Multilevel growth curve models that incorporate a random coefficient model for the level 1 variance function

Abstract

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.

Keywords

Heteroscedasticity multilevel model repeated measures variance model Avon Longitudinal Study of Parents and Children

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