Improvements to PLSc: Remaining problems and simple solutions

The recent article by Dijkstra and Henseler (2015b) presents a consistent partial least squares (PLSc) estimator that corrects for measurement error attenuation and provides evidence showing that, generally, PLSc performs comparably to a wide variety of more conventional estimators for structural equation models (SEM) with latent variables. However, PLSc does not adjust for other limitations of conventional PLS, namely: (1) bias in estimates of regression coefficients due to capitalization on chance; and (2) overestimation of composite reliability due to the proportionality relation between factor loadings and indicator weights. In this article, we illustrate these problems and then propose a simple solution: the use of unit-weighted composites, rather than those constructed from PLS results, combined with errors-in-variables regression (EIV) by using reliabilities obtained from factor analysis. Our simulations show that these two improvements perform as well as or better than PLSc. We also provide examples of how our proposed estimator can be easily implemented in various proprietary and open source software packages

Consistent and asymptotically normal PLS estimators for linear structural equations

A vital extension to partial least squares (PLS) path modeling is introduced: consistency. While maintaining all the strengths of PLS, the consistent version provides two key improvements. Path coefficients, parameters of simultaneous equations, construct correlations, and indicator loadings are estimated consistently. The global goodness-of-fit of the structural model can also now be assessed, which makes PLS suitable for confirmatory research. A Monte Carlo simulation illustrates the new approach and compares it with covariance-based structural equation modelin

Partial least squares path modeling: Time for some serious second thoughts

Partial least squares (PLS) path modeling is increasingly being promoted as a technique of choice for various analysis scenarios, despite the serious shortcomings of the method. The current lack of methodological justification for PLS prompted the editors of this journal to declare that research using this technique is likely to be deck-rejected (Guide and Ketokivi, 2015). To provide clarification on the inappropriateness of PLS for applied research, we provide a non-technical review and empirical demonstration of its inherent, intractable problems. We show that although the PLS technique is promoted as a structural equation modeling (SEM) technique, it is simply regression with scale scores and thus has very limited capabilities to handle the wide array of problems for which applied researchers use SEM. To that end, we explain why the use of PLS weights and many rules of thumb that are commonly employed with PLS are unjustifiable, followed by addressing why the touted advantages of the method are simply untenable

a confirmatory approach to study tourism technology and tourist behavior

Purpose: As technology in tourism and hospitality (TTH) develops technical artifacts according to visitors’ demands, it must deal with both behavioral and design constructs in the context of structural equation modeling (SEM). While behavioral constructs are typically modeled as common factors, the study at hand introduces the composite into TTH to model artifacts. To deal with both kinds of constructs, this paper aims to exploit partial least squares path modeling (PLS-PM) as a confirmatory approach to estimate models containing common factors and composites. Design/methodology/approach: The study at hand presents PLS-PM in its current form, i.e. as a full-fledged approach for confirmatory purposes. By introducing the composite to model artifacts, TTH scholars can use PLS-PM to answer research questions of the type “Is artifact xyz useful?”, contributing to a further understanding of TTH. To demonstrate the composite model, an empirical example is used. Findings: PLS-PM is a promising approach when the model contains both common factors and composites. By applying the test for overall model fit, empirical evidence can be obtained for latent variables and artifacts. In doing so, researchers can statistically test whether a developed artifact is useful. Originality/value: To the best of the authors’ knowledge, this is the first study to discuss the practical application of composite and common factor models in TTH research. Besides introducing the composite to model artifacts, the study at hand also guides scholars in the assessment of PLS-PM results.publishersversionpublishe

Multiple Subject Barycentric Discriminant Analysis (MUSUBADA): How to Assign Scans to Categories without Using Spatial Normalization

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can analyze datasets with different voxel numbers per participant and, so does not require spatial normalization. MUSUBADA statistical inferences are implemented with cross-validation techniques (e.g., jackknife and bootstrap), its performance is evaluated with confusion matrices (for fixed and random models) and represented with prediction, tolerance, and confidence intervals. We present an example where we predict the image categories (houses, shoes, chairs, and human, monkey, dog, faces,) of images watched by participants whose brains were scanned. This example corresponds to a DA question in which the data table is made of subtables (one per subject) and with more variables than observations

Extraordinary Claims Require Extraordinary Evidence: A Comment on “Recent Developments in PLS”

Evermann and Rönkkö (2023) review recent developments in partial least squares (PLS) with the aim of providing guidance to researchers. Indeed, the explosion of methodological advances in PLS in the last decade necessitates such overview articles. In so far as the goal is to provide an objective assessment of the technique, such articles are most welcome. Unfortunately, the authors’ extraordinary and questionable claims paint a misleading picture of PLS. Our goal in this short commentary is to address selected claims made by Evermann and Rönkkö (2023) using simulations and the latest research. Our objective is to bring a positive perspective to this debate and highlight the recent developments in PLS that make it an increasingly valuable technique in IS and management research in general

HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling

Roemer, E., Schuberth, F., & Henseler, J. (2021). HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling. Industrial Management and Data Systems, 121(12), 2637-2650. https://doi.org/10.1108/IMDS-02-2021-0082Purpose: One popular method to assess discriminant validity in structural equation modeling is the heterotrait-monotrait ratio of correlations (HTMT). However, the HTMT assumes tau-equivalent measurement models, which are unlikely to hold for most empirical studies. To relax this assumption, the authors modify the original HTMT and introduce a new consistent measure for congeneric measurement models: the HTMT2. Design/methodology/approach: The HTMT2 is designed in analogy to the HTMT but relies on the geometric mean instead of the arithmetic mean. A Monte Carlo simulation compares the performance of the HTMT and the HTMT2. In the simulation, several design factors are varied such as loading patterns, sample sizes and inter-construct correlations in order to compare the estimation bias of the two criteria. Findings: The HTMT2 provides less biased estimations of the correlations among the latent variables compared to the HTMT, in particular if indicators loading patterns are heterogeneous. Consequently, the HTMT2 should be preferred over the HTMT to assess discriminant validity in case of congeneric measurement models. Research limitations/implications: However, the HTMT2 can only be determined if all correlations between involved observable variables are positive. Originality/value: This paper introduces the HTMT2 as an improved version of the traditional HTMT. Compared to other approaches assessing discriminant validity, the HTMT2 provides two advantages: (1) the ease of its computation, since HTMT2 is only based on the indicator correlations, and (2) the relaxed assumption of tau-equivalence. The authors highly recommend the HTMT2 criterion over the traditional HTMT for assessing discriminant validity in empirical studies.publishersversionpublishe

On the Adoption of Partial Least Squares in Psychological Research: Caveat Emptor

The partial least squares technique (PLS) has been touted as a viable alternative to latent variable structural equation modeling (SEM) for evaluating theoretical models in the differential psychology domain. We bring some balance to the discussion by reviewing the broader methodological literature to highlight: (1) the misleading characterization of PLS as an SEM method; (2) limitations of PLS for global model testing; (3) problems in testing the significance of path coefficients; (4) extremely high false positive rates when using empirical confidence intervals in conjunction with a new "sign change correction" for path coefficients; (5) misconceptions surrounding the supposedly superior ability of PLS to handle small sample sizes and non-normality; and (6) conceptual and statistical problems with formative measurement and the application of PLS to such models. Additionally, we also reanalyze the dataset provided by Willaby et al. (2015; doi:10.1016/j.paid.2014.09.008) to highlight the limitations of PLS. Our broader review and analysis of the available evidence makes it clear that PLS is not useful for statistical estimation and testing

Multiple Subject Barycentric Discriminant Analysis (MUSUBADA): How to Assign Scans to Categories without Using Spatial Normalization

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can analyze datasets with different voxel numbers per participant and, so does not require spatial normalization. MUSUBADA statistical inferences are implemented with cross-validation techniques (e.g., jackknife and bootstrap), its performance is evaluated with confusion matrices (for fixed and random models) and represented with prediction, tolerance, and confidence intervals. We present an example where we predict the image categories (houses, shoes, chairs, and human, monkey, dog, faces,) of images watched by participants whose brains were scanned. This example corresponds to a DA question in which the data table is made of subtables (one per subject) and with more variables than observations