Advocating better habitat use and selection models in bird ecology

Studies on habitat use and habitat selection represent a basic aspect of bird ecology, due to its importance in natural history, distribution, response to environmental changes, management and conservation. Basically, a statistical model that identifies environmental variables linked to a species presence is searched for. In this sense, there is a wide array of analytical methods that identify important explanatory variables within a model, with higher explanatory and predictive power than classical regression approaches. However, some of these powerful models are not widespread in ornithological studies, partly because of their complex theory, and in some cases, difficulties on their implementation and interpretation. Here, I describe generalized linear models and other five statistical models for the analysis of bird habitat use and selection outperforming classical approaches: generalized additive models, mixed effects models, occupancy models, binomial N-mixture models and decision trees (classification and regression trees, bagging, random forests and boosting). Each of these models has its benefits and drawbacks, but major advantages include dealing with non-normal distributions (presence-absence and abundance data typically found in habitat use and selection studies), heterogeneous variances, non-linear and complex relationships among variables, lack of statistical independence and imperfect detection. To aid ornithologists in making use of the methods described, a readable description of each method is provided, as well as a flowchart along with some recommendations to help them decide the most appropriate analysis. The use of these models in ornithological studies is encouraged, given their huge potential as statistical tools in bird ecology.Fil: Palacio, Facundo Xavier. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Zoología de Vertebrados. Sección Ornitología; Argentin

A simple forward selection procedure based on false discovery rate control

We propose the use of a new false discovery rate (FDR) controlling procedure as a model selection penalized method, and compare its performance to that of other penalized methods over a wide range of realistic settings: nonorthogonal design matrices, moderate and large pool of explanatory variables, and both sparse and nonsparse models, in the sense that they may include a small and large fraction of the potential variables (and even all). The comparison is done by a comprehensive simulation study, using a quantitative framework for performance comparisons in the form of empirical minimaxity relative to a "random oracle": the oracle model selection performance on data dependent forward selected family of potential models. We show that FDR based procedures have good performance, and in particular the newly proposed method, emerges as having empirical minimax performance. Interestingly, using FDR level of 0.05 is a global best.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS194 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Longitudinal analysis on AQI in 3 main economic zones of China

textIn modern China, air pollution has become an essential environmental problem. Over the last 2 years, the air pollution problem, as measured by PM 2.5 (particulate matter) is getting worse. My report aims to carry out a longitudinal data analysis of the air quality index (AQI) in 3 main economic zones in China. Longitudinal data, or repeated measures data, can be viewed as multilevel data with repeated measurements nested within individuals. I arrive at some conclusions about why the 3 areas have different AQI, mainly attributed to factors like population, GDP, temperature, humidity, and other factors like whether the area is inland or by the sea. The residual variance is partitioned into a between-zone component (the variance of the zone-level residuals) and a within-zone component (the variance of the city-level residuals). The zone residuals represent unobserved zone characteristics that affect AQI. In this report, the model building is mainly according to the sequence described by West et al (2007) with respect to the bottom-up procedures and the reference by Singer, J. D., & Willett, J. B (2003) which includes the non-linear situations. This report also compares the quartic curve model with piecewise growth model with respect to this data. The final model I reached is a piece wise model with time-level and zone-level predictors and also with temperature by time interactions.Statistic