4.4 A Multidimensional Poverty Composite Indicator based on
4.4.5 Conclusions for Higher-Order MP-CI
The empirical case of a Multidimensional Poverty Composite Indicator was analyzed in order to show and compare three main approaches for the PLS-PM parameter estimation in the presence of Higher-Order Constructs. In particular, this paragraph has focused on the Second-Order Constructs similar to the Type II category reported by Jarvis et al. [71], where the model defines reflective First-Order constructs and a formative Second- Order Construct.
The case study has revealed that the Hybrid Approach has bad perfor- mances in terms of measurement indexes and global indexes, and, in addi- tion it produces non-significant parameters. Moreover, in the Repeated In- dicators Approach, the path coefficients reported in Table 4.4 (0.288; 0.203; 0.304; 0.341) define the intensity of the causal relationships between the MP-CI and its four dimensions, represented by First-Order LVs. This means, for instance, keeping the other parameters constant, if we increase Health by a quantity equal to 1, the perception of poverty will increase by 0.288. In the Two Step Approach, the relationships between Health, Education,
Employment and Living Standards are structural coefficients of a mea- surement model. The path coefficients (0.328; 0.274; 0.297; 0.252) reflect the composition of the Second-Order MP-CI ; they do not represent how much the First-Order Dimensions affect the Higher-Order Construct, but, rather, the extent to which the higher level of abstraction is formed by its Lower-Order Constructs.
4.5
Conclusions
Generally, the choice of the best approach clearly depends on the type of design.
In the case where a Second-Order Construct is formatively related to the First-Order Dimensions and each construct is reflectively measured by its MVs, the Two Step Approach works better than the other two approaches. As regards the amount of explained variance, the Two Step Approach pro- duces better explained relationships between the two orders of the model. Additionally, with regard to the parameter estimation, in general, the Two Step Approach is the best.
Next, we can conclude that for the Repeated Indicators Approach, the Second- Order LV, being hierarchically superior, could be seen as a context variable and the focus is on the impact of the First-Order LVs on the Higher-Order LV. In the Two Step Approach, the Second-Order LV is measured by the First-Order LV and the aim is to understand to what extent each First-Order LV reflects (in terms of covariance) the composition of the Second-Order level. Moreover, the Two Step Approach proves suitable for the estima- tion of formative Second-Order Constructs since it produces estimates that are better than those obtained through the Repeated Indicators Approach. In addition, the Two Step Approach is more theoretically consistent than the Repeated Indicators Approach in the definition of the Second-Order LV measurement model. As a matter of fact, reflectively measured constructs require homogeneous indicators and the Two Step Approach, using an LV component instead of the entire set of MVs, reduces the heterogeneity in the indicators.
New methods in PLS Path
Modeling for the building a
System of Composite
Indicators
5.1
Introduction
The importance of modeling and estimating Higher-Order Construct, from both a theoretical and an empirical point of view, has been recognized by many researchers since the dawn of factor analysis [67]; [151] and has been emphasized in many studies recently [34];[81];[97]. Unfortunately, the research is almost exclusively conducted in the area of covariance-based SEM. Neverthless, the aim of estimating Higher-Order Constructs can be achieved by means of PLS-PM [95];[186]. Three different approaches that allow you to model and estimate Second (and Higher)-Order Constructs and their relationship with other constructs in a nomological network have been adopted in the literature. In the Chapter 4 these approaches to Higher- Order Constructs have been described in detail and some of their limita- tions discussed.
Now we will only focus on certain of these limitations, that are typical of Two Step Approach: namely, the meaning of component for each Lower-
Order Construct and the possibility of choosing the number of these com- ponents in the analysis of the Higher-Order Construct.
In the classic Two Step Approach, the only first component of the Lower- Order Constructs is estimated without the Higher-Order Construct. This first component is the one that best represents its block of MVs. Next, these first components are included in the analysis as indicators of the Higher- Order Construct.
Therefore, this approach presents two important limitations related to com- ponents of each block: only one component is chosen for each block, and this has a strong representative power but a weak predictive power in the analysis of the Higher-Order Construct. For these reasons, in order to over- come these two drawbacks, in this work two alternative methods to esti- mate the Higher-Order Constructs are proposed. In particular, in order to resolve the issue related to the predictive power of the component for each Lower-Order Construct, the Mixed Two Step Approach is proposed and, regarding the choice of the number of components for each block, the Par- tial Least Squares Component Regression Approach is proposed. These approaches will be described in detail in the next section, and for each ap- proach a simulation and an application on real data will be presented.