Covariate misclassification is well known to yield biased estimates in single level regression models. The impact on hierarchical count models has been less studied. A fully Bayesian approach to modeling both the misclassified covariate and the hierarchical response is proposed. Models with a single diagnostic test and with multiple diagnostic tests are considered. Simulation studies show the ability of the proposed model to appropriately account for the misclassification by reducing bias and improving performance of interval estimators. A real data example further demonstrated the consequences of ignoring the misclassification. Ignoring misclassification yielded a model that indicated there was a significant, positive impact on the number of children of females who observed spousal abuse between their parents. When the misclassification was accounted for, the relationship switched to negative, but not significant. Ignoring misclassification in standard linear and generalized linear models is well known to lead to biased results. We provide an approach to extend misclassification modeling to the important area of hierarchical generalized linear models.
A high-resolution column of 57 loess samples was collected from the Dry Creek archaeological site in the Nenana River Valley in central Alaska. Numerical grain-size partitioning using a mixed Weibull function was performed on grain-size distributions to obtain a reconstructed record of wind intensity over the last ~15,000 yr. Two grain-size components were identified, one with a mode in the coarse silt range (C1) and the other ranging from medium to very coarse sand (C2). C1 dominates most samples and records regional northerly winds carrying sediment from the Nenana River. These winds were strong during cold intervals, namely, the Carlo Creek glacial readvance (14.2–14 ka), a late Holocene Neoglacial period (4.2–2.7 ka), and recent glacier expansion; weak during the Allerød (14–13.3 ka) and Younger Dryas (12.9–11.7 ka); and variable during the Holocene thermal maximum (11.4–9.4 ka). Deposition of C2 was episodic and represents locally derived sand deposited by southerly katabatic winds from the Alaska Range. These katabatic winds occurred mainly prior to 12 ka and after 4 ka. This study shows that numerical grain-size partitioning is a powerful tool for reconstructing paleoclimate and that it can be successfully applied to Alaskan loess.
For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-space separation of the individual populations and the Bayes probability of misclassification. We also give necessary and sufficient conditions which provide the smallest reduced dimension that essentially retains the Bayes probability of misclassification from the original full-dimensional space in the reduced space. Moreover, our new LDR procedure requires no computationally expensive optimization procedure. Finally, for the case where parameters are unknown, we devise a LDR method based on our new theorem and compare our LDR method with three competing LDR methods using Monte Carlo simulations and a parametric bootstrap based on real data.
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