Individual Trajectories Flashcards
Research design of growth curve models
What are growth curve models?
Estimation of individual differences in within-person change over time
Growth curve models estimate smoothed trajectories that are unique to each individual based on the set of observed repeated measures. This results in a collection of individual-specific trajectories that then become the unit of analysis, allowing us to ask such questions as: What is the average trajectory? How much do individual trajectories differ from one another? Can we predict these differences as a function of other individual characteristics?
Approach to studying change:
What can we ask?
- How does an outcome change in people over time?
1) Can be linear individual change (i.e. age, running a marathon, life expectancy) but does not have to be, can also be:
2) Non-linear//Curvylinear (i.e. income)
3) Fluctuating (i.e. mental health)
2) How do people differ in level and changes?
natural question: Why/for whom are declines/rises steeper?
+
also: How does intial change relate to subsequent change?
How to model the shape of the mean trajectory?
Polynomials / model fit / splines
How to analyze variance around the mean trajectory?
Random slope model
How to study if initial level is related to subsequent change?
Intercept slope covariance (fanning out/in)
How to measure time
a) BMI
b) Grief
c) Income
d) Feel German 1st generation immigrant
e) Reading ability
a) Quite stable over short periods -> every year/every other year
b) Most of grieving over after 6 months -> monlthy/weekly?
c) Common every year but u could also think of labor market entry as when clock starts ticking
d) Time since arrival, then every few years?
e) Time in school, maybe at higher frequency then yearly
Problem with cross-sectional data: church attendance with age
no within person change over time, just that older cohorts go more often to church but cross-section would suggest that with age individuals attend church more often
–> cohort effects from overlapping data
Linear model for studying BMI change over time
+ growth parameters
+ growth difference parameters
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Interpret coefficients
Interpret the variance components
How should we model this?
Random Slope
Interpret:
How does the age effect change from cohort 1950 to 1990?
How much does the cross-level interaction explain age slope variance?
Regression model: What would be a good age specification? (shape of the mean trajectory)
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Why do we need a statistical model for this? What are
the advantages of a statistical model compared to the
descriptive analysis on the left-hand side?
Which functional form (age trajectory) is right?
What is the equivalent of adj. R-square to evaluate model fit?
Explain components
Why use a growth curve for group differences?
much more interesting, you can see when the pattern emerges, where does grow/stagnate/etc.
Overcontrolled?
Do not control for mediators in the first step!
Effect of education is negative –> cohort effect
would be even stronger if there had not been an educational expansion
- How does an outcome change in people over time?
Variation
wild heterogeneity around the mean trajectory possible
