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

Measurement error correlation within blocks of indicators in consistent partial least squares:Issues and remedies

Purpose The purpose of this paper is to enhance consistent partial least squares (PLSc) to yield consistent parameter estimates for population models whose indicator blocks contain a subset of correlated measurement errors. Design/methodology/approach Correction for attenuation as originally applied by PLSc is modified to include a priori assumptions on the structure of the measurement error correlations within blocks of indicators. To assess the efficacy of the modification, a Monte Carlo simulation is conducted. Findings In the presence of population measurement error correlation, estimated parameter bias is generally small for original and modified PLSc, with the latter outperforming the former for large sample sizes. In terms of the root mean squared error, the results are virtually identical for both original and modified PLSc. Only for relatively large sample sizes, high population measurement error correlation, and low population composite reliability are the increased standard errors associated with the modification outweighed by a smaller bias. These findings are regarded as initial evidence that original PLSc is comparatively robust with respect to misspecification of the structure of measurement error correlations within blocks of indicators. Originality/value Introducing and investigating a new approach to address measurement error correlation within blocks of indicators in PLSc, this paper contributes to the ongoing development and assessment of recent advancements in partial least squares path modeling

Robust partial least squares path modeling

Schamberger, T., Schuberth, F., Henseler, J., & Dijkstra, T. K. (2020). Robust partial least squares path modeling. Behaviormetrika, 47(1), 307-334. https://doi.org/10.1007/s41237-019-00088-2Outliers can seriously distort the results of statistical analyses and thus threaten the validity of structural equation models. As a remedy, this article introduces a robust variant of Partial Least Squares Path Modeling (PLS) and consistent Partial Least Squares (PLSc) called robust PLS and robust PLSc, respectively, which are robust against distortion caused by outliers. Consequently, robust PLS/PLSc allows to estimate structural models containing constructs modeled as composites and common factors even if empirical data are contaminated by outliers. A Monte Carlo simulation with various population models, sample sizes, and extents of outliers shows that robust PLS/PLSc can deal with outlier shares of up to 50 % without distorting the estimates. The simulation also shows that robust PLS/PLSc should always be preferred over its traditional counterparts if the data contain outliers. To demonstrate the relevance for empirical research, robust PLSc is applied to two empirical examples drawn from the extant literature.publishersversionpublishe

Common Beliefs and Reality about Partial Least Squares: Comments on Rönkkö and Evermann

This article addresses Rönkkö and Evermann’s criticisms of the partial least squares (PLS) approach to structural equation modeling. We contend that the alleged shortcomings of PLS are not due to problems with the technique, but instead to three problems with Rönkkö and Evermann’s study: (a) the adherence to the common factor model, (b) a very limited simulation designs, and (c) overstretched generalizations of their findings. Whereas Rönkkö and Evermann claim to be dispelling myths about PLS, they have in reality created new myths that we, in turn, debunk. By examining their claims, our article contributes to reestablishing a constructive discussion of the PLS method and its properties. We show that PLS does offer advantages for exploratory research and that it is a viable estimator for composite factor models. This can pose an interesting alternative if the common factor model does not hold. Therefore, we can conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines

Confirmatory Composite Analysis

This article introduces confirmatory composite analysis (CCA) as a structural equation modeling technique that aims at testing composite models. It facilitates the operationalization and assessment of design concepts, so-called artifacts. CCA entails the same steps as confirmatory factor analysis: model specification, model identification, model estimation, and model assessment. Composite models are specified such that they consist of a set of interrelated composites, all of which emerge as linear combinations of observable variables. Researchers must ensure theoretical identification of their specified model. For the estimation of the model, several estimators are available; in particular Kettenring's extensions of canonical correlation analysis provide consistent estimates. Model assessment mainly relies on the Bollen-Stine bootstrap to assess the discrepancy between the empirical and the estimated model-implied indicator covariance matrix. A Monte Carlo simulation examines the efficacy of CCA, and demonstrates that CCA is able to detect various forms of model misspecification

Child Well-Being in Rich Countries: UNICEF’s Ranking Revisited, and New Symmetric Aggregating Operators Exemplified

In a report published in 2007 UNICEF measured six dimensions of child well-being for the majority of the economically advanced nations. No overall scores are given, but countries are listed in the order of their average rank on the dimensions, which are therefore implicitly assigned ‘equal importance’. In this study we take ‘equal importance’ to mean that the final aggregation is symmetrical in the scores and the ranks, i.e. permuting them leaves the aggregate unchanged. We rank the countries by aggregating the numerical information using a variety of techniques, geared to the measurement scales we distinguish (‘ordinal’, ‘interval’, ‘ratio’). The aggregators are symmetrical and mildly demanding, emphasizing good performance across the board. The rankings obtained deviate from the UNICEF ranking, but not over-dramatically. Our purpose is not only to study alternative approaches for the particular data at hand, but also to introduce and exemplify new and useful aggregation techniques: we propose ways to select weights for OWA-operators and weighted geometric means, and we suggest how to circumvent the choice of a power for the power means. In addition we extend the Borda method so that it values dominance as well

Common Beliefs and Reality About PLS: Comments on Ronnkko and Evermann (2013)

Henseler, J., Dijkstra, T. K., Sarstedt, M., Ringle, C. M., Diamantopoulos, A., Straub, D. W., Ketchen Jr., D. J., Hair, J. F., Hult, G. T. M., & Calantone, R. J. (2014). Common Beliefs and Reality About PLS: Comments on Ronnkko and Evermann (2013). Organizational Research Methods, 17(2), 182-209. https://doi.org/10.1177/1094428114526928This article addresses Rönkkö and Evermann’s criticisms of the partial least squares (PLS) approach to structural equation modeling. We contend that the alleged shortcomings of PLS are not due to problems with the technique, but instead to three problems with Rönkkö and Evermann’s study: (a) the adherence to the common factor model, (b) a very limited simulation designs, and (c) overstretched generalizations of their findings. Whereas Rönkkö and Evermann claim to be dispelling myths about PLS, they have in reality created new myths that we, in turn, debunk. By examining their claims, our article contributes to reestablishing a constructive discussion of the PLS method and its properties. We show that PLS does offer advantages for exploratory research and that it is a viable estimator for composite factor models. This can pose an interesting alternative if the common factor model does not hold. Therefore, we can conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.publishersversionpublishe

On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model

The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP criterion value to its infimum will exhibit the features of a so-called “degeneracy”. That is, the parameter matrices become nearly rank deficient and the Euclidean norm of some factors tends to infinity. We also show that the CP criterion function does attain its infimum if one of the parameter matrices is constrained to be column-wise orthonormal