Path and Directionality Discovery in Individual Dynamic Models: A Regularized Unified Structural Equation Modeling Approach for Hybrid Vector Autoregression

Path and Direction Discovery in Individual Dynamic Factor Models: A Regularized Hybrid Unified Structural Equation Modeling with Latent Variable

There has been an increasing call to model multivariate time series data with measurement error. The combination of latent factors with a vector autoregressive (VAR) model leads to the dynamic factor model (DFM), in which dynamic relations are derived within factor series, among factors and observed time series, or both. However, a few limitations exist in the current DFM representatives and estimation: (1) the dynamic component contains either directed or undirected contemporaneous relations, but not both, (2) selecting the optimal model in exploratory DFM is a challenge, (3) the consequences of structural misspecifications from model selection is barely studied. Our paper serves to advance DFM with a hybrid VAR representations and the utilization of LASSO regularization to select dynamic implied instrumental variable, two-stage least squares (MIIV-2SLS) estimation. Our proposed method highlights the flexibility in modeling the directions of dynamic relations with a robust estimation. We aim to offer researchers guidance on model selection and estimation in person-centered dynamic assessments.

Tutorial on the Use of the regsem Package in R

Sparse estimation through regularization is gaining popularity in psychological research. Such techniques penalize the complexity of the model and could perform variable/path selection in an automatic way, and thus are particularly useful in models that have small parameter-to-sample-size ratios. This paper gives a detailed tutorial of the R package regsem, which implements regularization for structural equation models. Example R code is also provided to highlight the key arguments of implementing regularized structural equation models in this package. The tutorial ends by discussing remedies of some known drawbacks of a popular type of regularization, computational methods supported by the package that can improve the selection result, and some other practical issues such as dealing with missing data and categorical variables.