### Abstract

Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic—the proportion of common variance (PCV)—into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( (Formula presented.) ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as (Formula presented.), even with a relatively large sample size of 5,000. Finally, we investigated the use of (Formula presented.) in combination with R-PA and concluded that practitioners can gain additional information from (Formula presented.) and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.

Original language | English (US) |
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Journal | Educational and Psychological Measurement |

DOIs | |

State | Accepted/In press - Feb 1 2018 |

### Fingerprint

### Keywords

- effect size
- exploratory factor analysis
- parallel analysis

### ASJC Scopus subject areas

- Education
- Developmental and Educational Psychology
- Applied Psychology
- Applied Mathematics

### Cite this

*Educational and Psychological Measurement*. https://doi.org/10.1177/0013164418754611

**Proportion of Indicator Common Variance Due to a Factor as an Effect Size Statistic in Revised Parallel Analysis.** / Xia, Yan; Green, Samuel B.; Xu, Yuning; Thompson, Marilyn.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Proportion of Indicator Common Variance Due to a Factor as an Effect Size Statistic in Revised Parallel Analysis

AU - Xia, Yan

AU - Green, Samuel B.

AU - Xu, Yuning

AU - Thompson, Marilyn

PY - 2018/2/1

Y1 - 2018/2/1

N2 - Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic—the proportion of common variance (PCV)—into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( (Formula presented.) ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as (Formula presented.), even with a relatively large sample size of 5,000. Finally, we investigated the use of (Formula presented.) in combination with R-PA and concluded that practitioners can gain additional information from (Formula presented.) and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.

AB - Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic—the proportion of common variance (PCV)—into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( (Formula presented.) ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as (Formula presented.), even with a relatively large sample size of 5,000. Finally, we investigated the use of (Formula presented.) in combination with R-PA and concluded that practitioners can gain additional information from (Formula presented.) and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.

KW - effect size

KW - exploratory factor analysis

KW - parallel analysis

UR - http://www.scopus.com/inward/record.url?scp=85043397425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043397425&partnerID=8YFLogxK

U2 - 10.1177/0013164418754611

DO - 10.1177/0013164418754611

M3 - Article

AN - SCOPUS:85043397425

JO - Educational and Psychological Measurement

JF - Educational and Psychological Measurement

SN - 0013-1644

ER -