The Role of Omitted Variables in Estimates for a Continuous Time Cross-Lag Panel Model

Abstract

One assumption in regression-based models is that no theoretically important variables have been omitted from the model. Provided an omitted variable has a strong effect in the model, its omission can introduce bias in one or more parameter estimates. The exact discrete model, a continuous time panel model, has been extended to include heterogeneity in the intercept by estimation of manifest or trait variance. The inclusion of what is equivalent to a random effect should reduce bias due to omitted variables. Two simulations examined exact discrete model estimates’ to see if they were robust to omission of time-invariant predictors and both time-invariant and time-varying predictors. Auto-effects, cross-effects, and time-invariant effects were compared by computing bias and efficiency for a two predictor model, a one predictor model where some important variables were missing and some were present, and a model that only estimated the dynamic process. Relative bias and relative efficiency were computed to compare the two predictor model to the omitted variable models. Results were influenced the most by cross-effect conditions, strength of the omitted variable, and whether the omitted variable was related to other parameters in the model. In the first simulation, results also varied by size of the random intercept but did not always change the overall result. In the second simulation, most estimates showed less bias or more efficiency in the omitted variable models in conditions in which the time-varying effect was correlated with trait variance.