A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error

Roberto Mari () and Antonello Maruotti ()
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Roberto Mari: University of Catania
Antonello Maruotti: LUMSA University

Advances in Data Analysis and Classification, 2022, vol. 16, issue 2, No 3, 273-300

Abstract: Abstract We propose a novel approach for longitudinal data modeling within the Generalized Linear Models 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 time-varying error-free covariate (true score). This is done by assuming a first-order latent Markov chain for the true score. The estimation of the full joint model is hardly feasible when the number of covariates is large, as typical in real-data applications. Available algorithms are severely affected by numerical underflow and multiple local maxima. To overcome these problems, we propose an efficient two-step approach. With an extensive simulation study, we show that the two-step approach produces point estimates and standard errors which are almost identical to those obtained by the more time consuming, simultaneous (one-step) approach. The proposal is also illustrated by analyzing data from the Chinese Longitudinal Healthy Longevity Survey.

Keywords: Covariate measurement error; Generalized linear models for longitudinal data; Latent Markov models; Two-step estimator; 62H30; 62-07 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11634-021-00473-4

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