Articlegreen2012

Principles and Practice of Scaled Difference Chi-Square Testing

525 citations0/0 files storedStructural Equation Modeling A Multidisciplinary Journal

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001 Satorra, A. and Bentler, P. M. 2001. A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66: 507–514. [Crossref], [Web of Science ®] , [Google Scholar]) and new (Satorra & Bentler, 2010 Satorra, A. and Bentler, P. M. 2010. Ensuring positiveness of the scaled chi-square test statistic. Psychometrika, 75: 243–248. [Crossref], [Web of Science ®] , [Google Scholar]) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's maximum likelihood (ML) chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single- and multiple-group form for specifying the model M 10 that is involved in the new test.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 525 citations exist upstream.

References

1989Structural Equations with Latent Variables 1991Structural Equations with Latent Variables.1989EQS : structural equations program manual 1989LISREL 7 : user's reference guide 1985Optimism, coping, and health: Assessment and implications of generalized outcome expectancies.1996The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis.2001A Scaled Difference Chi-Square Test Statistic for Moment Structure Analysis 2004The Positive and Negative Affect Schedule (PANAS): Construct validity, measurement properties and normative data in a large non‐clinical sample

Cited by

2012Structural Equation Modeling 2015Four Research Designs and a Comprehensive Analysis Strategy for Investigating Common Method Variance with Self-Report Measures Using Latent Variables 2014Boredom and academic achievement: Testing a model of reciprocal causation.2013Reciprocal effects of work stressors and counterproductive work behavior: A five-wave longitudinal study.2016How does brand innovativeness affect brand loyalty?

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.