Trajectories of Health: Methods and Insights from Structural Equation Modeling Adam T. Perzynski, PhD Assistant Professor of Medicine and Sociology Important contributions from: Douglas Gunzler, PhD, Megan Holmes, PhD, Joseph Sudano, PhD & Susan Yoon, PhD
OUTLINE Part 1: An example using data on older adults Part 2: An example using data on kids
DISCLAIMER • Longitudinal latent variable models can be very complicated • There are many different flavors of models. • Jargon and Acronyms are bountiful (and occasionally used inconsistently)
PART 1 LONGITUDINAL PATTERNS OF DEPRESSIVE SYMPTOMS IN THE HEALTH AND RETIREMENT STUDY
AIM • Explore the use of Latent Class Growth Analysis to model changes in depressive symptoms over time in the Health and Retirement Study.
OVERVIEW • Most studies of older adults compare the change in mean scores between two waves. • A small number of studies have modeled change as a single growth trajectory
CHANGE IN MEANS BETWEEN WAVES • Often we simply calculate the mean depressive symptoms at Wave 1 (baseline). • Subract it from the mean at Wave 2 (followup).
WHAT IS A TRAJECTORY? • Regrettably , the term “trajectory” has taken on multiple meanings across disciplines and research studies. • A broad, inclusive definition of trajectory modeling is the analysis of patterns of change or stability . • Confusion is possible (if not likely)
EXAMPLE OF A SINGLE (LINEAR) GROWTH TRAJECTORY
SEM REPRESENTATION OF A SINGLE GROWTH TRAJECTORY Intercept Slope W1 W2 W… W7
CONTINUOUS LATENT GROWTH CURVE ANALYSIS • LGA / LGCA • Studies in older adults (ie George and Lynch 2003) typically find that the slope of the latent growth curve for depressive symptoms is small and positive, and that the slope of the curve is steepest in the oldest cohorts.
EXAMPLE FROM GEORGE AND LYNCH (2003)
EXAMPLE OF AN LGA FINDING
LGA ESTIMATES A SINGLE AGGREGATE TRAJECTORY • Assumes that the average population starting point (intercept for the growth curve) and average amount of change (slope) are a sufficient depiction of variation over time in depressive symptoms. • If discrete subtypes of depressive symptom trajectories exist, but are ignored (as in single latent growth curve and autoregressive models) the magnitude of associations could be grossly misestimated.
WHAT IS LATENT CLASS GROWTH ANALYSIS? • Latent Class Growth Analysis (LCGA), also referred to as growth mixture modeling, belongs to a family of statistical techniques referred to as general latent variable modeling or GLVM.
WHY WOULD WE EVER THINK WE SHOULD USE LCGA? • Studying the mean change or using a single trajectory for everyone assumes uniform heterogeneity in the population. • Researchers use familiar methods and typically assume that the underlying (latent or real) distribution of variables is continuous. • We have theoretical reasons to suspect that underlying distributions could be categorical. • Life course theorists (Dannefer) specifically caution that intracohort differentiation is unlikely to be homogeneous.
WHY WOULD WE USE LCGA? • We think individuals and cohorts diverge over time • Cumulative change differentiates individuals and cohorts.
PRIOR LCGA MODELS OF DEPRESSION OR DEPRESSIVE SYMPTOMS • LCGA models and closely related Longitudinal Latent Class Analysis (LLCA) have been used to estimate models of depressive symptoms in prior studies of – maternity (Campbell et al 2009; Mora et al 2009) – childhood and adolescence (Meadows et al 2006) – adolescence through young adulthood (Olino et al 2009) – response to antidepressants among adults (Muthen et al, 2007; Hunter et al 2009) – patients who have had a cardiovascular event (Kaptein et al 2006).
METHODS • 5,195 age-eligible respondents from the 1992 Health and Retirement Study cohort, who completed interviews in all seven waves through 2004. • Depressive symptoms in HRS are measured using a dichotomous, 8-item version of the CES-D. Analysis begins with Wave 2 data due to a change in response categories from Wave 1. • Using MPlus, we compared the fit of LCGA models of two to eight classes while also accounting for the HRS complex sampling design. • We then tested the effect of a small number of covariates. This is very similar to a multinomial logistic regression.
DEMOGRAPHIC CHARACTERISTICS • Gender – 60.3% female • Race/ethnicity – 76.4% non-Hispanic White – 14.4% Black – 7.4% Hispanic – 1.8% other racial/ethnic groups • Age – Median=55 • Education – Mean=12.4 years (SD=3.0).
RULE FOR DETERMINING THE NUMBER OF LATENT CLASSES • “How many trajectories are there?” • Measures of model fit including: – Lo-Mendell-Rubin Test (LMR test) – log-likelihood (LL) – Bayesian Information Criteria (BIC) (Vuong, 1989; Muthen, 2004; Muthen, & Muthen, 2005; Nylund et al, 2007). • Here we will use the LMR Test • Where k is the number of latent classes, this test gives a p- value for the k-1 versus the k-class model when running the k- class model (Vuong, 1989; Muthen, B. 2005). • The first time p > .05, k-1 is the preferred number of classes.
C = Categoric al Latent Classifica tion I = S = Slope Intercept W1 W2 W… W7
RESULTS • How many classes are there? • What do the classes look like? • How is this different from looking at means or single trajectory? • Are any demographic variables associated with being in a particular class?
HOW MANY CLASSES ARE THERE? Table 1. Depressive Symptoms LCGA Model Fit Comparison, N = 5,195 K LL BIC Adjusted BIC LMR Test LMR p Entropy 2 -56367.49 112983.09 112890.94 10525.69 0.000 0.955 3 -55146.65 110618.41 110497.66 2410.38 0.000 0.922 4 -54652.99 109708.09 109558.74 974.66 0.015 0.925 5 -54357.08 109193.27 109015.32 519.88 0.149 0.901 6 -54090.08 108736.27 108529.72 397.39 0.354 0.912 7 -54079.98 108793.06 108557.91 97.55 0.392 0.920 8 -53895.87 108501.85 108238.10 307.84 0.314 0.732
HOW MANY CLASSES ARE THERE? Table 1. Depressive Symptoms LCGA Model Fit Comparison, N = 5,195 K LL BIC Adjusted BIC LMR Test LMR p Entropy 2 -56367.49 112983.09 112890.94 10525.69 0.000 0.955 3 -55146.65 110618.41 110497.66 2410.38 0.000 0.922 4 -54652.99 109708.09 109558.74 974.66 0.015 0.925 5 -54357.08 109193.27 109015.32 519.88 0.149 0.901 6 -54090.08 108736.27 108529.72 397.39 0.354 0.912 7 -54079.98 108793.06 108557.91 97.55 0.392 0.920 8 -53895.87 108501.85 108238.10 307.84 0.314 0.732
WHAT DO THE CLASSES LOOK LIKE? Figure 1: Four Latent Classes of Depressive Symptoms over 12 Years of the HRS 6 Mean # of Depressive Symptoms 5 Many Persistent Symptoms = 5.4% Decreasing Symptoms = 9.6% Increasing Symptoms = 11.5% Almost No Symptoms = 73.5% 4 3 2 1 0 1994 1996 1998 2000 2002 2004 HRS Study Wave N = 5195
DOES ANYTHING INFLUENCE THE CHANCES OF BEING IN A PARTICULAR CLASS? Figure 2. Relationship between Years of Education and Depressive Symptoms Trajectory/Latent Class Membership 1.0 0.9 Many Symptoms Decreasing Symptoms 0.8 Latent Class Probability Increasing Symptoms Almost No Symptoms 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Years of Education N = 5195
WHAT PREDICTS TRAJECTORIES? Table. Effects of Demographics on the Likelikhood of a Depressive Symptoms Trajectory Many Symptoms Decreasing Increasing N = 5195 vs. Almost No Symptoms (reference category) OR b p OR b p OR b p Age 0.94 -0.057 0.010 0.96 -0.043 0.014 1.02 0.016 0.422 Female 2.19 0.785 0.000 1.53 0.428 0.001 1.41 0.346 0.002 Black 1.89 0.635 0.000 1.90 0.641 0.000 1.54 0.429 0.001 Hispanic 1.12 0.113 0.655 1.59 0.461 0.018 1.19 0.178 0.461 Low Education 1.32 0.274 0.000 0.84 -0.173 0.000 0.90 -0.105 0.000 • Females, African Americans and those with fewer years of education have a higher probability of being in the Many Symptoms trajectory.
PART 2 Cohort sequential methods for understanding development among maltreated children
BACKGROUND • Researchers seeking to understand child development over time face important challenges when using longitudinal data. • Some designs make it impractical to enroll only same aged individuals (e.g. developmental studies of children) • Children from different ages at the same measurement intervals • Study waves and child developmental stages become confounded with time
COHORT SEQUENTIAL METHOD • The cohort sequential design has been used previously in multiple studies of child well being (for example Cole et al, 2001 among others). • Prior cohort sequential models of child development are confined to single latent growth curve models
APPLYING THE COHORT SEQUENTIAL FRAMEWORK TO GROWTH MIXTURE MODELS
DEVELOPMENT EARLY EARLY INFANCY PRESCHOOL SCHOOL ADOLESCENCE BIRTH – 2 3 – 5 6 – 10 11 – 14
WEEK 1
WEEK 2
WAVE BY WAVE ANALYSIS LOOKS LIKE THIS
THE COHORT SEQUENTIAL MODEL REPRESENTS AGE AS TIME TO UNDERSTAND DEVELOPMENT
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