Introduction

2.9 Longitudinal & Time Series Analysis

Learning Objectives

By the end of this section, you should be able to:

• Distinguish between longitudinal studies and time series analysis
• Explain why standard ANOVA is insufficient for repeated observations over time
• Fit and interpret a linear mixed-effects model using lme4::lmer()
• Understand fixed effects, random effects, and partial pooling
• Diagnose model assumptions with residual plots
• Recognize autocorrelation and know how to address it

1. Introduction

What Are Longitudinal Studies?

In HCI research, we frequently want to know how user behavior changes over time. Does typing speed improve as someone practices a new keyboard layout? Do people continue using a new productivity tool after the novelty wears off? Does frustration with a voice assistant decrease as users learn its capabilities?

A longitudinal study collects repeated observations from the same participants over multiple time points. This design lets us track within-person change rather than relying on snapshots from different people at different times (cross-sectional designs).

Longitudinal Studies vs. Time Series Analysis

These two terms are related but distinct:

• Longitudinal analysis focuses on modeling change trajectories across participants. The key question is "how do people change over time, and do they differ in how they change?" Typical HCI examples involve a handful of sessions (3--10) with many participants.
• Time series analysis focuses on modeling the temporal structure within a single (or a few) data streams --- trends, cycles, and autocorrelation. The key question is "what patterns exist in this sequence of observations?" Typical examples involve many time points (dozens to thousands) from one or a few sources, such as daily app usage logs or continuous sensor data.