Table 1. Technical points in MoM and...

Table 1.

Technical points in MoM and additional points made in this rejoinder

Point^a	Additional evidence in existing literatre^b	Counter-evidence in existing literature^b	Conclusion
PLS does not maximize R² or explained variance	Simulation evidence in Rönkkö (2020)	None. Existing PLS literature does not provide evidence to support this claim Indeed, it is simple to show many methods that can outperform PLS on any specific criteria of maximization	PLS does not maximize R² or explained variance. The claim itself makes little sense and no supporting proofs exist
Improving reliability by differential indicator weighting is not a reason to use PLS	Simulation evidence in Rönkkö and Ylitalo (2010), Rönkkö and Evermann (2013) and Rönkkö et al. (2016)	None under likely real-world analysis conditions	It is unclear why a researcher should favor a method, which shows a trivial reliability improvement only in situations of very low inter-item correlation, and at the expense of proven serious drawbacks. Standard scale development procedures recommend against items with low inter-correlations, and where they should be included (e.g. formative indices); internal consistency is irrelevant
	The simulations in Henseler et al. (2014) also show that in most situations, PLS leads to a loss of reliability	PLS may offer small reliability improvements in simulation studies that are designed with conditions ideally favorable to PLS, such as extremely low inter-item correlations: e.g.
	Decades of evidence show that differential indicator weights generally provide only trivial advantages at best	Simulations in Henseler et al. (2014) show a <1% improvement in reliability for situations expressly designed to favor PLS
PLS weights bias composite correlations:	Simulations by Goodhue et al. (2015), Rönkkö (2014) and Rönkkö and Evermann (2013)	None. Rigdon (2016) claims weakly correlating composites are a known violation of PLS assumptions	It is impossible for researchers to know composites are weakly correlated a priori
a) If scales are weakly correlated		However, this is clearly not a well-known violation of specified PLS prerequisites, as we are not aware of any published guidelines in primer or introductory PLS literature that state this should be tested	That PLS is not robust to departures from this assumption should be pointed out in PLS introductory texts
b) Where there are cross-loadings or correlated errors between items in different scales
c) Particularly when sample size is small
AVE and CR should never be used with PLS/PLS should not be used to validate measures	Simulations by Evermann and Tate (2010), Rönkkö and Evermann (2013), Rönkkö and Cho (2022)	None. HTMT has been proposed as an improvement, but it is not a PLS-specific method, and CFA works better more generally. Evidence, which suggests HTMT generally outperforms CFA (e.g., Voorhees et al., 2016), is based on incorrect use of CFA (Rönkkö and Cho, 2022)	HTMT is a better method than using AVE with PLS. However, HTMT is not a PLS method
	These results are corroborated even by PLS advocates’ research (Henseler et al., 2014; McIntosh et al., 2014)		PLS introductory texts should remove mention of AVE and CR as measure validation and model assessment tools. Factor analysis should be used to test the assumptions of HTMT
Additional point not in MoM: The bootstrap “sign-change” options in PLS programs can produce 100% false positive rate	Simulation evidence in Rönkkö et al. (2015)	None. In fact, Henseler et al. (2016) recommend abandoning the sign-change corrections	Unfortunately, the damage to statistical decision-making has likely already been done, and is perhaps still continuing. The sign-change corrections only serve to increase false positive rate and the use of this feature should be discontinued

Point^a	Additional evidence in existing literatre^b	Counter-evidence in existing literature^b	Conclusion
PLS does not maximize R² or explained variance	Simulation evidence in Rönkkö (2020)	None. Existing PLS literature does not provide evidence to support this claimIndeed, it is simple to show many methods that can outperform PLS on any specific criteria of maximization	PLS does not maximize R² or explained variance. The claim itself makes little sense and no supporting proofs exist
Improving reliability by differential indicator weighting is not a reason to use PLS	Simulation evidence in Rönkkö and Ylitalo (2010), Rönkkö and Evermann (2013) and Rönkkö et al. (2016)	None under likely real-world analysis conditions	It is unclear why a researcher should favor a method, which shows a trivial reliability improvement only in situations of very low inter-item correlation, and at the expense of proven serious drawbacks. Standard scale development procedures recommend against items with low inter-correlations, and where they should be included (e.g. formative indices); internal consistency is irrelevant
	The simulations in Henseler et al. (2014) also show that in most situations, PLS leads to a loss of reliability	PLS may offer small reliability improvements in simulation studies that are designed with conditions ideally favorable to PLS, such as extremely low inter-item correlations: e.g.
	Decades of evidence show that differential indicator weights generally provide only trivial advantages at best	Simulations in Henseler et al. (2014) show a <1% improvement in reliability for situations expressly designed to favor PLS
PLS weights bias composite correlations:	Simulations by Goodhue et al. (2015), Rönkkö (2014) and Rönkkö and Evermann (2013)	None. Rigdon (2016) claims weakly correlating composites are a known violation of PLS assumptions	It is impossible for researchers to know composites are weakly correlated a priori
a) If scales are weakly correlated		However, this is clearly not a well-known violation of specified PLS prerequisites, as we are not aware of any published guidelines in primer or introductory PLS literature that state this should be tested	That PLS is not robust to departures from this assumption should be pointed out in PLS introductory texts
b) Where there are cross-loadings or correlated errors between items in different scales
c) Particularly when sample size is small
AVE and CR should never be used with PLS/PLS should not be used to validate measures	Simulations by Evermann and Tate (2010), Rönkkö and Evermann (2013), Rönkkö and Cho (2022)	None. HTMT has been proposed as an improvement, but it is not a PLS-specific method, and CFA works better more generally. Evidence, which suggests HTMT generally outperforms CFA (e.g., Voorhees et al., 2016), is based on incorrect use of CFA (Rönkkö and Cho, 2022)	HTMT is a better method than using AVE with PLS. However, HTMT is not a PLS method
	These results are corroborated even by PLS advocates’ research (Henseler et al., 2014; McIntosh et al., 2014)		PLS introductory texts should remove mention of AVE and CR as measure validation and model assessment tools. Factor analysis should be used to test the assumptions of HTMT
Additional point not in MoM: The bootstrap “sign-change” options in PLS programs can produce 100% false positive rate	Simulation evidence in Rönkkö et al. (2015)	None. In fact, Henseler et al. (2016) recommend abandoning the sign-change corrections	Unfortunately, the damage to statistical decision-making has likely already been done, and is perhaps still continuing. The sign-change corrections only serve to increase false positive rate and the use of this feature should be discontinued

Notes:

^aAll points made in MoM are supported by numerical illustrations, to prioritize understandability for non-methodological readers.

^bSources of evidence and counter evidence are considered in terms of a hierarchy of strength. While we recognize that for different purposes, different forms of evidence are more or less appropriate, the strength of evidence for or against the sort of claims we make in MoM can be ascertained according to the following hierarchy: the strongest evidence is a mathematical proof, followed by appropriate simulations, followed by numerical illustrations (e.g. using real data). Rhetoric alone is not considered to be evidence for or against these claims, and hence, we do not include sources that only rely on rhetoric here.

We also make the conceptual point that PLS is not a latent variable method at all despite referred to as such in the literature. In fact, some of the current PLS literature argues that PLS is not intended to estimate common factor-based population models and is in fact most suitable for examining “composite-based population models” (Dijkstra, 2017; Hair and Sarstedt, 2019; Sarstedt et al., 2016). Yet, as we show in MoM, in research practice PLS is nearly exclusively used to examine factor-model based conceptualizations. Indeed, it is clear that recent PLS work still claims that PLS can estimate reflective models (Schuberth, 2021), and even the most recent edition of Hair et al’s (2021), PLS primer text clearly indicates that PLS can handle reflective models, which from a measurement theory perspective are essentially equivalent to factor models, and certainly are not composite models (Markus and Borsboom, 2013)

Source: Authors thinking specifically for this paper

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