Determining the Number of Components from the Matrix of Partial Correlations

1976/09/01 by Wayne F. Velicer · 2,441 citations
Chemistry · Computer Science · Mathematics · #Applied mathematics #Component (thermodynamics) #Component analysis #Computational Drug Discovery Methods #Computer science #Correlation #Interpretation (philosophy) #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Partial correlation #Principal component analysis #Spectroscopy and Chemometric Analyses #Statistics

paper · doi:10.1007/bf02293557

published in Psychometrika 41(3), 321-327 (Springer Science+Business Media)

openalex publication_date 1976/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.

Citations

• The Scree Test For The Number Of Factors
• The Application of Electronic Computers to Factor Analysis

Cited by

• A New Compassion Scale for Children and Its Psychometric Properties
• Evolutionary Personality Psychology
• Towards a taxonomy of personality facets
• Selecting the number of components in PCA via random signflips
• Development and validation of an appearance motivation attitudes scale for sun protection
• The Vancouver Index of Acculturation (VIA): New evidence on dimensionality and measurement invariance across two cultural settings
• Learning with multiple external representations in physics: Concreteness fading versus simultaneous presentation
• Determining the Number of Factors to Retain in EFA: An easy-to-use computer program for carrying out Parallel Analysis
• Psychometric Properties of the Generalized Anxiety Disorder 7-Item Scale in Youth: Screening in a Primary Care Sample
• Beyond Distress and Fear: Differential Psychopathology Correlates of PTSD Symptom Clusters
• Modeling Retrospective Attribution of Responsibility to Hazard‐Managing Institutions: An Example Involving a Food Contamination Incident
• Exploratory Factor Analysis With Small Samples and Missing Data
• Measuring autistic burnout: A psychometric validation of the AASPIRE Autistic Burnout Measure in autistic adults
• A single low-dimensional neural component of motor unit activity explains force generation across repetitive isometric tasks
• Normative Data, Predictive Validity, and Factor Structure of a Fourth-Generation Risk Assessment Tool (ORAC-PCQ) in a Population of Adjudicated Individuals Serving Short Sentences in the Province of Québec (Canada)
• Measuring individual differences in students' knowledge about self-regulated learning strategies with a digital tool
• Examining the conceptual and empirical distinctiveness of Agreeableness and “dark” personality items
• Development and Validation of a New Measure of Intuition: The Types of Intuition Scale
• The dynamics of internalizing and externalizing comorbidity across the early school years
• The genetic diversity of Indonesian cattle has been shaped by multiple introductions and adaptive introgression
• Exploratory graph analysis: a new approach for estimating the number of dimensions in psychological research
• Bi-cross-validation for factor analysis
• Validation of the Short Version (TLS-15) of the Triangular Love Scale (TLS-45) across 37 Languages
• Representing Multidimensional Phenomena of Geographic Interest: Benefit of the Doubt or Principal Component Analysis?
• Toward a definition of intolerance of uncertainty: A review of factor analytical studies of the Intolerance of Uncertainty Scale
• Reliability and Factorial Validity of the Core Self-Evaluations Scale
• Exploratory Factor Analysis: A Guide to Best Practice
• A new look at Horn’s parallel analysis with ordinal variables.
• Erste Analyse der psychometrischen Eigenschaften und Struktur der deutschsprachigen 10- und 25-Item Version der Connor-Davidson Resilience Scale (CD-RISC)
• Self-efficacy and the stages of self-change of smoking
• Factor structure of the Differential Ability Scales–Second Edition: Exploratory and hierarchical factor analyses with the core subtests.
• Orthogonal higher order factor structure of the Stanford-Binet Intelligence Scales--fifth edition for children and adolescents.
• Exploratory and hierarchical factor analysis of the WJ-IV Cognitive at school age.
• Psychometric Evaluation of the Altered States of Consciousness Rating Scale (OAV)
• Assessing Disruptions in Meaning: Development of the Global Meaning Violation Scale
• Exploratory factor analysis in validation studies: Uses and recommendations
• Age and gender effect on alexithymia in large, Japanese community and clinical samples: a cross-validation study of the Toronto Alexithymia Scale (TAS-20). [europepmc]
• Psychometric evaluation of the altered states of consciousness rating scale (OAV). [europepmc]
• Construction and validation of a measure of integrative well-being in seven languages: the Pemberton Happiness Index. [europepmc]
• Validation of an instrument to evaluate quality of life in the aging population: WHOQOL-AGE. [europepmc]
• Neuroticism and Extraversion in Youth Predict Mental Wellbeing and Life Satisfaction 40 Years Later. [europepmc]
• Self-generated thoughts and depression: from daydreaming to depressive symptoms. [europepmc]
• Internet addiction: coping styles, expectancies, and treatment implications. [europepmc]
• A multidimensional approach to measuring well-being in students: Application of the PERMA framework. [europepmc]
• Mental imagery during daily life: Psychometric evaluation of the Spontaneous Use of Imagery Scale (SUIS). [europepmc]
• An in-depth psychometric analysis of the Connor-Davidson Resilience Scale: calibration with Rasch-Andrich model. [europepmc]
• Psychometric properties of the 7-item game addiction scale among french and German speaking adults. [europepmc]
• Psychometric properties of the Symptom Checklist-90 in adolescent psychiatric inpatients and age- and gender-matched community youth. [europepmc]
• The Modified Abbreviated Math Anxiety Scale: A Valid and Reliable Instrument for Use with Children. [europepmc]
• Psychotic-Like Experiences at the Healthy End of the Psychosis Continuum. [europepmc]
• The Development and Validation of the Bergen-Yale Sex Addiction Scale With a Large National Sample. [europepmc]
• The structure and function of pathogen disgust. [europepmc]
• Best Practices for Developing and Validating Scales for Health, Social, and Behavioral Research: A Primer. [europepmc]
• Inferring Population Structure and Admixture Proportions in Low-Depth NGS Data. [europepmc]
• The Light vs. Dark Triad of Personality: Contrasting Two Very Different Profiles of Human Nature. [europepmc]
• Filling the psycho-social gap in the EQ-5D: the empirical support for four bolt-on dimensions. [europepmc]
• Gender-related variables for health research. [europepmc]
• The Structure of the Toronto Alexithymia Scale (TAS-20): A Meta-Analytic Confirmatory Factor Analysis. [europepmc]
• Four dimensions characterize attributions from faces using a representative set of English trait words. [europepmc]
• Are fear of cancer recurrence and fear of progression equivalent constructs? [europepmc]
• Climate Change Anxiety Assessment: The Psychometric Properties of the Polish Version of the Climate Anxiety Scale. [europepmc]

Related

• Redundancy Analysis an Alternative for Canonical Correlation Analysis
• Multi-set Canonical Correlation Analysis simply explained
• Searching for the core variables in principal components analysis
• Canonical correlation analysis of high-dimensional data with very small sample support
• A Rationale and Test for the Number of Factors in Factor Analysis