Sparsest factor analysis for clustering variables: a matrix decomposition approach

Adachi, Keiichiro; Trendafilov, Nickolay T.

doi:10.1007/s11634-017-0284-z

Cited by 9 publications

(4 citation statements)

References 29 publications

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“…3 was applied to two real data sets. The first one is the Big Five Personality Test data set (Adachi and Trendafilov 2018) on personality traits (Sect. 5.1), and the second one is the ASia-Europe Meeting (ASEM) Connectivity Sustainability Index data set (Becker et al 2018) on relationships among countries, people and societies of the two regions (Sect.…”

Section: Applicationmentioning

confidence: 99%

Hierarchical disjoint principal component analysis

2022

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Dimension reduction, by means of Principal Component Analysis (PCA), is often employed to obtain a reduced set of components preserving the largest possible part of the total variance of the observed variables. Several methodologies have been proposed either to improve the interpretation of PCA results (e.g., by means of orthogonal, oblique rotations, shrinkage methods), or to model oblique components or factors with a hierarchical structure, such as in Bi-factor and High-Order Factor analyses. In this paper, we propose a new methodology, called Hierarchical Disjoint Principal Component Analysis (HierDPCA), that aims at building a hierarchy of disjoint principal components of maximum variance associated with disjoint groups of observed variables, from Q up to a unique, general one. HierDPCA also allows choosing the type of the relationship among disjoint principal components of two sequential levels, from the lowest upwards, by testing the component correlation per level and changing from a reflective to a formative approach when this correlation turns out to be not statistically significant. The methodology is formulated in a semiparametric least-squares framework and a coordinate descent algorithm is proposed to estimate the model parameters. A simulation study and two real applications are illustrated to highlight the empirical properties of the proposed methodology.

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Section: Applicationmentioning

confidence: 99%

Hierarchical disjoint principal component analysis

2022

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“…For the rotation, we considered the four widely used methods: Varimax, Promax, Quartimin and Geomin (Abdi, 2003;Browne, 2001). Moreover, 2O-DFA's performance was compared with the results obtained by SSFA (Adachi & Trendafilov, 2018) and FANC (Hirose & Yamamoto, 2014). SSFA was performed imposing the number of common factors equal to H , a convergence tolerance equal to 10 5 and 50 different initial solutions for the loading matrix.…”

Section: Simulation Studymentioning

confidence: 99%

“…Vichi (2017) proposed a model, named disjoint factor analysis (DFA), to identify the best SSM for the data, wherein the maximum likelihood estimation allows to make inference on the number of factors, on the relations between MVs and factors (i.e., loadings), and to assess the validity of the SSM for the observed data. Adachi and Trendafilov (2018) also proposed a matrix-based procedure for sparse FA such that each variable loads only on one common factor by obtaining a simple structure.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Disjoint Factor Analysis

Cavicchia

Vichi

2021

Psychometrika

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Hierarchical models are often considered to measure latent concepts defining nested sets of manifest variables. Therefore, by supposing a hierarchical relationship among manifest variables, the general latent concept can be represented by a tree structure where each internal node represents a specific order of abstraction for the latent concept measured. In this paper, we propose a new latent factor model called second-order disjoint factor analysis in order to model an unknown hierarchical structure of the manifest variables with two orders. This is a second-order factor analysis, which—respect to the second-order confirmatory factor analysis—is exploratory, nested and estimated simultaneously by maximum likelihood method. Each subset of manifest variables is modeled to be internally consistent and reliable, that is, manifest variables related to a factor measure “consistently” a unique theoretical construct. This feature implies that manifest variables are positively correlated with the related factor and, therefore, the associated factor loadings are constrained to be nonnegative. A cyclic block coordinate descent algorithm is proposed to maximize the likelihood. We present a simulation study that investigates the ability to get reliable factors. Furthermore, the new model is applied to identify the underlying factors of well-being showing the characteristics of the new methodology. A final discussion completes the paper.

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“…We prescribe each row of Ψ to have one non-zero element, denoted by ψ j , and allow the columns of Ψ to have more than one non-zero element. This sparse construct was already used in (Adachi and Trendafilov, 2017) to achieve sparse factor loadings Λ. Note, that the proposed new model (18) has a dense Λ and sparse (non-diagonal) Ψ.…”

Section: Modelmentioning

confidence: 99%

Semi-sparse PCA

Eldén

Trendafilov

2018

Psychometrika

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It is well-known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA). An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model/algorithm can act as a specific sparse PCA and as a low-rank-plus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new model, and the performance and behaviour of its algorithmic implementation.

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Sparsest factor analysis for clustering variables: a matrix decomposition approach

Cited by 9 publications

References 29 publications

Hierarchical disjoint principal component analysis

Hierarchical disjoint principal component analysis

Second-Order Disjoint Factor Analysis

Semi-sparse PCA

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