The Effects of Misspecified Measurement Interval in Multivariate Latent Differential Equation Models

Numerous statistical methods exist for the analysis of irregularly spaced time series data (Parzen, 1984). An extension of the Multivariate Latent Differential Equation (MLDE) model (Boker, Neale & Rausch, 2004) for accommodating irregularly-spaced data is provided. Moreover, the current dissertation focuses on how misspecifying an irregular sampling interval as an equal measurement interval effects the estimated model parameters of change of the MLDE model. The accuracy of the estimated model parameters of change was assessed through the use of Monte Carlo simulations. For exponential processes, relative to the MLDE model curvature parameter estimates from equally spaced data, the misspecification of irregularly spaced data has little to no effect on the bias but does decrease the precision of the curvature parameter estimates. For processes exhibiting cyclic change, if a high degree of misspecification exists in the sampling interval, relative to the MLDE model estimates of equally spaced data, the frequency parameter will be underestimated and the damping parameter will be overestimated. Utilizing FIML estimation to correctly define the sampling interval, however, may tend to overestimate the frequency of the process and overestimation of the damping will still exist. The amount of bias incurred in both the frequency and damping parameter due to the incorrect parameterization of time, however, does not appear to be substantial.