H-Likelihood Approach to Factor Analysis for Ordinal Data

Abstract

Marginal likelihood-based methods are commonly used in factor analysis for ordinal data. To obtain the maximum marginal likelihood estimator, the full information maximum likelihood (FIML) estimator uses the (adaptive) Gauss–Hermite quadrature or stochastic approximation. However, the computational burden increases rapidly as the number of factors increases, which renders FIML impractical for large factor models. Another limitation of the marginal likelihood-based approach is that it does not allow inference on the factors. In this study, we propose a hierarchical likelihood approach using the Laplace approximation that remains computationally efficient in large models. We also proposed confidence intervals for factors, which maintains the level of confidence as the sample size increases. The simulation study shows that the proposed approach generally works well.

Keywords:

• binary data
• confidence interval of factors
• second-order Laplace approximation
• underlying distribution approach

FUNDING

The research was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST; No. 2011-0030810), the Brain Research Program funded by the Ministry of Science, ICT & Future Planning (2014M3C7A1062896), and an NRF grant funded by the Korean government (MEST; No. NRF-2013R1A1A1012710).

Additional information

Funding

The research was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST; No. 2011-0030810), the Brain Research Program funded by the Ministry of Science, ICT & Future Planning (2014M3C7A1062896), and an NRF grant funded by the Korean government (MEST; No. NRF-2013R1A1A1012710).