Selecting the number of factors in principal component analysis by permutation testing-Numerical and practical aspects

AbstractExploratory Factor Analysis and Principal Component Analysis are two data analysis methods that are commonly used in psychological research. When applying these techniques, it is important to determine how many factors to retain. This decision is sometimes based on a visual inspection of the Scree plot. However, the Scree plot may at times be ambiguous and open to interpretation. This paper aims to explore a number of graphical and computational improvements to the Scree plot in order to make it more valid and informative. These enhancements are based on dynamic and interactive data visualization tools, and range from adding Parallel Analysis results to "linking" the Scree plot with other graphics, such as factor-loadings plots. To illustrate our proposed improvements, we introduce and describe an example based on real data on which a principal component analysis is appropriate. We hope to provide better graphical tools to help researchers determine the number of factors to retain.

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Principal Component Analysis Using the Factor Procedure

Author Cocitation Analysis ◽

10.4018/978-1-59904-738-6.ch008 ◽

2010 ◽

pp. 171-193

Author(s):

Sean Eom

Keyword(s):

Principal Component Analysis ◽

Factor Analysis ◽

Principal Component ◽

Component Analysis ◽

Statistical Techniques ◽

Data Input ◽

Number Of Factors ◽

Rotation Method ◽

Definition Of

This chapter describes the factor procedure. The first section of the chapter begins with the definition of factor analysis. This is the statistical techniques whose common objective is to represent a set of variables in terms of a smaller number of hypothetical variables (factor). ACA uses principal component analysis to group authors into several catagories with similar lines of research. We also present many different approaches of preparing datasets including manual data inputs, in-file statement, and permanent datasets. We discuss each of the key SAS statements including DATA, INPUT, CARDS, PROC, and RUN. In addition, we examine several options statements to specify the followings: method for extracting factors; number of factors, rotation method, and displaying output options.

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On Reliability and Number of Principal Components: Joinder with Cliff and Kaiser

Perceptual and Motor Skills ◽

10.2466/pms.1992.75.3.929 ◽

1992 ◽

Vol 75 (3) ◽

pp. 929-930 ◽

Cited By ~ 10

Author(s):

Oliver C. S. Tzeng

Keyword(s):

Principal Component Analysis ◽

Principal Components ◽

Correlation Matrix ◽

Principal Component ◽

Component Analysis ◽

Number Of Factors ◽

Number Of Principal Components ◽

Scree Test

This note summarizes my remarks on the application of reliability of the principal component and the eigenvalue-greater-than-1 rule for determining the number of factors in principal component analysis of a correlation matrix. Due to the unpredictability and uselessness of the reliability approach and the Kaiser-Guttman rule, research workers are encouraged to use other methods such as the scree test.

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Impact of Outliers Arising From Unintended and Unknowingly Included Subpopulations on the Decisions About the Number of Factors in Exploratory Factor Analysis

Educational and Psychological Measurement ◽

10.1177/0013164411429821 ◽

2012 ◽

Vol 72 (3) ◽

pp. 388-414 ◽

Cited By ~ 1

Author(s):

Yan Liu ◽

Bruno D. Zumbo

Keyword(s):

Principal Component Analysis ◽

Factor Analysis ◽

Sample Size ◽

Exploratory Factor Analysis ◽

Principal Component ◽

Component Analysis ◽

Chi Square ◽

Number Of Factors ◽

Decision Methods ◽

Sequential Tests

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included subpopulation affected the decisions about the number of factors to retain using four commonly used methods separately. The results showed that all the decision methods could provide biased results and the number of factors could be inflated, deflated, or remain the same depending on the decision methods used and outlier conditions. The findings also revealed that symmetric outliers did not affect the three principal component analysis–based methods but affected chi-square (ML) sequential tests. Finally, sample size did not play a role in the effect of outliers.

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Theoretical Justification of Decision Rules for the Number of Factors: Principal Component Analysis as a Substitute for Factor Analysis in One-Factor Cases

JOURNAL OF THE JAPAN STATISTICAL SOCIETY ◽

10.14490/jjss.37.175 ◽

2007 ◽

Vol 37 (2) ◽

pp. 175-190

Author(s):

Manabu Sato ◽

Masaaki Ito

Keyword(s):

Principal Component Analysis ◽

Factor Analysis ◽

Decision Rules ◽

Principal Component ◽

Component Analysis ◽

Theoretical Justification ◽

Number Of Factors

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A German version of the Intermittent Claudication Questionnaire (ICQ): cultural adaptation and validation

VASA ◽

10.1024/0301-1526/a000218 ◽

2012 ◽

Vol 41 (5) ◽

pp. 333-342 ◽

Cited By ~ 3

Author(s):

Kirchberger ◽

Finger ◽

Müller-Bühl

Keyword(s):

Principal Component Analysis ◽

Intermittent Claudication ◽

Completion Time ◽

Short Form ◽

Principal Component ◽

Component Analysis ◽

German Version ◽

Average Completion Time ◽

Sf 36 ◽

Related Quality

Background: The Intermittent Claudication Questionnaire (ICQ) is a short questionnaire for the assessment of health-related quality of life (HRQOL) in patients with intermittent claudication (IC). The objective of this study was to translate the ICQ into German and to investigate the psychometric properties of the German ICQ version in patients with IC. Patients and methods: The original English version was translated using a forward-backward method. The resulting German version was reviewed by the author of the original version and an experienced clinician. Finally, it was tested for clarity with 5 German patients with IC. A sample of 81 patients were administered the German ICQ. The sample consisted of 58.0 % male patients with a median age of 71 years and a median IC duration of 36 months. Test of feasibility included completeness of questionnaires, completion time, and ratings of clarity, length and relevance. Reliability was assessed through a retest in 13 patients at 14 days, and analysis of Cronbachs alpha for internal consistency. Construct validity was investigated using principal component analysis. Concurrent validity was assessed by correlating the ICQ scores with the Short Form 36 Health Survey (SF-36) as well as clinical measures. Results: The ICQ was completely filled in by 73 subjects (90.1 %) with an average completion time of 6.3 minutes. Cronbachs alpha coefficient reached 0.75. Intra-class correlation for test-retest reliability was r = 0.88. Principal component analysis resulted in a 3 factor solution. The first factor explained 51.5 of the total variation and all items had loadings of at least 0.65 on it. The ICQ was significantly associated with the SF-36 and treadmill-walking distances whereas no association was found for resting ABPI. Conclusions: The German version of the ICQ demonstrated good feasibility, satisfactory reliability and good validity. Responsiveness should be investigated in further validation studies.

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