Longitudinal mixed-effects models for latent cognitive function

A mixed-effects regression model with a bent-cable change-point predictor is formulated to describe potential decline of cognitive function over time in the older population. For the individual trajectories, cognitive function is considered to be a latent variable measured through an item response theory model given longitudinal test data. Individual-specific parameters are defined for both cognitive function and the rate of change over time, using the change-point predictor for non-linear trends. Bayesian inference is used, where the Deviance Information Criterion and the L-criterion are investigated for model comparison. Special attention is given to the identifiability of the item response parameters. Item response theory makes it possible to use dichotomous and polytomous test items, and to take into account missing data and survey-design change during follow-up. This will be illustrated in an application where data stem from the Cambridge City over-75s Cohort Study.