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One common approach to handle covariate measurement error in Generalized Linear Models is
classical error modeling. In the past 20 years, classical error modeling has been brought
to (Non-Parametric) Maximum Likelihood (ML) estimation, by means of finite mixture modeling:
the supposedly continuous true score is modeled as a 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 present paper formulates a joint model
for the outcome variable, the covariate observed with error, and the
true score, accounting for its underlying dynamics by assuming a first-order latent Markov chain.
From an applied researcher perspective, this methodology can safely handle both the case where the
underlying characteristic is stable over time, as well as providing a suitable framework even when
changes across measurement occasions are substantial, with estimation done within a familiar ML
environment. It is demonstrated, by means of extensive simulation studies and a real-data
application, that the methodology delivers correct estimates of the model parameters of interest,
as well as good coverages.