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New Directions in Latent Growth Modeling

New Directions in Latent Growth Modeling. Aline Sayer University of Massachusetts at Amherst sayer@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. Overview.

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New Directions in Latent Growth Modeling

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  1. New Directions in Latent Growth Modeling Aline Sayer University of Massachusetts at Amherst sayer@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

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

  3. 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

  4. Piecewise model for change in alcohol expectancies

  5. 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

  6. Transition point is unknown • Possible solution: treat as a latent class problem • Membership in the latent trajectory class defined by the transition point

  7. 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)

  8. LGM for linear change in alcohol expectancies from 5th to 7th grade

  9. Measurement model for alcohol expectancies

  10. Second-order latent growth model

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