A latent process model for monitoring progress towards hard-to-measure targets, with applications to mental health and online educational assessments

The recent shift to remote learning and work has aggravated long-standing problems, such as the problem of monitoring the mental health of individuals and the progress of students towards learning targets. We introduce a novel latent process model with a view to monitoring the progress of individuals towards a hard-to-measure target of interest, measured by a set of variables. The latent process model is based on the idea of embedding both individuals and variables measuring progress towards the target of interest in a shared metric space, interpreted as an interaction map that captures interactions between individuals and variables. The fact that individuals are embedded in the same metric space as the target helps assess the progress of individuals towards the target. We demonstrate, with the help of simulations and applications, that the latent process model enables a novel look at mental health and online educational assessments in disadvantaged subpopulations.