Pairwise stochastic approximation for confirmatory factor analysis of categorical data.

Area of Science:

• Statistics
• Computational Statistics

Background:

• Pairwise likelihood is a common method for estimating latent variable models, offering computational efficiency over full likelihood by avoiding high-dimensional integrals.
• However, pairwise likelihood can still be computationally intensive for large-scale problems with many variables.

Purpose of the Study:

• To develop a computationally efficient approximation for the pairwise likelihood estimator suitable for large-scale latent variable models.
• To address the computational demands of pairwise likelihood in factor analysis of categorical data.

Main Methods:

• An approximation of the pairwise likelihood estimator using stochastic gradients derived from subsampling pairwise log-likelihood contributions.
• A subsampling scheme is employed to control per-iteration computational complexity.
• The proposed stochastic estimator is shown to be asymptotically equivalent to the standard pairwise likelihood estimator.

Main Results:

• The stochastic approximation method is computationally advantageous for large datasets.
• Finite-sample performance can be enhanced by compounding sampling variability with subsampling uncertainty.
• The method's efficacy is validated through simulation studies and real-world data applications.

Conclusions:

• The proposed stochastic gradient-based approximation offers an efficient solution for estimating latent variable models using pairwise likelihood, especially in large-scale settings.
• This approach maintains statistical validity while significantly reducing computational burden.