According Hair et. (2017), the main reasons to include higher order model is to:  

1. Make the path model more parsimonous by reducing the number of relationships in the structural model

2. Resolve multicollinearity issue among formative indicators. 

Issue

The PLS path modeling algorithm requires that every latent variable has at least one manifest indicator. Phantom variables are not possible. In other words, Higher-order component (HOC) by itself is not identified in PLS-SEM but needs indicators to be estimated.

Solution 

Used repeated-indicator approach (Wold, 1982; Lohmoller, 1989) by repeating the indicators of all lower-order components (LOCS) on the HOC. 

Becker, Klein, and Wetzels (2012) have proposed  the extended repeated indicators approach, which requires establishing additional relationships from the exogenous construct to all the LOCs. Instead of interpreting its direct effect, researchers need to interpret its total effect on the HOC via the HOC’s LOCs.

In short, interpret the total effect (Direct + Indirect Effect) of Y5 on Y4 via all LOCs instead of direct effect p54 only. 

As an alternative, researchers have proposed the two-stage approach, which uses the construct scores estimated in the first stage as indicators of the HOC in the second stage. Depending on whether the first stage estimation only considers the LOCs or the entire HOC, identified via the repeated indicators approach, researchers distinguish between the disjoint two-stage approach and the embedded two-stage approach.

EMBEDDED TWO-STAGE APPROACH

All constructs except the HOC are measured with single items capturing the latent variable scores from stage 1.

disjoint TWO-STAGE APPROACH

All constructs are measured with multi-tems. HOC is measured with latent variable scores of LOCs obtained from stage 1. 

Model Specification

The HOC serves as an exogenous construct in the path model: 

• Use the repeated indicators approach when the focus is on minimizing the parameter bias in the higher-order construct’s measurement model relationships. 

• Use the two-stage approach when the focus is on minimizing the parameter bias in the structural model relationships. 

The HOC serves as an endogenous construct in the path model: 

• Use the extended repeated indicators approach or two-stage approach for reflective-formative and formative-formative type higher-order constructs. 

• The embedded and disjoint two-stage approaches produce very similar results and can both be used. 

Estimation OF HOC

• Use Mode A for reflective-reflective (Type I) and formative-reflective (Type III).

• Use Mode B for reflective-formative (Type II) and formative-formative (Type IV).

Measurement model evaluation 

Apply standard model evaluation criteria on the measurement models for the LOCs. 

Interpret the relationships between the HOC and LOCs as the measurement model of the HOC: 

• Reflective-reflective and formative-reflective type HOCs: Interpret the relationships between HOC and LOCs as loadings and assess convergent validity, internal consistency reliability, and discriminant validity metrics. 

• Reflective-formative and formative-formative type HOCs: Interpret the relationships between HOC and LOCs as weights and assess convergent validity, collinearity, and the significance and relevance of the weights.  

Structural model evaluation 

• Apply standard model evaluation criteria on the structural model. 

• Do not consider the LOCs as elements of the structural model.

• Reflective-formative and formative-formative HOCs estimated using the extended repeated indicators approach: Interpret the total effects of the antecedent constructs on the HOC. 

Further Readings

Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLS-SEM: guidelines for using reflective-formative type models. Long range planning, 45(5-6), 359-394.

Crocetta, C., Antonucci, L., Cataldo, R., Galasso, R., Grassia, M. G., Lauro, C. N., & Marino, M. (2021). Higher-order PLS-PM approach for different types of constructs. Social Indicators Research, 154(2), 725-754.

Sarstedt, M., Hair Jr, J. F., Cheah, J. H., Becker, J. M., & Ringle, C. M. (2019). How to specify, estimate, and validate higher-order constructs in PLS-SEM. Australasian Marketing Journal (AMJ), 27(3), 197-211.

Duarte, P., & Amaro, S. (2018). Methods for modelling reflective-formative second order constructs in PLS: An application to online travel shopping. Journal of Hospitality and Tourism Technology. DOI: 10.1108/JHTT-09-2017-0092

Nawanir, G., Fernando, Y., & Lim, K. T. (2018). A Second-order Model of Lean Manufacturing Implementation to Leverage Production Line Productivity with the Importance-Performance Map Analysis. Global Business Review, 19(3_suppl), S114-S129. doi:10.1177/0972150918757843 Click here.

Nawanir, G., Lim, K. T., Othman, S. N., & Adeleke, A. Q. (2018). Developing and validating lean manufacturing constructs: an SEM approach. Benchmarking: An International Journal, 25(5), 1382-1405. doi:doi:10.1108/BIJ-02-2017-0029. Click here.