In this Chapter, we have considered a CI system formed by EIs on a non nu- merical scale, including some kind of CI relationship, and testing whether there is a mediating and/or moderating effect. We have shown how the es- timation of LVs changes, and so the entire descriptive and predictive power of the model, if we consider the indicators according to their real nature and if we include mediating relationships among the constructs. Moreover, we have treated the problem of the heterogeneity of data. We have seen how
a unique model for the construction of CIs is not always well suited to the entire population that we are studying, but that are local models for each population according to its own characteristics; we have experienced this phenomenon through two approaches known in the literature, the PATH- MOX and REBUS-PLS Approaches, that, as they are constructed from two different perspectives, lead to different results. It is important to point out the main difference between REBUS-PLS and PATHMOX: REBUS-PLS Ap- proach does not require the identification of a target variable and it allows us to obtain units classification taking into account units performance for both the structural and the measurement model, while in PATHMOX Ap- proach the available external information is used to identify different seg- ments and to cluster units.
Higher-Order Constructs in
PLS-PM
4.1
Introduction
As has been said in the first Chapter, many phenomena are complex and based on different levels of abstraction. Just think of the concept of poverty, that for many years was measured by referring only to the country’s in- come. Sen [152] was the first person to recognize that the concept of poverty requires a multidimensional approach that focuses its attention not only on the strictly monetary characteristics of the phenomenon, but also on other aspects of people’s daily lives, such as labor, environment, social re- lations, knowledge and health, which represent its sub-dimensions. There- fore, PLS-PM is a suitable tool for the investigation of this kind of model with a high level of abstraction, in cases where the building of a system of CIs depends on different levels of construction.
Almost 25 years ago Noonan and Wold [115] observed: "Path analysis with hierarchically structured LVs within the framework of PLS is at an early stage of development, and research is still under way". Fortunately, in the last few years, research into the use of Higher-Order Construct Models using PLS-PM has been undertaken and several applications developed. The use of Higher-Order Construct Models has allowed researchers to ex- tend the application of PLS-PM to more advanced and complex models.
In the content of PLS-PM models, Higher-Order Construct have shown an increasing popularity in the last few years. Several authors have discussed both the theoretical and empirical contributions hierarchical models can make [33];[71];[73];[97];[178]. Both Covariance-Based structural equation modeling (CB-SEM) and PLS-PM can be used to estimate the parameters in Higher-Order Construct models [178]. For Covariance-Based SEM, guide- lines and empirical illustrations are generally available [33]. For PLS-PM, guidelines are mainly available for Higher-Order Construct models with reflective relationships ([94];[178];[186]). However, Ringle et al. [73] show that Higher-Order Construct models with reflective relationships in the First-Order and Second-Order of the hierarchy represent only a minority (20%) of the models applied in MIS Quarterly. Thus, there is a great need for guidelines on using hierarchical construct models with formative rela- tionships in PLS-PM, as the Second-Order model for social capital by Koka and Prescott [85] clearly exemplifies.
Higher-Order Constructs Models, also known as Hierarchical Models, or Multidimensional Constructs are explicit representations of multidimen- sional constructs that exist at a higher level of abstraction and are related to other constructs at a similar level of abstraction completely mediating the influence from or to their underlying dimensions [13]; [12]. Law et al. [90] define “[...] a construct as multidimensional when it consists of a number of interrelated attributes or dimensions and exists in multidimen- sional domains. These dimensions can be conceptualized under an over- all abstraction, and it is theoretically meaningful and parsimonious to use this overall abstraction as a representation of the dimensions.” Establishing such a higher model component, usually required in the context of PLS-PM [94], most often involves testing Second-Order Constructs that contain two layers of constructs. This kind of model is often limited to a Second-Order hierarchical structure, and can be defined as a construct involving more than one dimension [33]; [71]; [89]; [97]; [113]; [118]. As such, it can be dis- tinguished from unidimensional constructs, which are characterized by a single underlying dimension [113].
There are three main reasons for the inclusion of a Higher-Order Constructs Model in PLS-PM.
- First, by establishing Higher-Order Constructs Models, researchers can reduce the number of relationships in the structural model, mak- ing the PLS-PM more parsimonious and easier to grasp.
- Secondly, Higher-Order Constructs Models prove valuable if the con- structs are highly correlated; the estimations of the structural model relationships may be biased as a result of collinearity issues, and dis- criminant validity may not be established. In situations characterized by collinearity among the constructs, a Second-Order Construct can reduce such collinearity issues and may solve discriminant validity problems.
- Thirdly, establishing Higher-Order Constructs Models can also prove valuable if formative indicators exhibit high levels of collinearity. Pro- vided that theory supports this step, researchers can split up the set of indicators and establish separate constructs in a Higher-Order struc- ture.
The utility of these models is based on a number of theoretical and em- pirical grounds [33]. Proponents of the use of Higher-Order Constructs have argued that they allow for more theoretical parsimony and reduce model complexity [33]; [90]; [97]. Edwards [33] summarizes this argument as theoretical utility; theory requires general constructs consisting of spe- cific dimensions. This is closely related to the trade-off between accuracy and generalization as suggested by Gorsuch [51], who argues that "factors are concerned with narrow areas of generalization where the accuracy is great [whereas] higher-order factors reduce accuracy for an increase in the breadth of generalization. Law et al. [90] even state that "treating dimen- sions as a set of individual variables precludes any general conclusion be- tween a multidimensional construct and other constructs".