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Factor analysis: The effects of dis...

Dukes, Kimberly Ann.

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Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain./
Author:	Dukes, Kimberly Ann.
Description:	1035 p.
Notes:	Major Professor: Ralph B. D'Agostino.
Contained By:	Dissertation Abstracts International63-02B
Subject:	Statistics -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3043286
ISBN:	0493570470

Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.
Dukes, Kimberly Ann.

Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain. - 1035 p.

Major Professor: Ralph B. D'Agostino.

Thesis (Ph.D.)--Boston University, 2002.

The primary goal of factor analysis (FA) is to understand the underlying structure or covariation in a set of distinct items. There are several steps involved in performing FA. Here we focus on the most important step, determining the appropriate number of factors to retain.

ISBN: 0493570470Subjects--Topical Terms:

773967
Statistics

Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.
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035 $a (UnM)AAI3043286
035 $a AAI3043286
040 $a UnM $c UnM
100 1 $a Dukes, Kimberly Ann. $3 1260344
245 1 0 $a Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.
300 $a 1035 p.
500 $a Major Professor: Ralph B. D'Agostino.
500 $a Source: Dissertation Abstracts International, Volume: 63-02, Section: B, page: 0864.
502 $a Thesis (Ph.D.)--Boston University, 2002.
520 $a The primary goal of factor analysis (FA) is to understand the underlying structure or covariation in a set of distinct items. There are several steps involved in performing FA. Here we focus on the most important step, determining the appropriate number of factors to retain.
520 $a Based on the FA population model, we used Monte Carlo simulation to estimate the accuracy of twelve popular rules. Six component analysis (CA)-based rules were also tested including λ ≥ 1, minimum average partial method, Bartlett's χ<super>2</super> test, Horn's Parallel Analysis (PA), 80% explained variance and Image λ ≥ 1. Six factor analysis (FA)-based rules were tested including Kaiser-Guttman's eigenvalue (% variance explained) λ ≥ 0 and λ ≥ 1, Cureton and D'Agostino's λ ≥ (n<super>0.6</super>)/15 (where n = the number of variables), λ ≥ mean squared multiple correlation (SMC), 100% explained variance and a maximum likelihood based χ<super>2</super> test. Five conditions of simulation were investigated: distribution of the items (normal, ordinal, binomial), the true number of factors (2 to 10 by 2), strengths of the factor loadings (0.3 to 0.9 by 0.1), the number of variables loading on each factor (3, 4, 5, 6, 9, 12) and the number of observations per variable (5, 10, 20, 30)
520 $a The results indicated that among the CA-based rules, PA produced the highest accuracy (more than 87% of the time the true number of factors was retained) and among the FA-based rules, the λ ≥ (n<super>0.6</super>)/15 rule produced the highest accuracy (>77%) over all conditions of simulation. The default rules in popular statistical computing packages (e.g., SAS, S-Plus) are not the most accurate. The λ ≥ 1 CA-based rule and the 100% variance FA-based rule were <57% and <48% accurate, respectively, over all conditions of simulation. The distribution of the items had minimal effect on rules' performance. The magnitude of the factor loadings generally had the most impact on the accuracy of the rules. The remaining conditions of simulation have less clear effects on rules' performance. Optimal results are achieved with PA, assuming adequate computer resources, and as an alternative the λ ≥ (n<super>0.6</super>)/15 is recommended. Best results are achieved with factor loadings of 0.5 or greater and at least ten observations per variable
590 $a School code: 0017
650 $a Statistics $3 773967
690 $a 046
710 2 $a Boston University $3 1260282
773 0 $t Dissertation Abstracts International $g 63-02B
790 $a 001
790 1 $a D'Agostino, Ralph B., $e adviso
791 $a Ph.D
792 $a 200
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3043286