Hierarchical likelihood approach to non-Gaussian factor analysis

ABSTRACT

Factor models, structural equation models (SEMs) and random-effect models share the common feature that they assume latent or unobserved random variables. Factor models and SEMs allow well developed procedures for a rich class of covariance models with many parameters, while random-effect models allow well developed procedures for non-normal models including heavy-tailed distributions for responses and random effects. In this paper, we show how these two developments can be combined to result in an extremely rich class of models, which can be beneficial to both areas. A new fitting procedures for binary factor models and a robust estimation approach for continuous factor models are proposed.

Keywords:

• Factor analysis
• hierarchical likelihood
• random-effect model
• structural equation model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by an National Research Foundation of Korea (NRF) grant funded by Korea government (MEST) (No. 2011-0030810) and the Brain Research Program through the NRF funded by the Ministry of Science, ICT and Future Planning (2014M3C7A1062896).