Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Mixed rain forest in southeastern Brazil: tree species regeneration and floristic relationships in a remaining stretch of forest near the city of Itaberá, Brazil

The aim of this work was to evaluate the floristic composition, richness, and diversity of the upper and lower strata of a stretch of mixed rain forest near the city of Itaberá, in southeastern Brazil. We also investigated the differences between this conservation area and other stretches of mixed rain forest in southern and southeastern Brazil, as well as other nearby forest formations, in terms of their floristic relationships. For our survey of the upper stratum (diameter at breast height [DBH] > 15 cm), we established 50 permanent plots of 10 × 20 m. Within each of those plots, we designated five, randomly located, 1 × 1 m subplots, in order to survey the lower stratum (total height > 30 cm and DBH < 15 cm). In the upper stratum, we sampled 1429 trees and shrubs, belonging to 134 species, 93 genera, and 47 families. In the lower stratum, we sampled 758 trees and shrubs, belonging to 93 species, 66 genera, and 39 families. In our floristic and phytosociological surveys, we recorded 177 species, belonging to 106 genera and 52 families. The Shannon Diversity Index was 4.12 and 3.5 for the upper and lower strata, respectively. Cluster analysis indicated that nearby forest formations had the strongest floristic influence on the study area, which was therefore distinct from other mixed rain forests in southern Brazil and in the Serra da Mantiqueira mountain range.