scholarly journals An Entropy-Based Approach for Measuring Factor Contributions in Factor Analysis Models

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 634 ◽  
Author(s):  
Nobuoki Eshima ◽  
Minoru Tabata ◽  
Claudio Giovanni Borroni
Keyword(s):  
Factor Analysis ◽  
Conventional Method ◽  
Latent Variables ◽  
Common Factor ◽  
Present Approach ◽  
Factor Loadings ◽  
Numerical Example ◽  
Manifest Variable ◽  
The Common ◽  
Analysis Models

In factor analysis, factor contributions of latent variables are assessed conventionally by the sums of the squared factor loadings related to the variables. First, the present paper considers issues in the conventional method. Second, an alternative entropy-based approach for measuring factor contributions is proposed. The method measures the contribution of the common factor vector to the manifest variable vector and decomposes it into contributions of factors. A numerical example is also provided to demonstrate the present approach.

Dimensions of Jewish-American Identity

1973 ◽  
Vol 33 (3) ◽  
pp. 891-900 ◽  
Author(s):  
Itai Zak
Keyword(s):  
United States ◽  
Factor Analysis ◽  
Test Scores ◽  
Common Factor ◽  
The United States ◽  
American Identity ◽  
Jewish American ◽  
Cast Doubt ◽  
The Common ◽  
High Degree

The main problem posed in this study is: What are the content and structure of Jewish and American identity? The Jewish-American Identity Scale, which was adapted and refined for this study, was administered in 1971 to four samples, totaling 1006 Jewish-American college students from various parts of the United States. Initially, factor analysis was applied to the separate samples. Intersample comparisons of factor structures indicated a high degree of congruency; consequently, the samples were combined for subsequent analyses. Factor analysis of the test scores demonstrated that most of the common factor variance was appropriated by two relatively orthogonal factors. Items dealing with American identity and those dealing with Jewish identity had medium to high loadings on the two respective factors. These findings supported the hypothesis of the duality and the orthogonality of dimensions of Jewish and American identity, and cast doubt on the notion forwarded by some researchers that Jewish-American identity forms a bipolar continuum.

Exploratory Factor Analysis

2018 ◽  
Author(s):  
Brian D. Haig
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Common Factor ◽  
Methodological Issues ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
Scientific Inference ◽  
Confirmatory Factor ◽  
The Common

Chapter 6 argues that exploratory factor analysis is an abductive method of theory generation that exploits a principle of scientific inference known as the principle of the common cause. Factor analysis is an important family of multivariate statistical methods that is widely used in the behavioral and social sciences. The best known model of factor analysis is common factor analysis, which has two types: exploratory factor analysis and confirmatory factor analysis. A number of methodological issues that arise in critical discussions of exploratory factor analysis are considered. It is suggested that exploratory factor analysis can be profitably employed in tandem with confirmatory factor analysis.

scholarly journals An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 140
Author(s):  
Nobuoki Eshima ◽  
Claudio Giovanni Borroni ◽  
Minoru Tabata ◽  
Takeshi Kurosawa
Keyword(s):  
Factor Analysis ◽  
Correlation Analysis ◽  
Canonical Correlation ◽  
Common Factor ◽  
Common Factors ◽  
Correlation Coefficients ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Numerical Examples ◽  
The Common

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.

Research on Blind Source Separation with Noise Based on Multi Factor Analysis

2014 ◽  
Vol 644-650 ◽  
pp. 3947-3950
Author(s):  
Guo Hua Liu ◽  
Zeng Shan Yin ◽  
Zheng Wei Wang ◽  
Xiao Song Yao ◽  
Wen Zhe Yang
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Blind Source Separation ◽  
Random Error ◽  
Common Factor ◽  
Source Separation ◽  
Processing Method ◽  
Fastica Algorithm ◽  
Multifactor Analysis ◽  
The Common

The pre-processing method of blind source separation based on multifactor analysis is proposed to solve the blind source with noise. Firstly, the shortcomings of existing methods of blind source separation are point out after analyzing their principles. The multifactor analysis is introduced in blind source separation and the maximum likelihood estimate based on expectation maximum is used to estimate the common factor and random error. Finally the FastICA algorithm is used to separate BSS result. The validity and the advantage of this method are illustrated by an example.

Structure of Ethnic Identity of Arab-Israeli Students

1976 ◽  
Vol 38 (1) ◽  
pp. 239-246 ◽  
Author(s):  
Itai Zak
Keyword(s):  
Factor Analysis ◽  
Ethnic Identity ◽  
Common Factor ◽  
Self Esteem ◽  
American Identity ◽  
The Other ◽  
Jewish American ◽  
Self Identity ◽  
The Common ◽  
Arab Minority

The main problems posed in this study were: What is the structure of the Arab-Israeli identity? What is the relation of ethnic identity to another self-referent scale? The Ethnic Identity and Self-esteem scales were administered in the summer of 1973–74 to 532 Arab-Israeli university students. Factor analysis of the items demonstrated that most of the common factor variance was appropriated by three factors, all of which were clearly recognized as already known constructs. Despite the peculiar situation of the Arab minority in Israel, two relatively orthogonal factors, an Arab identity and an Israeli identity, emerged while the other factor represented a self-esteem construct. These findings supported the conclusions of previous research on Jewish-American identity and raised questions about the notion that ethnic-majority identity forms a bipolar continuum. The ethnic identity is then discussed in relation to the broader concept of self-identity.

scholarly journals Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Ye-Mao Xia ◽  
Jian-Wei Gou
Keyword(s):  
Factor Analysis ◽  
Latent Variables ◽  
Structural Parameters ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Semiparametric Modeling ◽  
Simulation Based ◽  
Competing Models ◽  
Parametric Families ◽  
Analysis Models

Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology.

scholarly journals The contruction and evaluation of an attention questionnaire

2007 ◽  
Vol 33 (2) ◽  
Author(s):  
Johann M Schepers
Keyword(s):  
Factor Analysis ◽  
Locus Of Control ◽  
Factor Structure ◽  
Internal Control ◽  
Common Factor ◽  
Common Factors ◽  
Principal Factor ◽  
First Year ◽  
The Common ◽  
First Year University

The principal objective of the study was the construction and evaluation of an attention questionnaire. A corollary of the study was to determine the common factors between the Attention Questionnaire (AQ) and the Locus of Control Inventory (LCI). The AQ and the LCI (1999) were applied jointly to a sample of 1577 first-year university students. To start with the AQ was subjected to a principal factor analysis. It yielded three factors which were identified as Concentration Ability, Arousal and Distractibility. Three scales were formed which yielded reliabilities of 0,886, 0,757 and 0,863 respectively. Multiple battery factor analysis was used to establish the common factor structure of the two instruments. Autonomy and Internal Control were strongly related to Concentration Ability.

scholarly journals Can Variances of Latent Variables be Scaled in Such a Way That They Correspond to Eigenvalues?

2017 ◽  
Vol 6 (6) ◽  
pp. 35 ◽  
Author(s):  
Karl Schweizer ◽  
Stefan Troche ◽  
Siegbert Reiß
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Simulation Study ◽  
Latent Variables ◽  
Latent Variable ◽  
Factor Model ◽  
Estimation Method ◽  
Factor Loadings ◽  
Confirmatory Factor ◽  
Theoretical Foundations

The paper reports an investigation of whether sums of squared factor loadings obtained in confirmatory factor analysis correspond to eigenvalues of exploratory factor analysis. The sum of squared factor loadings reflects the variance of the corresponding latent variable if the variance parameter of the confirmatory factor model is set equal to one. Hence, the computation of the sum implies a specific type of scaling of the variance. While the investigation of the theoretical foundations suggested the expected correspondence between sums of squared factor loadings and eigenvalues, the necessity of procedural specifications in the application, as for example the estimation method, revealed external influences on the outcome. A simulation study was conducted that demonstrated the possibility of exact correspondence if the same estimation method was applied. However, in the majority of realized specifications the estimates showed similar sizes but no correspondence. 

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