Incorporating Measurement Error in the Dynamic Structural Equation Modeling Using a Single Indicator or Multiple Indicators

Dynamic Structural Equation Modeling (DSEM) was recently introduced as an advanced multilevel time series method to analyze Intensive Longitudinal Data (ILD). Although measurement error is likely to be embedded in ILD, many applications of intensive longitudinal studies often rely on composite scores without modeling measurement error. However, measurement error can be captured in the DSEM framework using a single indicator or multiple indicators. In this paper, we discussed and compared three multilevel DSEM models that analyze within-person dynamic process of a construct with different approaches to addressing measurement error: (1) single-indicator multilevel AR(1) model without measurement error; (2) single-indicator multilevel AR(1) model with measurement error; (3) multiple-indicator multilevel dynamic factor AR(1) model. The difference between (1) and (2) and the similarity between (2) and (3) were highlighted. An experience sampling data set was analyzed to show the difference and similarity of the numerical results from the three approaches.