Multiscale measurement error models for aggregated small area health data.

Spatial data are often aggregated from a finer (smaller) to a coarser (larger) geographical level. The process of data aggregation induces a scaling effect which smoothes the variation in the data. To address the scaling problem, multiscale models that link the convolution models at different scale levels via the shared random effect have been proposed. One of the main goals in aggregated health data is to investigate the relationship between predictors and an outcome at different geographical levels. In this paper, we extend multiscale models to examine whether a predictor effect at a finer level hold true at a coarser level. To adjust for predictor uncertainty due to aggregation, we applied measurement error models in the framework of multiscale approach. To assess the benefit of using multiscale measurement error models, we compare the performance of multiscale models with and without measurement error in both real and simulated data. We found that ignoring the measurement error in multiscale models underestimates the regression coefficient, while it overestimates the variance of the spatially structured random effect. On the other hand, accounting for the measurement error in multiscale models provides a better model fit and unbiased parameter estimates.