Handbook of Regression Analysis Chatterjee, Samprit; Simonoff, Jeffrey S
2013, 2013., 2012, 2013-01-03, 2013-05-30, Volume:
5
eBook
A Comprehensive Account for Data Analysts of the Methods and Applications of Regression Analysis.Written by two established experts in the field, the purpose of the Handbook of Regression Analysis is ...to provide a practical, one-stop reference on regression analysis. The focus is on the tools that both practitioners and researchers use in real life. It is intended to be a comprehensive collection of the theory, methods, and applications of regression methods, but it has been deliberately written at an accessible level.The handbook provides a quick and convenient reference or “refresher” on ideas and methods that are useful for the effective analysis of data and its resulting interpretations. Students can use the book as an introduction to and/or summary of key concepts in regression and related course work (including linear, binary logistic, multinomial logistic, count, and nonlinear regression models). Theory underlying the methodology is presented when it advances conceptual understanding and is always supplemented by hands-on examples.References are supplied for readers wanting more detailed material on the topics discussed in the book. R code and data for all of the analyses described in the book are available via an author-maintained website.
This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually ...model the data using the methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields.
An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the ...relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concepts and applications, offers a complete, easily accessible introduction to the fundamentals of regression analysis. Assuming only a basic knowledge of elementary statistics, Applied Regression Analysis, Third Edition focuses on the fitting and checking of both linear and nonlinear regression models, using small and large data sets, with pocket calculators or computers. This Third Edition features separate chapters on multicollinearity, generalized linear models, mixture ingredients, geometry of regression, robust regression, and resampling procedures. Extensive support materials include sets of carefully designed exercises with full or partial solutions and a series of true/false questions with answers. All data sets used in both the text and the exercises can be found on the companion disk at the back of the book. For analysts, researchers, and students in university, industrial, and government courses on regression, this text is an excellent introduction to the subject and an efficient means of learning how to use a valuable analytical tool. It will also prove an invaluable reference resource for applied scientists and statisticians.
Unconditional Quantile Regressions Firpo, Sergio; Fortin, Nicole M.; Lemieux, Thomas
Econometrica,
20/May , Volume:
77, Issue:
3
Journal Article
Peer reviewed
Open access
We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. ...The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.
Statistical regression analysis is a powerful and reliable method to determine the impact of one or several independent variable(s) on a dependent variable. It is the most widely used of all ...statistical methods and has broad applicability to numerous practical problems. However, various problems can arise, when for instance the sample size is too small, distributional assumptions are not fulfilled, the relationship between independent and dependent variables is vague or when there is an ambiguity of events. Moreover, the complexity of real-life problems often makes the underlying models inadequate, since information is frequently imprecise in many ways. To relax these rigidities, numerous researchers have modified and extended concepts of statistical regression analysis by means of concepts of fuzzy set theory. By now, there is a large number of papers on the topic of fuzzy regression analysis, especially concerning possibilistic, fuzzy least squares or machine learning approaches. Additionally, the variety of approaches includes probabilistic, logistic, type-2 and clusterwise fuzzy regression methods, among many others. Besides papers mainly devoted to advances in methodology, there are also several papers presenting case studies in various research fields. To structure this diversity of papers, proposals and applications we give in this paper a comprehensive systematic review and provide a bibliography on the topic of fuzzy regression analysis. Thus, the paper intends to consolidate the topic in order to aid new researchers in this area, focuses the field’s attention on key open questions, and highlights possible directions for future research.
•Comprehensive systematic review on the topic of fuzzy regression analysis.•Structuring and categorizing the diversity of papers, proposals and practical applications.•Extensive bibliography of 455 relevant articles.•Critical discussion of the presented methods and approaches.•Several directions for fruitful future research.
Fast Calibrated Additive Quantile Regression Fasiolo, Matteo; Wood, Simon N.; Zaffran, Margaux ...
Journal of the American Statistical Association,
07/2021, Volume:
116, Issue:
535
Journal Article
Peer reviewed
Open access
We propose a novel framework for fitting additive quantile regression models, which provides well-calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing ...parameters, for model structures as diverse as those usable with distributional generalized additive models, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorous and computationally efficient, because they are based on the general belief updating framework of Bissiri, Holmes, and Walker to loss based inference, but compute by adapting the stable fitting methods of Wood, Pya, and Säfken. We show how the pinball loss is statistically suboptimal relative to a novel smooth generalization, which also gives access to fast estimation methods. Further, we provide a novel calibration method for efficiently selecting the "learning rate" balancing the loss with the smoothing priors during inference, thereby obtaining reliable quantile uncertainty estimates. Our work was motivated by a probabilistic electricity load forecasting application, used here to demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN).
Supplementary materials
for this article are available online.
When the outcome is binary, psychologists often use nonlinear modeling strategies such as logit or probit. These strategies are often neither optimal nor justified when the objective is to estimate ...causal effects of experimental treatments. Researchers need to take extra steps to convert logit and probit coefficients into interpretable quantities, and when they do, these quantities often remain difficult to understand. Odds ratios, for instance, are described as obscure in many textbooks (e.g., Gelman & Hill, 2006, p. 83). I draw on econometric theory and established statistical findings to demonstrate that linear regression is generally the best strategy to estimate causal effects of treatments on binary outcomes. Linear regression coefficients are directly interpretable in terms of probabilities and, when interaction terms or fixed effects are included, linear regression is safer. I review the Neyman-Rubin causal model, which I use to prove analytically that linear regression yields unbiased estimates of treatment effects on binary outcomes. Then, I run simulations and analyze existing data on 24,191 students from 56 middle schools (Paluck, Shepherd, & Aronow, 2013) to illustrate the effectiveness of linear regression. Based on these grounds, I recommend that psychologists use linear regression to estimate treatment effects on binary outcomes.
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed ...in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that (1) circumvent the need for analytic approximations, numerical integration, or Metropolis–Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya–Gamma distribution, are implemented in the R package BayesLogit . Supplementary materials for this article are available online.
Machine learning (ML) techniques have been utilized for the crop monitoring and yield estimation/prediction using remotely sensed data. However, these methods have been investigated less for yield ...prediction of some crops, such as silage maize, which can be cultivated at various times in different fields of an area. Inconsistency between fields for satellite-derived normalized difference vegetation index (NDVI) temporal profiles can lead to some difficulties in yield prediction methods using time series of remotely sensed data. Therefore, this research has investigated silage maize yield prediction based on time series of NDVI dataset derived from Landsat 8 OLI. This paper employed advanced ML techniques including boosted regression tree (BRT), random forest regression (RFR), support vector regression, and Gaussian process regression (GPR) approaches and compared their performance with some proposed conventional regression methods. For this purpose, the NDVI values of all silage maize fields were averaged and integrated to produce a two-dimensional dataset for each year. The ML techniques were employed 100 times and their evaluation metrics were used to evaluate their performances and also analyze their stability. Finally, all the results of each ML technique were averaged to produce silage maize yields. The comparisons between the results of these methods indicate that the BRT technique, with the average R value higher than 0.87, outperforms other ones for all years. It was followed by RFR with almost same performance as GPR technique. This research demonstrated that some advanced ML approaches can predict the silage maize yield and they are less sensitive to inconsistency of NDVI time series. The results also showed that RFR was the most stable method to predict the maize yield in 2015, while it was trained using 2013-2014 dataset.
A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well ...as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: * Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. * Delivers a balance between methodolgy and application * Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. * Features a supporting website ( www.wiley.com/go/quantile_regression ) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
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