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EXPLORING SOCIAL NETWORKS WITH PARTIAL LEAST SQUARES - PATH MODELING

Due to the nature of the data in Social Sciences and assuming that the most part of time real applications call for prediction it seems quite natural to extend the Doreian et al. (2013) proposal to a prediction oriented SEM, namely to PLS-PM.At this aim paper we deal with network data and structural equation models looking at the component based SEM method, i.e. Partial Least Squares-Path Modeling. In the last years, PLS-PM became more popular, through the vast literature on this subject in terms of the large number of methodological developments and applications. However, the problem of estimating PLS-PM in presence of network effects seems to be innovative. This requires PLS-PM to be re-examined by including network effects.We want to compare the estimators’ behavior of two types of methods: the classical network effects model and the PLS-PM including network data. In the new specification of PLS-PM measurement model, we define i) an exogenous latent variable emerging from the synthesis of observed network lagged variables, ii) one or more exogenous latent variables describing attribute data, and iii) an endogenous latent variable as synthesis of several outcomes. These latent components are then related to specify the structural model according to their own exogenous or endogenous nature.The two methods will be compared in an original way by means of Monte Carlo simulations, highlighting strong points and drawbacks deriving from a direct (NEM) or indirect representation (PLS-PM) of network effects.The PLS approach to path models with latent variables (LVs) was first presented by Herman Wold in 1979. It was proposed as a component-based estimation procedure alternative to the classical covariance-based approach using Maximum Likelihood estimators (SEM-ML).The PLS Path Modeling follows the SEM notations and symbols, including the use of a path diagram to picture the relations among the latent variables and between each manifest variable and the corresponding latent variable. Namely, the manifest variables are pictured as rectangles or squares, while circles represent the latent variables. Arrows define the relations among latent and/or manifest variables.As in SEM, even in the PLS-PM, the overall relations between manifest and latent variables are modeled trough a system of equations. Two different kinds of equations are used. The first ones are the ones defining the so-called measurement model, i.e. the ones describing the relation between each manifest variable and the corresponding latent variable. The second ones are the ones defining the inner or structural model, i.e. the ones describing the relations among the latent variables.The specification of the PLS-PM including network effect will be analyzed in order to highlight properties of the derived estimates and compare results obtained within the specification of the Network Effect Model (NEM).The idea is to set-up a Monte Carlo simulation scheme where population parameters are fixed and used in determining a “true” var-covar matrix. Then, resampling from the population a large number of datasets coherent with the specified structure but for some random disturbances, the two methods (PLS-PM and NEM) will be carried out and corresponding estimates will be compared. In this way, we will be able to analyze some statistical properties of the estimators in terms of bias and consistency. The sampled data should be consistent both for the network effect and for the structural equation model.