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One common approach to handle covariate measurement error in Generalized Linear Models (GLM) is classical error modeling. In the past 20 years, classical error modeling has been brought to (Non-Parametric) Maximum Likelihood (NPML) es- timation, by means of finite mixture modeling: the supposedly continuous true score is modeled as a discrete (multinomial) static latent variable, and is handled as a part of the model. Nonetheless, the true score is not allowed to vary over time: if the true score has own underlying dynamics, these are either unaccounted for or mistaken for measurement error, or possibly both. The aim of the present paper is to formulate a joint model for the outcome variable, the covariate observed with error (measure- ment model), and the true score model that accounts for the underlying dynamics in the true score. The true score and its dynamics are modeled non-parametrically as a first-order latent (hidden) Markov chain. Estimation is done extending the NPML approach, in a full maximum likelihood environment with a well-know modification of the EM algorithm (forward-backward algorithm). From an applied researcher per- spective, our methodology can safely handle both the case where the latent underly- ing characteristic is stable over time, as well as providing a suitable framework even when changes across measurement occasions are substantial. Within a GLM frame- work, it is demonstrated, by means of extensive simulation studies, that this is cru- cial to get correct estimates of the regression coefficients, as well as good coverages. In the real-data application, the effect of heart rate on the occurrence of cardiovas- cular diseases in a sample of Chinese elderly patients is measured. Modeling the true (unobserved) heart rate and its dynamics - which, in elderly patients, are likely to be non negligible - will be showed to allow a correct assessment of risk factors of cardio- vascular diseases occurrence.

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