Factor Score Regression With Social Relations Model Components: A Case Study Exploring Antecedents and Consequences of Perceived Support in Families

Abstract

The family social relations model (SRM) is applied to identify the sources of variance in interpersonal dispositions in families, but the antecedents or consequences of those sources are rarely investigated. Simultaneous modeling of the SRM with antecedents or consequences using structural equation modeling (SEM) allows to do so, but may become computationally prohibitive in small samples. We therefore consider two factor score regression (FSR) methods: regression and Bartlett FSR. Based on full information maximum likelihood (FIML), we derive closed-form expressions for the regression and Bartlett factor scores in the presence of missingness. A simulation study in both a complete- and incomplete-case setting compares the performance of these FSR methods with SEM and an ANOVA-based approach. In both settings, the regression FIML factor scores as explanatory variable produces unbiased estimators with precision comparable to the SEM-estimators. When SRM-effects are used as dependent variables, none of the FSR methods are a suitable alternative for SEM. The latter result deviates from previous studies on FSR in more simple settings. As an example, we explore whether gender and past victimhood of relational and physical aggression are antecedents for family dynamics of perceived support, and whether those dynamics predict physical and relational aggression.

Croon’s Bias-Corrected Factor Score Path Analysis for Small- to Moderate-Sample Multilevel Structural Equation Models

“…Recent developments have provided a theoretical and empirical basis for the application of Croon’s bias-corrected estimator to a broad range of settings and have identified the estimator as an important small to moderate sample estimation alternative for SEMs (Devlieger et al, 2016; Devlieger & Rosseel, 2017; Loncke et al, 2018). For instance, past literature with single-level structural equation models has shown that Croon’s estimator outperforms ML in a wide variety of settings including small to moderate samples, missing data, measurement misspecifications, structural misspecifications, and correlated error terms (Devlieger et al, 2016; Devlieger & Rosseel, 2017; Hayes & Usami, 2019; Kelcey, 2019; Loncke et al, 2018; Lu et al, 2011). Given the potential analytic advantages of Croon’s limited information estimator in buttressing evidence from small- to moderate-scale studies, an open set of questions is if and how these methods can be extended to multilevel settings where governing sample sizes (i.e., the number of organizations) tend to be small to moderate and model complexity tends to be high.…”

“…Recent developments have provided a theoretical and empirical basis for the application of Croon's bias-corrected estimator to a broad range of settings and have identified the estimator as an important small to moderate sample estimation alternative for SEMs (Devlieger et al, 2016;Devlieger & Rosseel, 2017;Loncke et al, 2018). For instance, past literature with single-level structural equation models has shown that Croon's estimator outperforms ML in a wide variety of settings including small to moderate samples, missing data, measurement misspecifications, structural misspecifications, and correlated error terms (Devlieger et al, 2016;Devlieger & Rosseel, 2017;Hayes & Usami, 2019;Kelcey, 2019;Loncke et al, 2018;Lu et al, 2011).…”

Motivational Differences? Comparing Private, Public and Hybrid Organizations

“…To corroborate the robustness of the findings, we conducted two alternative regressions, one with the original summative indexes as the dependent variables (giving no substantially different results), and another with the regression factor scores. The last analysis is more similar to SEM as the factor scores produces indexes where the individual items are weighted according to their score on the latent variable (Loncke et al 2018). Using both ordinary regression scores and Bartlett scores, none of these alternative analyses seriously altered the results.…”

Factor Score Estimation in Multi-Method Measurement Designs With Planned Missing Data

“…In the maximum likelihood framework, factor scores are conceptualized as fixed entities that can be obtained by maximizing the likelihood of the observed data given the factor score estimates (Estabrook & Neale, 2013;Loncke et al, 2018;Skrondal & Rabe-Hesketh, 2004). The maximum likelihood estimator yields conditionally unbiased factor scores that correspond to the traditional Bartlett scores in CFA models (Skrondal & Rabe-Hesketh, 2004).…”

“…where Λ is the factor loading matrix, Θ is the residual covariance matrix of the manifest variables and j y is the response vector of subject j (Bartlett, 1937;Hardt et al, 2019). Often, the residual covariance matrix Θ is replaced with the model implied covariance matrix, which yields identical results (Bentler & Yuan, 1997;Loncke et al, 2018).…”