The higher-order Composite Indicator Legitimacy to violence.

The purpose of this study is to present and compare three main approaches to higher order construct PLS-Path Modeling presented in literature, Repeated indicators, Two-Step and Hybrid Approach, through an application in psychological field. In this paper, we use the psychological concept of Legitimacy to Violence as higherorder Latent Variable (LV) structural equation model, estimated through the PLS-PM approach. Then we illustrate how the gender's variable influences this latent concept. The higher-order Composite Indicator Legitimacy to Violence is determined by five sub-dimensions: justification for the peer violence, beliefs sexist and justification of domestic violence, justification of intolerance and violence against minorities, hostile sexism and benevolent sexism. The higher-order model presented is reflective both at the measurement and at the structural level. The three approaches are performed by Gaston's 'plspm' package in R programming language. The higher-order construct has a good and significant impact on the lower-order CIs, only the Benevolent Sexism's path coefficients are low compared to other blocks, in particular for the Hybrid approach, even if they are significant in each approach. The amount of variability of the MVs captured by the Legitimacy to Violence construct is very scarce when the Repeated Indicators and Hybrid Approaches are adopted; conversely, communality is enough good when the higher-order construct is measured through the Two-Step Approach. Looking GoF would be preferred Two Step Approach, as it has a higher GoF’s value than the others. Gender is introduced in this study as a moderator of the relation between lower-order dimensions and higher-order Legitimacy to Violence. Significant differences between women and men are present in dimensions of justification for the peer violence and beliefs sexist and justification of domestic violence.