HIGH-ORDER CONSTRUCTS FOR THE STRUCTURAL EQUATION MODEL Enrico Ciavolino (1) * Mariangela Nitti (2) (1) Dipartimento di Filosofia e Scienze Sociali, Università del Salento (2) Dipartimento di Scienze Pedagogiche, Psicologiche e Didattiche, Università del Salento Abstract: The aim of the paper is to present a structural equation model based on high order latent variables. The non parametric estimation method used is the partial least squares which enables the definition of complex structure in the data with few model assumptions. The paper contribution is the analysis of the latent dimensions with a third level of abstraction by considering two main approaches presented in literature: the repeated indicators and the two-step approach. Empirical evidences and simulations results are provided in order to show the methodology and check the reliability of the approaches at issue. Keywords: structural equation model, partial least squares, high-order construct, latent dimension of sense. 1. Introduction PLS enables researchers in many field of social sciences to investigate models at high level of abstraction. The dimensions of a higher-order construct could be conceptualized under an overall abstraction, and it is theoretically meaningful to use this abstraction for the representation of the dimensions, instead of merely interrelating them. In this paper, a third-order latent construct model estimated by PLS-SEM is presented. Two model- building approaches (named repeated indicators and two-step approach) are compared through a simulation study for determining which method better represents the relationships among constructs levels. The work is articulated as follows: in section 2 PLS estimator and its extension to higher- order construct modeling are described; section 3 presents a case study in which Latent Dimensions of Sense (LDS) are modeled as a third-order latent variable;in section 4, the description of the montecarlo simulation is reported for the third-order model, in way to compare the two model- building approaches and draw conclusion on their performances. 2. PLS-path modeling for higher-order constructs Due to its ability of estimating complex models, PLS Path Modeling can be used to investigate models with a high level of abstraction. As a matter of fact, many studies in social sciences involve the conceptualization of multi-dimensional constructs, that is, composed of different but strictly related conceptual dimensions. The basic PLS design was completed for the first time in 1966 by Herman Wold for the use in multivariate analysis, and subsequently extended for its application in the Structural Equation Modeling (SEM) in 1975 by Wold himself. An extensive review on PLS approach is given the Handbook of PLS (Esposito Vinzi, Chin, Henseler, Wang, 2010). The model-building procedure can be thought of as the analysis of two conceptually different models. A measurement (or outer) model specifies the relationship of the observed variables with their (hypothesized) underlying (latent) constructs; a structural (or inner) model then specifies the causal relationships among latent constructs, as posited by some theory. The two sub models' equations are the following: ξ (m,1) =B (m,m) ∙ξ (m,1) +τ (m,1) * Corresponding Author: enrico.ciavolino@unisalento.it