Abstract
In the context of Partial Least Squares-Path Modeling (PLS-PM), higher-order constructs have enjoyed increasing popularity in the last few years in relation to the investigation of models with a high level of abstraction, particularly in cases where the building of a system of indicators depends on different levels of information. Higher-order constructs in PLS-PM are considered as explicit representations of multidimensional constructs which are related to other constructs at a higher level of abstraction, thereby mediating completely the influence received from, or exercised on, their underlying dimensions. This chapter investigates the status and evolution of research studies on higher-order constructs in PLS-PM and focuses attention on the potentiality of their recent methodological developments, specifically on how they can help researchers in the estimation of complex and multidimensional phenomena. Different approaches will be discussed and compared using a case study within a social context.
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Notes
- 1.
\(P_{q}\) is the number of MVs in the q-th block.
- 2.
For a more detailed illustration see Ball (1963).
- 3.
The analysis was performed using the SmartPLS statistical programming language (https://www.smartpls.com/) (Ringle et al., 2022) and the R programming language. The external commands to the package were manually implemented to obtain the different HOCs for the individual approaches. We are working on implementing a package that includes building HOCs automatically.
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Appendix: A Bibliometric Review of Higher Order PLS-PM
Appendix: A Bibliometric Review of Higher Order PLS-PM
In order to perform an overview of the contributions of PLS-PM to case of a hierarchical relationship among LVs, a bibliometric study of international papers on the subject has been conducted.
The analysis of the literature has been performed using the Bibliometrix R-Tool (Aria & Cuccurullo, 2017), a recent R-package which facilitates a complete bibliometric analysis employing specific tools for both bibliometric and scientometric quantitative research. With the aim of understanding how the research on hierarchical PLS-PM issues has evolved, data were retrieved from the Web of Science’s (WOS) database of the Institute for Scientific Information (ISI), which is recognized as covering a broad range of relevant journals and peer-reviewed articles of high quality (Skute et al., 2019).
We extracted documents published between 1991 and 2021 (incl.) according to the following topics:
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“Hierarchical” and “PLS Path Modeling” or “Partial-Least Squares-Path Modeling” or “PLS-PM” or “PLS-SEM”;
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“Higher order” and “PLS Path Modeling” or “Partial-Least Squares-Path Modeling” or “PLS-PM” or “PLS-SEM”; and
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“second order” and “PLS Path Modeling” or “Partial-Least Squares-Path Modeling” or “PLS-PM” or “PLS-SEM”
The data were downloaded on 10th March 2022. This process resulted in a final sample of 518 articles, relating to 357 sources (journal, books, etc.). Table 9.10 shows the main information relating to the bibliographic data frame.
Growth trajectory of the literature on hierarchical PLS-PM, 1993–2021 (n = 518)
The annual scientific production in this research area is shown in Fig. 9.16. Comparing the quantity of publications over the past thirty years, it is evident that initially the increase in the number of publications was very small, emphasizing the fact that for many years hierarchical PLS-PM was not taken much into consideration by researchers. In 2001 the first works on this topic began to appear, the number expanding significantly from 2011, thereby demonstrating that this new aspect of the model was starting to arouse the interest of researchers, above all to address and solve problems related to latent dimensions. In particular, starting from 2015 we notice an exponential growth, with researchers paying far more attention to this development of the PLS model and, above all, proposing new and alternative approaches for the estimation of these models. In the last year, 2022, the number of publications is very low because, obviously, the research concerned only the first two months of the year. Generally, the annual percentage growth rate of the HOC PLS-PM contributions over the thirty years of analysis is equal to 15.06%.
As can be seen from the trend of publications over time, PLS-PM has enjoyed increasing popularity over the years for the measurement of concepts that depend on different aspects and that are based on different types of relationships.
Looking at the authorship pattern, the documents were written by 1,471 researchers, with an average value of 0.35 documents per author. Only 2.5% of these documents were written by a single author. Instead, almost all the documents were written by multiple co-authors (97.5%), emphasizing the need for collaborations between authors, even from different countries and/or belonging to different research domains. From the index “authors per document”, it is possible to state that each document was written on average by 2.84 authors, therefore almost three authors per article. This ratio evaluates the extent to which scholars publish single-authored or co-authored publications, a statistic which can also be seen as a proxy for the average size of the research team (Aria et al., 2020). This finding is also confirmed by another index, “co-authors per document”, which considers the number of times an author appeared in the collection of data, namely 3.24. From both these two measures there emerges an average number of authors for each article equal to 3. The last measure that substantially confirms the results obtained from the previous two metrics is the collaboration index which is equal to 3.03.
The countries are listed and sorted by the number of citations. As you can observe in Table 9.11, the Netherlands is in first place for citations, followed by Germany.
Finally, we have considered the fields of application of HOC PLS-PM. It can be seen in Table 9.12, which shows a summary of the first five subject categories, hierarchical models are widely applied in business.
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Cataldo, R., Grassia, M.G., Lauro, C.N. (2023). Alternative Approaches to Higher Order PLS Path Modeling: A Discussion on Methodological Issues and Applications. In: Latan, H., Hair, Jr., J.F., Noonan, R. (eds) Partial Least Squares Path Modeling. Springer, Cham. https://doi.org/10.1007/978-3-031-37772-3_9
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