points) and high (estimates of voter sophistication) variance. These results demonstrate the value of including known error variance in second-stage estimates without resorting to the use of structural-equation model approaches. -2.389 0.097 < .001 -2.394 0.094 < .001 Member black -0.081 0.081 n.s. -0.087 0.082 n.s. Member Hispanic -0.226 0.091 ≈ .013 -0.212 0.091 ≈ .020 Bush vote % '04 0.025 0.002 < .001 0.025 0.002 < .001 Member female -0.133 0.054 ≈ .013 -0.133 0.054 ≈ .013 Member GOP 1.448 0.057 < .001 1.447 0.057 < .001 Dist. minority % 0.001 0.001 n.s. 0.001 0.001 n.s