Growth curve approaches to longitudinal data in gerontology research

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Growth curve approaches to longitudinal data in
gerontology research Time-varying and
Time-invariant Covariates in a Latent Growth
Model of Negative Interactions and Depression in
Widowhood Jason T. Newsom D. Morgan Portland
State University, Portland, OR Individual
Differences in Memory Function Among Older Adults
Richard N. Jones, K. Kleinman, J. Allaire, P.
Malloy, A. Rosenberg, J.N. Morris, M. Marsiske.
Hebrew Rehabilitation Center for Aged, Boston MA
Change Point Models Allow for Estimation of the
Time at Which Cognitive Decline Accelerates in
Preclinical Dementia Charles B. Hall, R.B.
Lipton, M. Sliwinski, J.Ying, M.Katz, L. Kuo,
H.Buschke Albert Einstein College of Medicine,
New York, NY Dual Sensory Impairment and Change
in Personal ADL Function Among Elderly Over Time
A SEM Latent Growth Approach Ya-ping Su, M.
Brennan and A. Horowitz Lighthouse
International, New York, NY Discussant Karen
Bandeen-Roche School of Public Health John
Hopkins University, Baltimore, MD
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• Growth Curve Analysis
• Purpose is to model change over time
• Linear or nonlinear models possible
• Variability in change over time by modeling
  individual growth curves
• Variability in initial or average levels
• Predictors can be used to account for
  variability
• Two general approaches
• Hierarchical linear models (HLM)
• Structural equation models (SEM)

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Example Growth Curves
High Variability in Intercepts and Slopes
Y
t
Low Variability in Intercepts and Slopes
Y
t
Low Variability in Intercepts and High
Variability in Slopes
Y
t
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• HLM Approach to Growth Curves
• Conceptualization
• Two levels within individual and between
  individual
• Regression equation for each level

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• HLM Approach to Growth Curves Level 1 Within
  Individual
• Examines change in the dependent variable as a
  function of time for each individual
• Intercepts and slopes obtained for each
  individual
• Intercept is initial or average value of the
  dependent variable for a given individual
  (depending on coding of time variable)
• Slope describes linear increase or decrease in
  the dependent variable over time of a given
  individual
• With predictors, intercepts and slopes
  represent adjusted means and slopes

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HLM Approach to Growth Curves Level 2 Between
Individuals

• Intercepts and slopes obtained from Level 1
  serve as dependent variables
• With no predictors, Level 2 intercept
  represents average of intercepts or slopes from
  Level 1
• With no predictors, Level 2 residual provides
  information about variance of intercepts or
  slopes across individuals
• Can incorporate predictors measured at the
  individual level (gender, income, etc.)
• Predictors explain variation in intercepts or
  slopes across individuals

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• SEM Approach to Growth Curves
• General conceptualization and interpretation
  the same as HLM approach
• Use latent variables and their loadings to
  represent Level 1 parameters
• Possible with any SEM software program
• Requires time structured data but can model
  complex error structures or latent variables over
  time

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SEM Approach to Growth CurvesExample of a latent
growth curve model with four time points
yt1
yt2
yt3
yt4
2
3
1
1
1
1
1
h0 (Intercept)
h1 (Slope)
0
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SEM Approach to Growth Curves Output

• Structural means must be estimated
• Mean of intercept latent variable represents
  average initial value or average mean value
  across individuals
• Mean of slope latent variable represents
  average slope
• Variance of intercept latent variable
  represents variability of initial or average
  value across individuals
• Variance of slope latent variable represents
  variability in growth across individuals
• Correlation between intercept and slope
  variables represents association between initial
  value and growth