'Paleontological Institute at The University of Kansas'
Abstract
Prior studies have shown that analyzing a continuous time panel model with the Exact Discrete Model (EDM) is less biased and more efficient than approximate methods such as Latent Differential Equations (LDE). Simulation models have included observed variables, latent variables, or a mix of the two types, but prior work has not examined the effects of measurement error on estimation when only a single observation is made at each occasion. This paper compares the performance of the EDM and LDE when measurement error is varied. Data conforming to a first order differential equation was generated for two variables across four time points using a variety of sample sizes, auto-effect values, and cross-effect values. EDM auto-effects were shown to be underestimated and become increasingly biased as measurement error increased while LDE estimates were positively biased, but addition of measurement error had little effect. Estimates for negative cross-effects had smaller absolute bias than positive cross-effects in both models, with LDE estimates closer to the true value than EDM. If expected measurement error is less than 10%, then EDM will produce more accurate estimates than LDE. For measurement error ranging from 10% - 15% each model produced some less biased and more efficient parameters than the other. For measurement error than exceeds 15%, LDE will provide less biased parameters for all but strongly negative cross-effects
