New Directions in Latent Growth Modeling

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New Directions in Latent Growth Modeling
Aline Sayer University of Massachusetts at
Amherst sayer_at_psych.umass.edu SAMSI 2004-2005
Program on Latent Variables in the Social
Sciences Session on Multilevel Models New
Developments and Challenges September 14, 2004
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Overview

• Piecewise growth models (aka spline or regression
  discontinuity models)
• Second-order latent growth models

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Modeling development that is discontinuous with
time

• Can easily fit model if transition point is
  specified a priori and is the same for all
  individuals
• Include a time-varying covariate in the level-1
  model that is coded to reflect the expected shift
  in the trajectory
• Sayer Willett, Multivariate Behavioral
  Research, 1998

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Piecewise model for change in alcohol expectancies
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Transition point is known but varies across
individuals

• Assumption is that all individuals are drawn from
  the same population
• Implication is that the the same functional form
  of growth must be fit to everyone.
• The sign and magnitude of the random coefficients
  can vary across individuals

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Transition point is unknown

• Possible solution treat as a latent class
  problem
• Membership in the latent trajectory class defined
  by the transition point

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Incorporating multiple indicators into LGMs

• Provide a measurement model for the construct
  that is changing with time
• Permits tests of measurement invariance
• Decomposes error into time-specific and
  measurement error variance
• Sayer Cumsille in New methods for the analysis
  of change (Collins Sayer, 2001)

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LGM for linear change in alcohol expectancies
from 5th to 7th grade
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Measurement model for alcohol expectancies
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Second-order latent growth model