Research Article
On Different Extraction Methods of Factor Analysis
Awogbemi Clement Adeyeye,
Koyejo Samuel Olusegun,
Olowu Abiodun Rafiu
Issue:
Volume 11, Issue 3, June 2023
Pages:
48-55
Received:
1 October 2023
Accepted:
8 November 2023
Published:
21 November 2023
Abstract: This study aims at examining and comparing different methods of extracting factor analysis and applying such to real life scenario. Factor analysis simplifies complex and diverse relationships existing among a set of observed variables. This is carried out by unfolding common factor connecting unrelated variables that provide insight to the underlying data structure. Since common factors have unit variance, the variance of a given variable is partitioned into common variance and unique variance which were used to generate the total variance. The model assumptions for both random and non-random factor score analyses were examined to ascertain whether or not the model contains the model parameters to be estimated. Different methods of extracting factor analysis were examined and applied for possible comparison. The centroid method maximizes the sum of loadings without giving recourse to the signs; the principal factor method accounts for the maximum feasible amount of variance in the variables being factored and the maximum likelihood method maximizes the relationship between the sample of data and the population from which the sample is drawn. It was established that the principal component method is scale invariant while the maximum likelihood method of factor analysis provides the best estimate for the reproduced correlation matrix with convergence to the best value. It is therefore asserted that different extraction methods produce different solutions.
Abstract: This study aims at examining and comparing different methods of extracting factor analysis and applying such to real life scenario. Factor analysis simplifies complex and diverse relationships existing among a set of observed variables. This is carried out by unfolding common factor connecting unrelated variables that provide insight to the underly...
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, as n → ∞. Then the series ∑nun converges if λ > 1 and diverges if λ < 1. However no conclusion can be made if λ = 1. Indeed the infinite series 
and 
satisfy both the expansion with λ = 1. The first one converges and the second one diverges. The aim of the present paper deals with the convergence of a generalized Riemann-Bertrand infinite series. This will allows us to improve the expansion so that something can be said if l = 1: this corresponds to the improvement of the Raabe-Duhamel convergence criterion. This improvement is based on the convergence of a new type of infinite series. These type of series are generalization of the Riemann and Bertrand infinite series.