Estimating and Testing Random Intercept Multilevel Structural Equation Models with Model Implied Instrumental Variables.

This study develops a new limited information estimator for random intercept Multilevel Structural Equation Models (MSEM). It is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative or supplement to maximum likelihood (ML) in SEMs (Bollen, 1996). We also develop a multilevel overidentification test statistic that applies to equations at the within or between levels. Our Monte Carlo simulation analysis suggests that MIIV-2SLS is more robust than ML to misspecification at within or between levels, performs well given fewer that 100 clusters, and shows that our multilevel overidentification test for equations performs well at both levels of the model.

An introduction to model implied instrumental variables using two stage least squares (MIIV-2SLS) in structural equation models (SEMs).

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. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Harmonizing altered measures in integrative data analysis: A methods analogue study.

In the current study, we used an analogue integrative data analysis (IDA) design to test optimal scoring strategies for harmonizing alcohol- and drug-use consequence measures with varying degrees of alteration across four study conditions. We evaluated performance of mean, confirmatory factor analysis (CFA), and moderated nonlinear factor analysis (MNLFA) scores based on traditional indices of reliability (test-retest, internal, and score recovery or parallel forms) and validity. Participants in the analogue study included 854 college students (46% male; 21% African American, 5% Hispanic/Latino, 56% European American) who completed two versions of the altered measures at two sessions, separated by 2 weeks. As expected, mean, CFA, and MNLFA scores all resulted in scales with lower reliability given increasing scale alteration (with less fidelity to formerly developed scales) and shorter scale length. MNLFA and CFA scores, however, showed greater validity than mean scores, demonstrating stronger relationships with external correlates. Implications for measurement harmonization in the context of IDA are discussed.

Simplifying the implementation of modern scale scoring methods with an automated R package: Automated moderated nonlinear factor analysis (aMNLFA).

When generating scores to represent latent constructs, analysts have a choice between applying psychometric approaches that are principled but that can be complicated and time-intensive versus applying simple and fast, but less precise approaches, such as sum or mean scoring. We explain the reasons for preferring modern psychometric approaches: namely, use of unequal item weights and severity parameters, the ability to account for local dependence and differential item functioning, and the use of covariate information to more efficiently estimate factor scores. We describe moderated nonlinear factor analysis (MNLFA), a relatively new, highly flexible approach that allows analysts to develop precise factor score estimates that address limitations of sum score, mean score, and traditional factor analytic approaches to scoring. We then outline the steps involved in using the MNLFA scoring approach and discuss the circumstances in which this approach is preferred. To overcome the difficulty of implementing MNLFA models in practice, we developed an R package, aMNLFA, that automates much of the rule-based scoring process. We illustrate the use of aMNLFA with an empirical example of scoring alcohol involvement in a longitudinal study of 6998 adolescents and compare performance of MNLFA scores with traditional factor analysis and sum scores based on the same set of 12 items. MNLFA scores retain more meaningful variation than other approaches. We conclude with practical guidelines for scoring.

An Empirical Assessment of the Sensitivity of Mixture Models to Changes in Measurement.

The current study explored the extent to which variations in self-report measures across studies can produce differences in the results obtained from mixture models. Data (N = 854) come from a laboratory analogue study of methods for creating commensurate scores of alcohol- and substance-use-related constructs when items differ systematically across participants for any given measure. Items were manipulated according to four conditions, corresponding to increasing levels of alteration to item stems, response options, or both. In Study 1, results from latent class analyses (LCA) of alcohol consequences were compared across the four conditions, revealing differences in class enumeration and configuration. In Study 2, results from factor mixture models (FMM) of alcohol expectancies were compared across two of the conditions, revealing differences in patterns and magnitude of the factor loadings and thresholds. The results suggest that even subtle differences in measurement can have substantively meaningful effects on mixture model results.