Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence “Time is the one immaterial object which we cannot influence—neither speed up nor slow down, add to nor diminish.” Maya Angelou Thanks for inviting me here today. We’re going to be talking about our recent book Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence, published by Oxford Univ Press.   In the book, we present what we hope is an accessible yet in-depth presentation of two of today’s most popular statistical methods: §        multilevel models for studying individual change (also known as individual growth models). These are methods are for studying systematic change over time—e.g., changes in test scores, self-esteem—in short, any continuous outcome. §        survival analysis models (also known as hazard models) for studying event occurrence. These are methods for studying whether and when events occur—dropping out, leaving teaching, graduation, first word, first step, first date—in short, any specific identifiable change of state. Our goal in writing the book was to improve the practice of quantitative research by bringing sophisticated statistical methods to bear on important empirical questions. Over the next two days, we’re going to essentially give you a crash course in the book, going chapter by chapter through illustrative examples. 1.     Handouts match the powerpoint slides 2.     Everything is explained in ALDA in greater detail 3.   The UCLA website has code in all the major packages for fitting the models to data Before getting into the actual details, we thought we’d begin by trying to give you a longitudinal overview of the state of longitudinal research Judith D. Singer & John B. Willett Harvard Graduate School of Education ALDA websites: gseacademic.harvard.edu/alda www.oup-usa.org/alda www.ats.ucla.edu/stat/examples/alda

the figures for ages after 6 were all guesses. The first recorded longitudinal study of event occurrence: Graunt’s Notes on the Bills of Mortality (1662) Graunt’s accomplishments Analyzed mortality statistics in London and concluded correctly that more female than male babies were born and that women lived longer than men. Created the first life table assessing out of every 100 babies born in London, how many survived until ages 6, 16, 26, etc  Age Died Survived 0 - 100 6 36 64 24 40 15 25 9 16 6 10 4 6 3 3 2 1 86 1 0 Unfortunately, the table did not give a realistic representation of true survival rates because the figures for ages after 6 were all guesses. Rothman, KJ., (1996) Lessons from John Graunt, Lancet, Vol. 347, Issue 8993

Adolescent growth spurt The first longitudinal study of growth: Filibert Gueneau de Montbeillard (1720-1785) Recorded his son’s height every six months from his birth in 1759 until his 18th birthday Adolescent growth spurt Buffon (1777) Histoire Naturelle & Scammon, RE (1927) The first seriation study of human growth, Am J of Physical Anthropology, 10, 329-336/

Does a galloping horse ever have all four feet off the ground at once? Making continuous TIME amenable to study: Eadweard Muybridge (1887) Animal Locomotion Does a galloping horse ever have all four feet off the ground at once? Hired in 1872 to settle a bet on whether a galloping horse has all four feet off the ground at once 781 photographic sequences documenting movement over time www.artsmia.org/playground/muybridge/

What about now?: How much longitudinal research is being conducted? Annual searches for keyword 'longitudinal' in 6 OVID databases, between 1982 and 2002 Economics (361%) Sociology (245%) Agriculture/ Forestry (326%) Medicine (451%) Psychology (365%) Education (down 8%) Let me begin with two windows on the status of longitudinal research. First, as a crude indicator, we started by asking How much longitudinal research is actually being conducted and how has this changed over time? Using the 20 year period from 1982 to 2002 as our window, we did bibliographic searches for the keyword ‘longitudinal” in each of 6 fields. What we discovered was that in most fields, the prevalence of longitudinal research has been skyrocketing: GRAPHS   The only field that has not seen any increase during this 20 year period is education! In fact, there was an 8% decline! Education is falling behind not just in randomized controlled trials, but in other areas of quantitative research as well. Given the power of modern longitudinal methods to address research questions about change and event occurrence, this as a serious problem that needs addressing.

What’s the “quality” of today’s longitudinal studies? Read 150 articles published in 10 APA journals in 1999 and 2003 First, the good news: More longitudinal studies are being published, and an increasing %age of these are “truly” longitudinal ’03 ‘99 47% 33% % longitudinal 26% 36% 2 waves 45% 38% 4 or more waves 29% 3 waves Now, the bad news: Very few of these longitudinal studies are using “modern” analytic methods 15% 7% Growth modeling 5% 2% Survival analysis 9% 6% Ignoring age-heterogeneity 8% “Simplifying” analyses by…. Setting aside waves Combining waves 17% Separate but parallel analyses 32% 38% Wave-to-wave regression 29% 40% Repeated measures ANOVA

Part of the problem may well be reviewers’ ignorance Comments received this year from two reviewers for Developmental Psychology of a paper that fit individual growth models to 3 waves of data on vocabulary size among young children: Reviewer A: “I do not understand the statistics used in this study deeply enough to evaluate their appropriateness. I imagine this is also true of 99% of the readers of Developmental Psychology. … Previous studies in this area have used simple correlation or regression which provide easily interpretable values for the relationships among variables. … In all, while the authors are to be applauded for a detailed longitudinal study, … the statistics are difficult. … I thus think Developmental Psychology is not really the place for this paper.” Reviewer B: “The analyses fail to live up to the promise…of the clear and cogent introduction. I will note as a caveat that I entered the field before the advent of sophisticated growth-modeling techniques, and they have always aroused my suspicion to some extent. I have tried to keep up and to maintain an open mind, but parts of my review may be naïve, if not inaccurate.”

What kinds of research questions require longitudinal methods? Questions about systematic change over time Questions about whether and when events occur Espy et al. (2000) studied infant neurofunction 40 infants observed daily for 2 weeks; 20 had been exposed to cocaine, 20 had not. Infants exposed to cocaine had lower rates of change in neurodevelopment. South (2001) studied marriage duration. 3,523 couples followed for 23 years, until divorce or until the study ended. Couples in which the wife was employed tended to divorce earlier. 1. Within-person descriptive: How does an infant’s neurofunction change over time? 2 Within-person summary: What is each child’s rate of development? 3 Between-person comparison: How do these rates vary by child characteristics? Within-person descriptive: Does each married couple eventually divorce? Within-person summary: If so, when are couples most at risk of divorce? Between-person comparison: How does this risk vary by couple characteristics? Individual Growth Model/ Multilevel Model for Change Discrete- and Continuous-Time Survival Analysis

Four important advantages of modern longitudinal methods You have much more flexibility in research design Not everyone needs the same rigid data collection schedule—cadence can be person specific Not everyone needs the same number of waves—can use all cases, even those with just one wave! You can identify temporal patterns in the data Does the outcome increase, decrease, or remain stable over time? Is the general pattern linear or non-linear? Are there abrupt shifts at substantively interesting moments? You can include time varying predictors (those whose values vary over time) Participation in an intervention Family composition, employment Stress, self-esteem You can include interactions with time (to test whether a predictor’s effect varies over time) Some effects dissipate—they wear off Some effects increase—they become more important Some effects are especially pronounced at particular times.

Structure of the workshop www.ats.ucla.edu/stat/examples/alda Exploring longitudinal data on change 1 Ch 2 A framework for investigating change over time   Ch 1 Table of contents Datasets Chapter Title SPSS SPlus Stata SAS HLM MLwiN Mplus Modeling discontinuous and nonlinear change 1   Ch 6 Treating time more flexibly Ch 5 Doing data analysis with the multilevel model for change Ch 4 Introducing the multilevel model for change Ch 3 A framework for investigating event occurrence   1 Ch 9 Modeling change using covariance structure analysis Ch 8 Examining the multilevel model’s error covariance structure Ch 7 Extending the Cox regression model 1   Ch 15 Fitting the Cox regression model Ch 14 Describing continuous-time event occurrence data Ch 13 Extending the discrete-time hazard model Ch 12 Fitting basic discrete-time hazard models Ch 11 Describing discrete-time event occurrence data Ch 10