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There recently has been growing interest in the study of psychological and neurological processes at an individual level. One goal in such endeavors is to construct person-specific dynamic assessments using time series techniques such as Vector Autoregressive (VAR) models. However, two problems exist with current VAR specifications: 1) VAR models are restricted in that contemporaneous relations are typically modeled either as undirected relations among residuals or directed relations among observed variables, but not both; 2) current estimation frameworks are limited by the reliance on stepwise model building procedures. This study adopts a new modeling approach. We first extended the current unified SEM (uSEM) framework, a widely used structural VAR model, to a hybrid representation (i.e., "huSEM") to include both undirected and directed contemporaneous effects, and then replaced the stepwise modeling with a LASSO-type regularization for a global search of the optimal sparse model. Our simulation study showed that regularized huSEM performed uniformly the best over alternative VAR representations and/or modeling approaches, with respect to accurately recovering the presence and directionality of hybrid relations and reliably removing false relations when the data are generated to have two types of contemporaneous relations. The present study to our knowledge is the first application of the recently developed regularized SEM technique to the estimation of huSEM, which points to a promising future for statistical learning in psychometric models.

Structural equation models (SEMs) are widely used to handle multiequation systems that involve latent variables, multiple indicators, and measurement error. Maximum likelihood (ML) and diagonally weighted least squares (DWLS) dominate the estimation of SEMs with continuous or categorical endogenous variables, respectively. When a model is correctly specified, ML and DWLS function well. But, in the face of incorrect structures or nonconvergence, their performance can seriously deteriorate. Model implied instrumental variable, two stage least squares (MIIV-2SLS) estimates and tests individual equations, is more robust to misspecifications, and is noniterative, thus avoiding nonconvergence. This article is an overview and tutorial on MIIV-2SLS. It reviews the six major steps in using MIIV-2SLS: (a) model specification; (b) model identification; (c) latent to observed (L2O) variable transformation; (d) finding MIIVs; (e) using 2SLS; and (f) tests of overidentified equations. Each step is illustrated using a running empirical example from Reisenzein's (1986) randomized experiment on helping behavior. We also explain and illustrate the analytic conditions under which an equation estimated with MIIV-2SLS is robust to structural misspecifications. We include additional sections on MIIV approaches using a covariance matrix and mean vector as data input, conducting multilevel SEM, analyzing categorical endogenous variables, causal inference, and extensions and applications. Online supplemental material illustrates input code for all examples and simulations using the R package MIIVsem.

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Researchers across varied fields increasingly are collecting and analyzing intensive longitudinal data (ILD) to examine processes across time at the individual level. Two types of relations are typically examined: lagged and contemporaneous. Lagged relations capture how variables at a prior time point can be used to explain variance in variables at a later time point. These are always modeled using autoand cross-regressions by means of vector autoregression (VAR). By contrast, there are two types of relations commonly used to model the contemporaneous relations, which model how variables relate instantaneously. Until now, researchers must opt to either model contemporaneous relations as undirected relations among residuals (e.g., partial or full correlations) or as directed relations among the variables (e.g., paths or regressions). The choice for how to model contemporaneous relations has implications for inferences as well as the potential to introduce bias in the VAR lagged relations if the wrong type of relation is used. This article introduces a novel data-driven method, hybrid-group iterative multiple model estimation (GIMME), that provides a solution to the problem of having to choose one or the other type of contemporaneous relation to model. The modeling framework utilized in hybrid-GIMME allows for both types of contemporaneous relations in addition to the standard VAR relations. Both simulated and empirical data were used to test the performance of hybrid-GIMME. Results suggest this is a robust method for recovering contemporaneous relations in an exploratory manner, particularly with an ample number of time points per person.