Exploratory Factor Analysis (EFA) is one of the primary statistical tools available for the verification of the structure of a psychological measure. In the case of a nested test the structure of the higher levels is verified by performing EFA on the factor scores of the lower levels, a process known as higher order factor analysis (HOFA). One of the most significant decisions made during the EFA process is how many factors to extract. A number of methods have been developed to empirically answer this question. These methods have been proven highly accurate under normal circumstances. Since HOFA is an EFA of factor scores, the number of items per factor is typically very limited. Research indicates that the established methods lose accuracy when the number of variables per factor is low, the situation created by HOFA. Alternate methods such as Factor replication and Salient loading criteria do not show these tendencies. The current study compared the accuracy and consistency of the Kaiser Rule, scree plot, multi level scree plot, Traditional Minimum Average Partial, Forth-Power Minimum Average Partial, Traditional Parallel Analysis, 95th Percentile Parallel Analysis, Factor Replication, and Salient Loading Criteria while performing higher order factor analysis. It was hypothesized that traditional methods (Kaiser Rule, Traditional Minimum Average Partial, Forth-Power Minimum Average Partial, Traditional Parallel Analysis, and 95th Percentile Parallel Analysis) would be less accurate than alternatives (scree plot, multilevel scree plot, Factor Replication, and Salient Loading Criteria). In order to more accurately represent the complexities of the experimental setting, respondent generated data was used. Procedural solutions were compared to known solutions, established in the research literature. Accuracy of each procedure was assessed in terms of percent correct solutions and mean difference from correct solution. Consistency was measured in terms of variation in the mean difference estimate. Both versions of PA maintained their accuracy and both versions of MAP failed in HOFA conditions. Salient loadings and the Kaiser rule were the only alternatives that were more accurate than MAP.
School of Behavioral Health
Boyd, Kendal C.
Owen, Jason E.
Vermeersch, David A.
Doctor of Philosophy (PhD)
Year Degree Awarded
Date (Title Page)
Library of Congress/MESH Subject Headings
Factor Analysis; Quantitative Research; Psychometrics; Variability (Psychometrics); Number Concept
Subject - Local
Exploratory Factor Analysis; Higher Order Factor Analysis; Kaiser Rule;
Loma Linda University Libraries
This title appears here courtesy of the author, who has granted Loma Linda University a limited, non-exclusive right to make this publication available to the public. The author retains all other copyrights.
Porritt, Marc Thomas, "Performance of Number of Factors Procedures in Higher Order Analysis: A Comparative Study" (2012). Loma Linda University Electronic Theses, Dissertations & Projects. Paper 223.
Loma Linda University Electronic Theses and Dissertations
Loma Linda University. Del E. Webb Memorial Library. University Archives