  The analysis of data arising from environmental health studies which collect
a large number of measures of exposure can benefit from using latent variable
models to summarize exposure information. However, difficulties with estimation
of model parameters may arise since existing fitting procedures for linear
latent variable models require correctly specified residual variance structures
for unbiased estimation of regression parameters quantifying the association
between (latent) exposure and health outcomes. We propose an estimating
equations approach for latent exposure models with longitudinal health outcomes
which is robust to misspecification of the outcome variance. We show that
compared to maximum likelihood, the loss of efficiency of the proposed method
is relatively small when the model is correctly specified. The proposed
equations formalize the ad-hoc regression on factor scores procedure, and
generalize regression calibration. We propose two weighting schemes for the
equations, and compare their efficiency. We apply this method to a study of the
effects of in-utero lead exposure on child development.
