Identification and Estimation of General Nonlinear Structured Latent Factor Model for Functional Data

Nonlinear structured latent factor model captures the relationship between observed variables and latent variables in a nonlinear way, offering greater flexibility compared to a linear factor model.Functional data characterizes features of data that vary continuously over time or space and is widely applied across various fields.This paper proposes a nonlinear structured latent factor model for functional data.We consider correlations for the latent factor to account for the dependence in functional data at different time points.The structured identifiability of latent factors is studied to ensure uniqueness, thereby allowing these factors to have a physical interpretation.A Gaussian process (GP) prior is utilized to estimate the unknown nonlinear link functions.To improve computational efficiency, an efficient algorithm is developed by using the nearest neighbor Gaussian process (NNGP).The consistency of the latent factors and the unknown parameters, as well as the posterior consistency of the unknown link functions, was established.Simulation studies were conducted to demonstrate the finite-sample performance and the flexibility of the proposed model, and the significant computational time savings achieved by NNGP compared to GP.The method was applied to analyse the gait data collected in our laboratory for early detection of neurodegenerative diseases.