Estimating and investigating multiple constructs multiple indicators social relations models with and without roles within the traditional structural equation modeling framework : A tutorial

Abstract

The present contribution provides a tutorial for the estimation of the social relations model (SRM) by means of structural equation modeling (SEM). In the overarching SEM-framework, the SRM without roles (with interchangeable dyads) is derived as a more restrictive form of the SRM with roles (with noninterchangeable dyads). Starting with the simplest type of the SRM for one latent construct assessed by one manifest round-robin indicator, we show how the model can be extended to multiple constructs each measured by multiple indicators. We illustrate a multiple constructs multiple indicators SEM SRM both with and without roles with simulated data and explain the parameter interpretations. We present how testing the substantial model assumptions can be disentangled from testing the interchangeability of dyads. Additionally, we point out modeling strategies that adhere to cases in which only some members of a group can be differentiated with regards to their roles (i.e., only some group members are noninterchangeable). In the online supplemental materials, we provide concrete examples of specific modeling problems and their implementation into statistical software (Mplus, lavaan, and OpenMx). Advantages, caveats, possible extensions, and limitations in comparison with alternative modeling options are discussed.