Level 1 variation in repeated measures models

Aim: To present a flexible model for repeated measures longitudinal growth data within individuals that allows trends
over time to incorporate individual-specific random effects. These may reflect the timing of growth events and
characterise within-individual variability which can be modelled as a function of age.
Subjects and methods: A Bayesian model is developed that includes random effects for the mean growth function, an
individual age-alignment random effect and random effects for the within-individual variance function. This model is
applied to data on boys’ heights from the Edinburgh longitudinal growth study and to repeated weight measurements of a
sample of pregnant women in the Avon Longitudinal Study of Parents and Children cohort.
Results: The mean age at which the growth curves for individual boys are aligned is 11.4 years, corresponding
to the mean ‘take off’ age for pubertal growth. The within-individual variance (standard deviation) is found to
decrease from 0.24 cm2 (0.50 cm) at 9 years for the ‘average’ boy to 0.07 cm2 (0.25 cm) at 16 years. Change
in weight during pregnancy can be characterised by regression splines with random effects that include a large
woman-specific random effect for the within-individual variation, which is also correlated with overall weight and
weight gain.
Conclusions: The proposed model provides a useful extension to existing approaches, allowing considerable flexibility
in describing within- and between-individual differences in growth patterns.