week 10 - LMM moderation and model comparison

moderation

tests whether the effect of one predictor on the outcome changes depending on the level of another variable

measured using an interaction term

cross level moderation

When a between-person variable moderates the effect of a within-person predictor.

E.g., Does average energy level (between) moderate the within-person link between daily exercise and stress?

within level moderation

When the moderator and predictor are both within-person.

E.g., On days when someone sleeps better than usual, does the link between caffeine and stress change?

Likelihood Ratio Test

To compare nested models and test whether the added complexity improves model fit. A low p-value suggests a better fit.

Akaike Information Criterion

compares model fit while penalising complexity.

Lower AIC = better model.

Bayesian Information Criterion

applies a stronger penalty for model complexity.

Lower BIC = better, especially with larger samples.

comparison criteria

AIC/BIC for non-nested models

Likelihood Ratio Test - nested models

polynomial terms

to model non-linear relationships, like curves or U-shaped trends, that a simple linear model cannot capture

time² term

it allows the effect of time to follow a curved trajectory (non-linear), revealing acceleration, deceleration or plateaus