2026 Theses Doctoral

Nonparametric and Semiparametric Dynamic Factor Models for Event History Data

Chen, Fangyi

This thesis develops two dynamic factor models for the statistical analysis of event history data. After a short introduction to survival and event history analysis in Chapter 1, we propose a semiparametric dynamic factor model for high-dimensional recurrent event time data in Chapter 2. With advances in data collection technology, there has been a resurgence of high-dimensional recurrent event data involving many event types and observations.

We propose a semiparametric dynamic factor model for the Euclidean embedding and dimension reduction of such high-dimensional recurrent event data. The model specification relies on the marginal mean rate function, which allows for flexible dependence structures. A nearly rate-optimal smoothing-based estimator is proposed, along with an information criterion that consistently selects the number of factors. We illustrate the method through simulation studies and an application to a real supermarket data with insightful intepretations, demonstrating the effectiveness of these inference tools. In Chapter 3, we propose a dynamic factor model for multivariate counting process data, motivated by process data arising from large-scale computer-based assessments. The proposed model can be viewed as an extension of the classical frailty models developed in survival analysis for multivariate recurrent event times, but with two important distinctions: (i) the factor (frailty) is of primary interest, and (ii) covariates are internal and embedded in the factor.

We establish a theoretical foundation with results on generic identifiability, consistency and asymptotic normality of the maximum likelihood estimator. Furthermore, to obtain a parsimonious model and to improve interpretation of parameters therein, variable selection and estimation for both fixed and random effects are developed through suitable penalization along with an efficient stochastic EM algorithm. Simulation studies demonstrate that the proposed approach effectively recovers the true underlying structure. The proposed method is applied to analyzing the log file of an item from the Programme for the International Assessment of Adult Competencies (PIAAC), where meaningful relationships are discovered.