| Linear spline LME model | Natural cubic spline LME model | SITAR | Latent trajectory model |
---|---|---|---|---|
Description | linear mixed-effects model with a linear spline function of the independent time variable | linear mixed-effects model with a restricted cubic spline function of the independent time variable | nonlinear mixed-effects model based on the shape invariant growth model | heterogenous growth curves fit to unknown subgroups of individuals |
Advantages | easy to interpret the spline slope coefficients; can describe growth rate during different periods of the growth process | continuous 1st & 2nd derivatives give smoother trajectory and can identify points of peaks/troughs; linearity constraint gives a more reliable trajectory shape as less erratic at the tails of distribution | has useful features of the natural cubic spline, easy to estimate individual growth features – most notably individual ages at peak growth velocity | can identify unobserved sub-groups of individuals sharing distinct growth trajectories if any exist |
Limitations | biologically implausible sudden changes in velocity (i.e., at the knots); erratic at the tails; cannot identify points of velocity maxima/minima; position (and location) of knots important | coefficients difficult to interpret (so plotting is more useful); can be challenging to estimate the individual growth curves due to complex spline basis functions used by the statistical software | may not work well for complex growth patterns e.g., with multiple peaks and troughs or where the growth curve does not plateau in adulthood | difficult to identify the optimal number of sub-groups; may identify implausible subgroups; trajectories tend not to replicate in other cohorts |
R package(s) | lme4; lspline | lme4; splines | sitar | lcmm, splines |