HDF 380K.3 · Analyzing Development & Change

Random Effects of Time Explorer

See how individual differences in level and change — the random effects of time — shape the trajectories, variances, and correlations of within-person change over time. Set them and watch all three update together — the G-side companion to the covariance-structure (R-side) explorer.

Shape of the mean trajectory

Where is time = 0? (centering)

c center at occasion

Fixed effects — the average curve (γ)

γ₀₀ is the average level at occasion 0 (the first wave).

γ₀₀ intercept

γ₁₀ linear slope

γ₂₀ quadratic

Random effects — how people differ (SD)

τ_U0 and r₀₁ describe the intercept at occasion 0 (the first wave); the centering control above re-expresses them at any other wave.

τ_U0 intercept SD

τ_U1 linear-slope SD

τ_U2 quad-slope SD

r₀₁ intercept–slope corr

Residual & design

σ_e residual SD

ρ AR(1) residual corr

n occasions

knot breakpoint

Teaching presets

Model

Individual trajectories

average (fixed) curve lower intercept higher intercept observed point (+ residual)

Total variance over time

Var(y_t) at each occasion —

Implied correlation matrix

Corr(y_s, y_t) across occasions ·

What you're seeing