Assessing Dimensionality in Non-Positive Definite Tetrachoric Correlation Matrices
Does Matrix Smoothing Help
Bibliographic Data
| ID | 19291397 |
|---|---|
| Authors | Justin D Kracht (0000-0002-3979-4472, University of Minnesota), Niels G Waller (0000-0003-1877-7232, University of Minnesota, corresponding author) |
| Year | 2022 |
| Volume | 57 |
| Issue | 2-3 |
| Pages | 385-407 |
| Publication date | 2022-05-04 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Multivariate Behavioral Research (JOURNAL) |
| Journal identifiers | ISSN: 0027-3171 • E-ISSN: 1532-7906 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/00273171.2020.1859350 |
| PMID | 33377397 |
| OpenAlex | W3114010412 |
| Language | EN |
| Citations received | 4 |
| References cited | 65 |
We performed two simulation studies that investigated dimensionality recovery in NPD tetrachoric correlation matrices using parallel analysis. In each study, the NPD matrices were rehabilitated by three smoothing algorithms. In Study 1, we replicated the work by Debelak and Tran on the assessment of dimensionality in one- or two-dimensional common factor models. In Study 2, we extended the Debelak and Tran design in three important ways. Specifically, we investigated: (a) a wider range of factors; (b) models with varying amounts of model error; and (c) models generated from more realistic population item parameters. Our results indicated that matrix smoothing of NPD tetrachoric correlation matrices improves the performance of parallel analysis with binary data. However, these improvements were modest and often of trivial size. To demonstrate the effect of matrix smoothing on an empirical data set, we applied parallel analysis and factor analysis to Adjective Checklist data from the California Twin Registry
Correlation · Curse of dimensionality · Factor analysis · Matrix (chemical analysis) · Polychoric correlation · Population · Principal component analysis · Range (aeronautics) · Set (abstract data type) · Smoothing · Statistics · Assisted Reproductive Technology and Twin Pregnancy · Cognitive Abilities and Testing · Computer Science · Engineering · Mathematics · Mental Health Research Topics
Evaluation of Factor Analytic Research Procedures by means of Simulated Correlation Matrices
An empirical Kaiser criterion.
Assessing the Size of Model Misfit in Structural Equation Models
Dimensionality assessment of ordered polytomous items with parallel analysis.
Factor Retention Decisions in Exploratory Factor Analysis
Item factor analysis
How to determine the number of factors to retain in exploratory factor analysis
A Note on the Relation Between Factor Analytic and Item Response Theory Models
A new look at Horn’s parallel analysis with ordinal variables.
Determining the number of factors using parallel analysis and its recent variants.
Reproducible Research in Computational Science
On the Relationship between iTem Response Theory and Factor Analysis of Discretized Variables
Cutoff criteria for fit indexes in covariance structure analysis
A Rationale and Test for the Number of Factors in Factor Analysis
Estimating the reproducibility of psychological science
In Search of Golden Rules
Testing Structural Equation Models
Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis
Discriminant Validity of NEO-PIR Facet Scales
Principal Component Analysis of Smoothed Tetrachoric Correlation Matrices as a Measure of Dimensionality
Performance of Parallel Analysis in Retrieving Unidimensionality in the Presence of Binary Data
Accuracy of the Parallel Analysis Procedure With Polychoric Correlations
Parallel Analysis with Unidimensional Binary Data
A Proposed Solution to the Problem With Using Completely Random Data to Assess the Number of Factors With Parallel Analysis
Evaluation of Parallel Analysis Methods for Determining the Number of Factors
Accuracy of Revised and Traditional Parallel Analyses for Assessing Dimensionality with Binary Data
An Investigation of the Parallel Analysis Criterion for Determining the Number of Common Factors
The Hull Method for Selecting the Number of Common Factors
Choosing the Optimal Number of Factors in Exploratory Factor Analysis
An Overview of Analytic Rotation in Exploratory Factor Analysis
The Problem with Having Two Watches
Empirical Comparison Between Factor Analysis and Multidimensional Item Response Models
Presidential Address
Recovery of Weak Common Factors by Maximum Likelihood and Ordinary Least Squares Estimation
Comparative fit indexes in structural models
Statistical significance in psychological research
Comparison of five rules for determining the number of components to retain
Representing sources of error in the common-factor model
A lower-bound method for the dimension-free measurement of internal consistency
| Unique citing works | 4 |
|---|---|
| Citations per year | 2 |
| Citation span | 2024 - 2026 (3) |
| Citation velocity | current |
| Highly cited | No |
| Citation types | Neutral: 4 |