Estimators for longitudinal latent exposure models: examining measurement model assumptions

Area of Science:

• Environmental Epidemiology
• Biostatistics
• Longitudinal Data Analysis

Background:

• Latent variable (LV) models are used in environmental epidemiology to summarize complex exposure data, but pose challenges in model specification, especially with longitudinal data.
• Assumptions within LV measurement models can significantly impact inferences about health effects, as seen in studies of prenatal lead exposure.

Purpose of the Study:

• To examine biases in maximum likelihood estimators when measurement model assumptions for longitudinal latent exposure are violated.
• To propose and evaluate instrumental variable (IV) estimators as an alternative for analyzing time-changing latent exposure variables in health studies.

Main Methods:

• Investigated biases of maximum likelihood estimators under violated measurement model assumptions.
• Adapted existing instrumental variable estimators for longitudinal exposure data.
• Compared performance of IV estimators against maximum likelihood estimators.

Main Results:

• Maximum likelihood estimators can be biased when measurement model assumptions for longitudinal latent exposures are violated.
• Instrumental variable estimators demonstrated unbiasedness across various data-generating models.
• Instrumental variable estimators showed advantages in terms of mean squared error compared to maximum likelihood methods.

Conclusions:

• Instrumental variable estimators provide a robust and unbiased approach for estimating health effects from longitudinal latent exposure data.
• Relaxing measurement model assumptions in LV analysis can lead to biased results; IV methods offer a reliable alternative.