Title: Time-varying measurement error in generalized linear models for longitudinal data: A two-step latent Markov approach
Authors: Roberto Di Mari - Department of Economics and Business, University of Catania (Italy) [presenting]
Antonello Maruotti - Libera Università Maria Ss Assunta (Italy)
Antonio Punzo - University of Catania (Italy)
Abstract: A novel approach is proposed for longitudinal data modeling within the Generalized Linear Models (GLM) family, whenever a covariate of interest is affected by measurement error. We jointly model the response (outcome model), the covariate observed with error (measurement model) and the underlying unobserved error-free covariate (true score) along with its dynamics, assumed to follow a first-order latent (hidden) Markov chain. In a full (semi-parametric) maximum likelihood environment, computation is done by means of the EM algorithm. The estimation of the full joint model is hardly feasible as the number of covariates is large, as is typically the case in real-data applications. Thus, we propose a two-step approach to efficiently estimate model parameters. By means of extensive simulation studies, we show that both the one-step and the two-step approaches allow 1) to get correct estimates of the regression coefficients, as well as 2) reliable standard errors. In the real-data application, by modeling the true (unobserved) heart rate and its dynamics, we are able to find a significant effect of heart rate dynamics on the occurrence of a cardiovascular disease in a sample of +80 Chinese elderly.