What Is the Common Factors Approach?

2021 ◽  
Keyword(s):  
Author(s):  
Wen-Xiu Ma

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.


Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 883
Author(s):  
Yaqing Liu ◽  
Hongbing Ouyang ◽  
Xiaolu Wei

The existing spatial panel structural vector auto-regressive model can effectively capture the time and spatial dynamic dependence of endogenous variables. However, the hypothesis that the common factors have the same effect for all spatial units is unreasonable. Therefore, incorporating time effects, spatial effects, and time-individual effects, this paper develops a more general spatial panel structural vector autoregressive model with interactive effects (ISpSVAR) that can reflect the different effects of common factors on different spatial units. Additionally, based on whether or not the common factors can be observed, this paper proposes procedures to estimate ISpSVAR separately and studies the finite sample properties of estimators by Monte Carlo simulation. The simulation results show the effectiveness of the proposed ISpSVAR model and its estimation procedures.


2018 ◽  
Vol 68 (1) ◽  
pp. 31-50 ◽  
Author(s):  
Barbara Danska-Borsiak

This article attempts to estimate the total factor productivity (TFP) for 35 NUTS-2 regions of the Visegrad Group countries and to identify its determinants. The TFP values are estimated on the basis of the Cobb-Douglas production function, with the assumption of regional differences in productivity. The parameters of the productivity function were analysed with panel data, using a fixed effects model. There are many economic variables that influence the TFP level. Some of them are highly correlated, and therefore the factor analysis was applied to extract the common factors – the latent variables that capture the common variance among those observed variables that have similar patterns of responses. This statistical procedure uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. Each component is interpreted using the contributions of variables to the respective component. I estimated a dynamic panel data model describing TFP formation by regions. An attempt was made to incorporate the common factors among the model’s explanatory variables. One of them, representing the effects of research activity, proved to be significant.


Mindfulness ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 2804-2817
Author(s):  
Kathrin Bednar ◽  
Martin Voracek ◽  
Ulrich S. Tran

Abstract Objectives This study investigated whether common factors underlie the established mindfulness facets, as assessed by the Five Facet Mindfulness Questionnaire (FFMQ) and some of the mechanisms, which have been previously proposed to explain the beneficial effects of mindfulness on mental health. Methods Multigroup exploratory structural equation models (ESEM) were fitted to samples of non-meditators and meditators (total N = 3265) to (1) identify the number of factors that underlie the facets and mechanisms of mindfulness, (2) establish measurement invariance, and (3) conduct path analyses to determine the associations of extracted factors with psychological symptoms. Results Five measurement-invariant common factors were found to underlie the mechanisms and facets of mindfulness. The FFMQ facets loaded distinctly, but none of them highest, on these common factors. The common factors represented different ways of focusing, dealing with distress, and relating towards one’s own thoughts, feelings, emotions, and body sensations. Three of the common factors appeared to specifically reflect meditation experience. The FFMQ facets accounted for less variance of depression, anxiety, somatization, and stress scores than marker scales of the five common factors, all of which derived from the proposed mechanisms. Conclusions The common factors appear to be elements of the supporting mechanisms and psychological faculties of mindfulness. Their existence may explain the mutual interrelations between mechanisms and self-reported mindfulness but also suggests that self-reported mindfulness may not be factorially distinct from its assumed mechanisms. Longitudinal studies as well as behavioral data are needed to probe the generalizability and causality of these psychometric results.


2019 ◽  
pp. 002216781985853
Author(s):  
David N. Elkins

Although common factors have been widely discussed in the clinical literature, the two questions addressed in this article remain relevant: (a) What are the common factors? (b) What do they mean for humanistic psychology? The first question is important because there is no “definitive list” of common factors, and lists presented in the literature often differ dramatically. In response to this question, the article suggests that an evidence-based list of nine common factors by Wampold provides a useful and credible list. The second question is also important, particularly to humanistic psychologists. Among other answers, the article shows that research findings on common factors provide scientific support for humanistic psychology’s emphasis on the importance of the human and relational factors in psychotherapy.


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