# A Latent Gaussian Process Model for Analyzing Intensive Longitudinal Data

## TL;DR

This paper introduces a Gaussian process-based latent curve model tailored for intensive longitudinal data, capturing individual dynamics with high temporal resolution and irregular observation times, advancing analysis in social sciences.

## Contribution

The paper presents a semi-parametric Gaussian process model for latent curves, improving analysis of intensive longitudinal data over traditional models.

## Key findings

- Model effectively captures individual-specific trajectories.
- Simulation studies validate estimation procedures.
- Application to real data demonstrates practical utility.

## Abstract

Intensive longitudinal studies are becoming progressively more prevalent across many social science areas, especially in psychology. New technologies like smart-phones, fitness trackers, and the Internet of Things make it much easier than in the past for data collection in intensive longitudinal studies, providing an opportunity to look deep into the underlying characteristics of individuals under a high temporal resolution. In this paper, we introduce a new modeling framework for latent curve analysis that is more suitable for the analysis of intensive longitudinal data than existing latent curve models. Specifically, through the modeling of an individual-specific continuous-time latent process, some unique features of intensive longitudinal data are better captured, including intensive measurements in time and unequally spaced time points of observations. Technically, the continuous-time latent process is modeled by a Gaussian process model. This model can be regarded as a semi-parametric extension of the classical latent curve models and falls under the framework of structural equation modeling. Procedures for parameter estimation and statistical inference are provided under an empirical Bayes framework and evaluated by simulation studies. We illustrate the use of the proposed model through the analysis of an ecological momentary assessment dataset.