Factor analysis and more general structural equation modeling have been used widely in social and behavioral sciences. From a statistical point of view, these methods are useful data analysis tools for fitting latent variable models which correspond well with subject-matter concepts in applied sciences.
Conventional models used in such analyses are linear in underlying factors or latent variables.
This convention could be a possible reason for the well known problem in behavioral sciences that the number of factors suggested by the theory often fails to explain data variability. Capabilities to consider and fit models nonlinear in underlying factors can enhance the utility of the latent variable modeling in applied sciences, and provide useful statistical tools for exploring nonlinear structure of multivariate data. In this talk, a general parametric nonlinear factor analysis model is introduced, and the associated identification problem is discussed. Model fitting and checking procedures are proposed and described. The results of a simulation study are also presented.