We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented.
We address the problem of estimating how different parts of the brain develop and change throughout the lifespan, and how these trajectories are affected by genetic and environmental factors. Estimation of these lifespan trajectories is statistically challenging, since their shapes are typically highly nonlinear, and although true change can only be quantified by longitudinal examinations, as follow-up intervals in neuroimaging studies typically cover less than 10% of the lifespan, use of cross-sectional information is necessary.
Analyzing data from multiple neuroimaging studies has great potential in terms of increasing statistical power, enabling detection of effects of smaller magnitude than would be possible when analyzing each study separately and also allowing to systematically investigate between-study differences. Restrictions due to privacy or proprietary data as well as more practical concerns can make it hard to share neuroimaging datasets, such that analyzing all data in a common location might be impractical or impossible.