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CFA with binary variables in small samples: a comparison of two methods.

Victoria Savalei1, Douglas G Bonett2, Peter M Bentler3

  • 1Department of Psychology, University of British Columbia Vancouver, BC, Canada.

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Summary
This summary is machine-generated.

A new odds-ratio (OR) correlation method improves small sample performance for binary data compared to traditional approaches. While OR with unweighted least squares (ULS) excels for parameter estimation, the LPB method with ULS offers better chi-square test control.

Keywords:
correlation structure modelsdichotomous variablesfactor analysisodds ratiotetrachoric correlation

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Asymptotically optimal correlation structure methods often fail with small sample binary data.
  • Existing methods like the LPB approach have limitations in small sample scenarios.

Purpose of the Study:

  • To propose a novel correlation structure methodology using an odds-ratio (OR) approximation as an alternative to the LPB approach.
  • To compare the performance of the OR approach with unweighted least squares (ULS) and generalized least squares (GLS) estimation methods against the LPB approach.

Main Methods:

  • Development of a new correlation structure methodology based on an odds-ratio (OR) approximation to the tetrachoric correlation coefficient.
  • Comparison of unweighted least squares (ULS) estimation with robust standard errors and generalized least squares (GLS) estimation.
  • Evaluation of confidence intervals, individual parameter tests, and goodness-of-fit chi-square tests.

Main Results:

  • The OR approach with ULS estimation demonstrated superior performance for confidence intervals and individual model parameter tests.
  • The LPB approach with ULS estimation showed better Type I error control for the goodness-of-fit chi-square test.

Conclusions:

  • The OR approximation offers a viable alternative for correlation structure analysis with small sample binary data, particularly for parameter estimation.
  • A hybrid approach, utilizing OR with ULS for parameter estimation and LPB with ULS for chi-square testing, may offer optimal performance.