  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.
