Hostname: page-component-5f745c7db-hj587 Total loading time: 0 Render date: 2025-01-06T06:42:20.112Z Has data issue: true hasContentIssue false
  • English
  • Français

Tests of Matrix Structure for Construct Validation

Published online by Cambridge University Press:  01 January 2025

Brian D. Segal ,
Thomas Braun ,
Richard Gonzalez  and
Michael R. Elliott
Brian D. Segal*
Affiliation:
University of Michigan
Thomas Braun
Affiliation:
University of Michigan
Richard Gonzalez
Affiliation:
University of Michigan
Michael R. Elliott
Affiliation:
University of Michigan
*
Correspondence should be made to Brian D. Segal, University of Michigan, Ann Arbor, MI, USA. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Psychologists and other behavioral scientists are frequently interested in whether a questionnaire measures a latent construct. Attempts to address this issue are referred to as construct validation. We describe and extend nonparametric hypothesis testing procedures to assess matrix structures, which can be used for construct validation. These methods are based on a quadratic assignment framework and can be used either by themselves or to check the robustness of other methods. We investigate the performance of these matrix structure tests through simulations and demonstrate their use by analyzing a big five personality traits questionnaire administered as part of the Health and Retirement Study. We also derive rates of convergence for our overall test to better understand its behavior.

Keywords

permutation testinghubert’s gammaquadratic assignment
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 65 - 83
Copyright
Copyright © 2018 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9647-4) contains supplementary material, which is available to authorized users.

References

Barrett, P. (2007). Structural equation modeling: Adjudging model fit. Personality and Individual Differences, 42, 815– 824. CrossRefGoogle Scholar
Beauducel, A., & Wittmann, W. (2005). Simulation study on fit indices in CFA based on data with slightly distorted simple structure. Structural Equation Modeling, 12 (1), 41– 75. CrossRefGoogle Scholar
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107 (2), 238– 246. 2320703 CrossRefGoogle ScholarPubMed
Bock, R. D., & Bargmann, R. E. (1966). Analysis of covariance structures. Psychometrika, 31 (4), 507– 534. CrossRefGoogle ScholarPubMed
Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21 (2), 230– 258. CrossRefGoogle Scholar
Chung, E., & Romano, J. P. (2013). Exact and asymptotically robust permutation tests. The Annals of Statistics, 41 (2), 484– 507. CrossRefGoogle Scholar
Fan, X., & Sivo, S. A. (2005). Sensitivity of fit indices to misspecified structural or measurement model components: Rationale of two-index strategy revisited. Structural Equation Modeling, 12 (3), 343– 367. 10.1207/s15328007sem1203_1 CrossRefGoogle Scholar
Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron, 1 3– 32. Google Scholar
Good, P. (2000). Permutation tests: A practical guide to resampling methods for testing hypotheses. (2). New York: Springer. CrossRefGoogle Scholar
Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2001). On clustering validation techniques. Journal of Intelligent Information Systems, 17 2/3 107– 145. CrossRefGoogle Scholar
Hawkins, D. L. (1989). Using U statistics to derive the asymptotic distribution of Fisher’s Z statistic. The American Statistician, 43 (4), 235– 237. Google Scholar
Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation modelling: Guidelines for determining model fit. The Electronic Journal of Business Research Methods, 6 (1), 53– 60. Google Scholar
HRS (2016). Health and retirement study (core data release) public use dataset.Google Scholar
Hu, L. -T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6 (1), 1– 55. CrossRefGoogle Scholar
Hubert, L., & Schultz, J. (1976). Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 29 (2), 190– 241. CrossRefGoogle Scholar
Jain, A. K., & Dubes, R. C. (1988). Algorithms for clustering data. Englewood Cliffs: Prentice Hall. Google Scholar
Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices. Psychometrika, 43 (4), 443– 477. CrossRefGoogle Scholar
Kline, R. B. (2011). Principles and practice of structural equation modeling. (3). New York: Guilford Press. Google Scholar
Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses. (3). New York: Springer. Google Scholar
Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27 (2), 209– 220. Google Scholar
Marsh, H. W., Hau, K. -T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentlers (1999) findings. Structural Equation Modeling, 11 (3), 320– 341. CrossRefGoogle Scholar
McDonald, R. P. (1974). Testing pattern hypotheses for covariance matrices. Psychometrika, 39 (2), 189– 201. CrossRefGoogle Scholar
R Core Team (2017). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. Google Scholar
Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48 (2), 1– 36. CrossRefGoogle Scholar
Srivastava, J. N. (1966). On testing hypotheses regarding a class of covariance structures. Psychometrika, 31 (2), 147– 164. 10.1007/BF02289504 5222204 CrossRefGoogle ScholarPubMed
Steiger, J. H. (1980). Testing pattern hypotheses on correlation matrices: Alternative statistics and some empirical results. Multivariate Behavioral Research, 15 (3), 335– 352. CrossRefGoogle ScholarPubMed
Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87 (2), 245– 251. CrossRefGoogle Scholar
Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25 173– 180. CrossRefGoogle ScholarPubMed
Steiger, J. H. (2007). Understanding the limitations of global fit assessment in structural equation modeling. Personality and Individual Differences, 42 (5), 893– 898. CrossRefGoogle Scholar
Steiger, J. H., & Lind, J. (1980). Statistically-based tests for the number of common factors. Iowa City: Paper presented at the annual spring meeting of the Psychometric Society.Google Scholar
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38 (1), 1– 10. CrossRefGoogle Scholar
Wasserstein, R. L., & Lazar, N. A. (2016). The ASA’s statement on p values: Context, process, and purpose. The American Statistician, 70 (2), 193– 242. CrossRefGoogle Scholar
Westfall, P. H., & Young, S. S. (1993). Resampling-based multiple testing: Examples and methods for p-value adjustment. New York, NY: Wiley. Google Scholar
Yuan, K-H (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40 (1), 115– 148. CrossRefGoogle ScholarPubMed
Zaki, M. J., & Meira, W. Jr. (2014). Data mining and analysis: Fundamental concepts and algorithms. New York, NY: Cambridge University Press. CrossRefGoogle Scholar
Supplementary material: File

Segal et al. supplementary material

Web Appendices for “Tests of matrix structure for construct validation”
Download Segal et al. supplementary material(File)
File 1.1 MB