Growth Curve Analysis: A Hands-On Tutorial on Using Multilevel Regression to Analyze Time Course Data

Growth Curve Analysis: A Hands-On Tutorial on Using Multilevel Regression to Analyze Time Course Data Daniel Mirman (daniel.mirman@drexel.edu) Department of Psychology, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104 USA and Moss Rehabilitation Research Institute, Elkins Park, PA 19027 USA Keywords: growth curve analysis; multilevel regression; R; longitudinal data; time course data; eye tracking; individual differences. cephalography, etc.). However, the statistical methods used by cognitive scientists to analyze these data have not kept pace. Too often repeated-measures ANOVA or bin-by-bin t- tests are used despite well-known problems with applying these methods to time course data. Growth curve analysis offers a way to model continuous effects of time and so capture critical time course patterns in longitudinal data. Foundational research in cognitive science examined in- dividual differences; from cognitive deficits in neurological disorders to superior cognitive performance by chess mas- ters and mnemonists, individual differences have shed a unique light on cognition. Even (co-)variation within a pop- ulation of college students can reveal aspects of the cogni- tive processes involved. However, the typical statistical methods used by cognitive scientists do not offer a way to quantify or analyze individual deviations from an overall group pattern. Growth curve analysis provides a statistical framework for quantifying and analyzing individual differ- ences in the context of a model of the overall group effects, thus adding a critical analytical tool for advancing theories of cognitive function. Objectives and Scope Growth curve analysis (multilevel regression) offers a sta- tistical framework for analyzing longitudinal or time course data and for quantifying differences between individuals in the context of a model of the overall group effects. These methods have been known to statisticians for many years (e.g., Wishart, 1938), but they have only recently become a prominent statistical tool in the cognitive sciences. Interest in using these statistical methods to analyze cognitive sci- ence data has outpaced cognitive scientists’ knowledge of how to implement them. This one-day tutorial will provide a hands-on introduction to using multilevel regression to an- alyze longitudinal or time course data and individual differ- ences in the cognitive sciences. The focus will be on practi- cal aspects of implementation and common pitfalls, rather than statistical theory. The tutorial will begin with the challenges of time course data, focusing on why traditional methods such as bin-by- bin t-tests and repeated-measures ANOVA are sub-optimal. It will then describe how growth curve analysis (GCA) ad- dresses those challenges and demonstrate how to use GCA to analyze simple linear data, non-linear data, and categori- cal outcome data (using logistic and quasi-logistic GCA). The final section will focus on using GCA to quantify and analyze individual differences. Throughout, example data sets will be provided for hands-on exercises that will give tutorial participants practice implementing the analyses, interpreting the results, and plotting data with model fits. There will also be time for tutorial participants to work on analyzing their own data with the instructor’s support. Target Audience and Pre-requisites This tutorial will provide a practical, hands-on introduction to growth curve analysis, so the primary target audience is scientists who are actively involved in analyzing time course data: graduate students, post-docs, senior scientists (faculty), and advanced undergraduates. The tutorial will be conducted in R using the lme4 pack- age for fitting GCA models and will include an introduction to using the ggplot2 package for plotting data and model fits. Tutorial participants are expected to have basic famili- arity with R, but no specific knowledge of the ggplot2 or lme4 packages is required. For those not yet familiar with R, there are many good introductory tutorials and books avail- able (a list of recommended ones is available at: http://www.danmirman.org/r-resources). The tutorial will include hands-on exercises and an op- portunity to work on participants’ own data, so participants are encouraged to bring their laptops with R installed (http://cran.r-project.org/) along with the lme4 and ggplot2 packages. RStudio (http://www.rstudio.com/) is a full-fea- tured cross-platform integrated development environment for R that makes R more user-friendly. It is highly recom- mended, but not required for this tutorial. Workshop materi- Relevance to Cognitive Science From learning and forgetting curves to studies of cognitive development, time course or longitudinal data play a critical role in cognitive science. Cognitive processes unfold and develop over time and understanding the dynamic time course of these processes is central to understanding cogni- tion. As experimental research methods have developed, cognitive science has acquired more and more techniques that produce a time-ordered series of observations for each participant (eye tracking, mouse/motion tracking, electroen-