Patterns › Dimension reduction

Latent growth curve (LGC)

A latent growth curve model decomposes repeated measures over time into a latent intercept (the starting level) and a latent slope (the rate of change).

What is Latent growth curve (LGC)?

The intercept factor loads 1 on every time point; the slope factor loads 0, 1, 2, … encoding time. The model fixes observed-variable intercepts to 0 and estimates latent means — so the intercept/slope means in the output are the average starting level and average change per unit time, and their variances quantify individual differences in both.

Curvature is testable by adding a quadratic factor (q =~ 0*t1 + 1*t2 + 4*t3 + 9*t4); time-invariant covariates can be regressed on i and s (i ~ x, s ~ x).

When should I use Latent growth curve (LGC)?

Longitudinal designs with ≥ 3 waves asking 'what is the average trajectory, and who deviates from it?'
Preferable to RM-ANOVA when individual slopes — not just mean differences — are of interest.

What data does it need?

One numeric column per time point (time-ordered) + growth model syntax + estimator + missing-data handling (FIML recommended for dropout).

What does it report?

Fit indices (χ², CFI, RMSEA, SRMR), latent means for i and s ('Intercepts' table), variances (individual differences), i–s covariance.

What does it assume?

Same measure at every wave (measurement invariance).
Multivariate normality; linear time coding unless modeled otherwise.
≥ 3 time points for an identified linear model.

How do I interpret the result?

Slope mean = average change per wave; a significant slope variance means people genuinely differ in their trajectories. A negative i–s covariance means high starters change more slowly.

References

Meredith & Tisak (1990). Latent curve analysis. Psychometrika 55.