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  1. Home
  3. Confirmatory Factor Analysis With Adaptive Quadrature Estimator Using Four Link Functions.
  1. Home
  3. Confirmatory Factor Analysis With Adaptive Quadrature Estimator Using Four Link Functions.

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Confirmatory Factor Analysis with Adaptive Quadrature Estimator Using Four Link Functions.

Kubra Atalay Kabasakal1, Ismail Dilek2, Burcu Atar1

  • 1Department of Educational Sciences, Hacettepe University, Ankara, Turkey.

Applied Psychological Measurement
|June 4, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

The probit link function generally performs best for ordinal confirmatory factor analysis (CFA) using adaptive quadrature (AQ) estimation. However, performance varies with data characteristics and the number of quadrature points used.

Keywords:
adaptive quadrature estimationconfirmatory factor analysislink functionsmeasurement intervalsnon-normal categorical data

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Quantitative Psychology

Background:

  • Ordinal confirmatory factor analysis (CFA) is crucial for understanding complex latent structures.
  • Adaptive quadrature (AQ) estimation offers a flexible approach for analyzing ordinal CFA models.
  • Selecting appropriate link functions and quadrature points is vital for accurate estimation.

Purpose of the Study:

  • To evaluate the performance of the adaptive quadrature (AQ) estimation method for ordinal confirmatory factor analysis (CFA).
  • To compare four link functions (complimentary log-log [CLL], logit, log-log, probit) under various conditions.
  • To investigate the impact of factor structures, sample sizes, latent trait distributions, and quadrature points.

Main Methods:

  • A simulation study was conducted to systematically assess estimation performance.
  • Empirical data analysis was used to validate simulation findings.
  • Key performance metrics included convergence rates, parameter recovery, and model fit.

Main Results:

  • The probit link function demonstrated superior performance across most conditions, showing high convergence rates and low parameter errors.
  • The logit link function generally exhibited the weakest performance.
  • A notable divergence was observed for asymmetric link functions: probit excelled in simulated skewed data, while log-log performed best on skewed empirical data.
  • The number of quadrature points significantly impacted estimation, with eight points causing failures in sparse real-world data.

Conclusions:

  • The probit link function is recommended for ordinal CFA using AQ estimation in most scenarios.
  • Careful consideration of link function choice is necessary, especially for skewed data.
  • The number of quadrature points should be judiciously selected to balance accuracy and avoid estimation failures with sparse data.