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Title: Longitudinal modeling of age-dependent latent traits Authors:  Oystein Sorensen - University of Oslo (Norway) [presenting]
Anders Fjell - University of Oslo (Norway)
Kristine Walhovd - University of Oslo (Norway)
Abstract: Latent variables are indispensable when measured responses reflect some underlying latent traits of interest. Often, latent traits depend smoothly on, e.g., age and location, with functional shapes hard to specify a priori. However, most latent variable models require parametric forms for both latent and observed variables, and flexible semiparametric models have limitations on the number of grouping levels or rely on restrictive assumptions like discrete-time. We present generalized additive latent and mixed models (GALAMM), extending generalized linear latent and mixed models (GLLAMM) by allowing both observed and latent variables to depend smoothly on observed variables. GALAMMs retain the flexibility offered by GLLAMMs, including an arbitrary number of grouping levels and the ability to fit a large number of response types. We show that any model in the GALAMM framework can be represented as a nonlinear mixed model and estimated by maximum likelihood. We compare algorithms for model fitting, and derive expressions for asymptotic covariance matrices. The motivating applications came from cognitive neuroscience, in which both latent cognitive abilities and structural characteristics of the brain follow smooth nonlinear trajectories across the lifespan, and we present examples where GALAMMs enabled answering research questions more easily than currently used tools.