Chapter 11: Factor Analysis (original) (raw)

Application of factor analysis....pdf

Several studies have suggested the efficacy of topological rotation as an adjunct to oblique analytical rotation in attaining improved approximation to maximum simple structure of the factor pattern matrix. Recently, using a higherorder scale factoring of the Objective Motivation Analysis Test (MAT), and the Eight State Questionnaire (8SQ), Boyle(1983) reported a 6.17% increase in the ±.10 hyperplane count after only five Rotoplot cycles. Four of the 11 extracted factors were simplified in line with Thurstone's simple structure requirements.

Joint Factor Analysis

1987

In this paper we discuss the problem of factor analysis from the Bayesian viewpoint. First, the classical factor analysis model is generalized in several directions. Then, prior distributions are adopted for the parameters of the generalized model and posterior dis-

An Exploratory Study of the Three Phases Analysis of Factor

2021

In this study, we examine factor analysis as a multivariate statistical tool, starting from the origin of factor analysis with regards to Spearman's approach of 1904 to the three phases of factor analysis. This is done with a view of determining the similarities and individual contributions of each of the three phases of factor analysis. This was achieved by examining the algorithms used in parameter estimations of the three phases of factor analysis. By inputting data into the algorithms and examining their outcomes and proffering recommendations based on the respective findings.

A new algorithm for the least-squares solution in factor analysis

Psychometrika, 1983

On the basis of the present situation and problems of factor analysis, this paper USES the methods of mathematical geometry and calculus to prove the interaction among factors when the factors in the two-factor and three-factor analysis equations are product function formulas. The exponential logarithmic scaling method is deduced and checked by calculation. The new factor analysis method can decompose the interaction between factors accurately and fairly. This approach is not limited to the analysis of differences between factors for the reporting period and the base period (actual and budgetary figures); In addition, it is a good way to decompose the interaction among factors by analyzing whether the differences among factors are increasing or decreasing. This provides an accurate basis for the success of retesting and adjusting the difference, and also provides a reliable basis for the attribution of the difference responsibility in the social and economic management activities. The correct factor analysis difference analysis, not only solved the longtime unresolved problems in economic management; It also solves the problem of comparative analysis of the difference between the success and failure of the experiment. The difference of factors determines the adjustment of the experiment. The correct difference analysis of factors plays a decisive role in the success of the reexperiment and has economic significance to improve the experimental results.

The American Statistician A Tale of Two Matrix Factorizations A Tale of Two Matrix Factorizations

In statistical practice, rectangular tables of numeric data are commonplace, and are often analyzed using dimensionreduction methods like the singular value decomposition and its close cousin, principal component analysis (PCA). This analysis produces score and loading matrices representing the rows and the columns of the original table and these matrices may be used for both prediction purposes and to gain structural understanding of the data. In some tables, the data entries are necessarily nonnegative (apart, perhaps, from some small random noise), and so the matrix factors meant to represent them should arguably also contain only nonnegative elements. This thinking, and the desire for parsimony, underlies such techniques as rotating factors in a search for "simple structure." These attempts to transform score or loading matrices of mixed sign into nonnegative, parsimonious forms are, however, indirect and at best imperfect. The recent development of nonnegative matrix factorization, or NMF, is an attractive alternative. Rather than attempt to transform a loading or score matrix of mixed signs into one with only nonnegative elements, it directly seeks matrix factors containing only nonnegative elements. The resulting factorization often leads to substantial improvements in interpretability of the factors. We illustrate this potential by synthetic examples and a real dataset. The question of exactly when NMF is effective is not fully resolved, but some indicators of its domain of success are given. It is pointed out that the NMF factors can be used in much the same way as those coming from PCA for such tasks as ordination, clustering, and prediction. Supplementary materials for this article are available online.

Application of Factor Analysis

Verma/Sports Research with Analytical Solution Using SPSS®, 2016

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we construct tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (1) isolating specific parameters affected by measurement invariance violations, and (2) identifying subgroups of individuals that violated measurement invariance based on a continuous auxiliary variable. The tests are presented and illustrated in detail, along with simulations examining the tests' abilities in controlled conditions.