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

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

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

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

Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation

Density of states, dynamic (optical) conductivity and phase diagram of paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean-field theory (DMFT+Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular "bare" density of states (DOS). The DMFT effective single impurity problem is solved by numerical renormalization group (NRG). Phases of "correlated metal", Mott insulator and correlated Anderson insulator are identified from the evolution of density of states, optical conductivity and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of the finite size, allowing us to construct the complete zero-temperature phase diagram of paramagnetic Anderson-Hubbard model. Localization length in our approximation is practically independent of the strength of Hubbard correlations. However, the divergence of localization length in finite size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.Comment: 10 pages, 10 figures, improve phase diagra

A systematic experimental neuropsychological investigation of the functional integrity of working memory circuits in major depression

Verbal and visuospatial working memory (WM) impairment is a well-documented finding in psychiatric patients suffering from major psychoses such as schizophrenia or bipolar affective disorder. However, in major depression (MDD) the literature on the presence and the extent of WM deficits is inconsistent. The use of a multitude of different WM tasks most of which lack process-specificity may have contributed to these inconsistencies. Eighteen MDD patients and 18 healthy controls matched with regard to age, gender and education were tested using process- and circuit-specific WM tasks for which clear brain-behaviour relationships had been established in prior functional neuroimaging studies. Patients suffering from acute MDD showed a selective impairment in articulatory rehearsal of verbal information in working memory. By contrast, visuospatial WM was unimpaired in this sample. There were no significant correlations between symptom severity and WM performance. These data indicate a dysfunction of a specific verbal WM system in acutely ill patients with MDD. As the observed functional deficit did not correlate with different symptom scores, further, longitudinal studies are required to clarify whether and how this deficit is related to illness acuity and clinical state of MDD patients

Self-similar Solutions to a Kinetic Model for Grain Growth

We prove the existence of self-similar solutions to the Fradkov model for two-dimensional grain growth, which consists of an infinite number of nonlocally coupled transport equations for the number densities of grains with given area and number of neighbours (topological class). For the proof we introduce a finite maximal topological class and study an appropriate upwind-discretization of the time dependent problem in self-similar variables. We first show that the resulting finite dimensional differential system has nontrivial steady states. Afterwards we let the discretization parameter tend to zero and prove that the steady states converge to a compactly supported self-similar solution for a Fradkov model with finitely many equations. In a third step we let the maximal topology class tend to infinity and obtain self-similar solutions to the original system that decay exponentially. Finally, we use the upwind discretization to compute self-similar solutions numerically.Comment: 25 pages, several figure

Patients with schizophrenia show deficits of working memory maintenance components in circuit-specific tasks

Working memory (WM) deficits are a neuropsychological core finding in patients with schizophrenia and also supposed to be a potential endophenotype of schizophrenia. Yet, there is a large heterogeneity between different WM tasks which is partly due to the lack of process specificity of the tasks applied. Therefore, we investigated WM functioning in patients with schizophrenia using process- and circuit-specific tasks. Thirty-one patients with schizophrenia and 47 controls were tested with respect to different aspects of verbal and visuospatial working memory using modified Sternberg paradigms in a computer-based behavioural experiment. Total group analysis revealed significant impairment of patients with schizophrenia in each of the tested WM components. Furthermore, we were able to identify subgroups of patients showing different patterns of selective deficits. Patients with schizophrenia exhibit specific and, in part, selective WM deficits with indirect but conclusive evidence of dysfunctions of the underlying neural networks. These deficits are present in tasks requiring only maintenance of verbal or visuospatial information. In contrast to a seemingly global working memory deficit, individual analysis revealed differential patterns of working memory impairments in patients with schizophrenia