1. Day 2 Applications of Growth Curve Models June 28 & 29, 2018
Growth Curve Modeling
Day 2 Applications of Growth Curve Models June 28 & 29, 2018
Michael Bader

2. Centering Time What intercept will help us interpret your results?
When should we make comparisons between people?
In some cases, re-centering time might help with estimation

3. Measuring Time
Find an appropriate unit to be the denominator of the rate
Age: is time relative to a person most important?
Period: is historical time most important?
Event: is the time since some event the most important?

4. Non-Linear Trends

5. Parametric Nonlinear Trends

6. Independent variables

7. Think about what unit at which you hypothesize the predictor acts
Does this predictor characterize the person? If yes, it is a time-invariant predictor
Does this predictor characterize a point of time in the person’s life? If yes, it is a time-varying predictor

8. Time-Invariant Predictors
Do we think that the trait
leads some group to have higher values at the outset than another group, but both groups generally change at a similar rate?
leads groups to change at different rates after having no meaningful difference in where they started?
is associated with both different starting values and different rates of change?

9. Time Invariant Predictors

10. Time Invariant Predictors

11. Time Invariant Predictors
We are just making a regression out of the intercepts!!!

12. If we think that the trait leads some group to have higher values at the outset than another group, but both groups generally change at a similar rate:

13. If we think that the trait leads groups to change at different rates after having no meaningful difference in where they started

14. If we think that the trait is associated with both different starting values and different rates of change?

15. All growth curve models are regressions!!!

16. Analysis of Metro Home Value by Region

17. Time Varying Predictors

18. Combining Time & Time-Varying Predictors
Special cases:
Interventions
Non-parametric (piecewise) change

19. Deflection of Slope
Individual’s rate of change will increase or decrease after some change

21. Adjustment & Deflection of Slope

22. Trajectory analysis

23. Latent Classes Identify groups (classes) based on common variation
Stochastic variation can be explained by membership in class

24. Latent Growth Trajectories
Variation across individuals is captured by latent class membership

25. Growth Mixture Models
Variation across individuals is captured by latent class membership and random variation off of class intercept and trend

26. Review

27. Base Models
All models have three components, ensure you have thought about how all three work:
Outcome (datum-level variation)
Deterministic (data-level variation)
Stochastic (datum-level variation)
Our goal is to minimize errors at different levels (“fancy means”)
Think about how your data vary over units and over time
Estimating models of your data
Simulate your model and make guesses about coefficients
Analyze collected data to using simulated model & code

28. Differences in Variation
Consider interpretation of analysis when choosing intercept
Think carefully about how time should be measured
Describe data by examining trends and deciding on shape of change
Decide on covariates to include in the models with careful attention to how you think that they affect the outcome
Determine whether data follow a single trajectory with random variation or follow categorically distinct trajectories

29. Thank You!
Questions: