Determining Dimensionality with Dichotomous Variables: A Monte Carlo Simulation Study and Applications to Missing Data in Longitudinal Research

Ting Dai and Adam Davey ()
Additional contact information
Ting Dai: Department of Educational Psychology, University of Illinois Chicago, Chicago, IL 60607, USA
Adam Davey: Department of Behavioral Health and Nutrition, University of Delaware, Newark, DE 19716, USA

Mathematics, 2023, vol. 11, issue 6, 1-25

Abstract: Dichotomous data correspond with various types of commonly encountered data, e.g., positive/negative, case/control, missing/observed, in many fields, including medicine, health, and social sciences. Despite their ubiquity, criteria for determining dimensionality from dichotomous variables are not yet established. We conducted a large-scale simulation (Study 1) to evaluate four criteria—Kaiser, empirical Kaiser, parallel analysis, and profile likelihood—to determine the dimensionality of dichotomous data across combinations of correlation matrices (Pearson r or tetrachoric ρ) and analysis methods (principal component analysis or exploratory factor analysis), and combinations of study characteristics: sample sizes (100, 250, and 1000), variable splits (10%/90%, 25%/75%, and 50%/50%), dimensions (1, 3, 5, and 10), and items per dimension (3, 5, and 10) with 1000 replications per condition. Parallel analysis performed best, recovering dimensionality in 87.9% of replications when using principal component analysis with Pearson correlations. Guidance for selecting criteria is provided. In Study 2, we applied this dimensionality reduction approach to two different longitudinal data sets where missing data posed difficulty for multivariate data analysis. The applications of this approach to longitudinal data suggest that the exploration of resulting missing data meta-patterns is useful in practice.

Keywords: dimensionality determination; binary variable; dichotomous variable; principal component analysis; parallel analysis; factor analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1411/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1411/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:6:p:1411-:d:1097477

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().