Generalized linear latent variable models for the analysis of cognitive functioning over time

Dimensions of cognitive functioning are potentially important, but often neglected determinants of the central economic outcomes that shape overallwell-being over the life course. The Health and Retirement Study and the Asset and Health Dynamic study (HRS/AHEAD) aim to examine the impact of cognitive performance and decline on key domains of interest(e.g., health and daily functioning, retirement, economic and health decisionmaking). The analysis of the HRS/AHEAD cognitive data is performed using latent variable models that easily allow to determine common factorsof the cognitive items and examine their dynamic over time. The estimation of these models is cumbersome when the observed cognitive itemsare of different nature as in the HRS/AHEAD study. Indeed, problems related to the integration of the likelihood function arise since analyticalsolutions do not exist. This problem is more evident in presence of longitudinal data when the number of latent variables increases proportionally tothe number of items. We analyze the performance of a new integration method, known as Dimension Reduction Method (DRM), in the estimation of the latent individual cognitive status over time of the HRS/AHEAD data. It provides parameter estimates as accurate as techniques commonlyapplied in the literature, but without sharing the same computational complexity of the latter. We show that it can be applied in situations in whichstandard techniques are unfeasible