Spline Regression Models shows the nuts-and-bolts of using dummy variables to formulate and estimate various spline regression models.
Author: Lawrence C. Marsh
Publisher: SAGE
ISBN: 0761924205
Category: Mathematics
Page: 69
View: 727
Spline Regression Models shows the nuts-and-bolts of using dummy variables to formulate and estimate various spline regression models. For some researchers this will involve situations where the number and location of the spline knots are known in advance, while others will need to determine the number and location of spline knots as part of the estimation process. Through the use of a number of straightforward examples, the authors will show readers how to work with both types of spline knot situations as well as offering practical, down-to-earth information on estimating splines.
Spline Regression Models shows the nuts-and-bolts of using dummy variables to formulate and estimate various spline regression models.
Author: Lawrence C. Marsh
Publisher: SAGE Publications, Incorporated
ISBN: 0761924205
Category: Social Science
Page: 80
View: 699
Spline Regression Models shows the nuts-and-bolts of using dummy variables to formulate and estimate various spline regression models. For some researchers this will involve situations where the number and location of the spline knots are known in advance, while others will need to determine the number and location of spline knots as part of the estimation process. Through the use of a number of straightforward examples, the authors will show readers how to work with both types of spline knot situations as well as offering practical, down-to-earth information on estimating splines.
This book introduces methods of robust optimization in multivariate adaptive regression splines (MARS) and Conic MARS in order to handle uncertainty and non-linearity.
Author: Ayşe Özmen
Publisher: Springer
ISBN: 9783319308005
Category: Business & Economics
Page: 139
View: 105
This book introduces methods of robust optimization in multivariate adaptive regression splines (MARS) and Conic MARS in order to handle uncertainty and non-linearity. The proposed techniques are implemented and explained in two-model regulatory systems that can be found in the financial sector and in the contexts of banking, environmental protection, system biology and medicine. The book provides necessary background information on multi-model regulatory networks, optimization and regression. It presents the theory of and approaches to robust (conic) multivariate adaptive regression splines - R(C)MARS – and robust (conic) generalized partial linear models – R(C)GPLM – under polyhedral uncertainty. Further, it introduces spline regression models for multi-model regulatory networks and interprets (C)MARS results based on different datasets for the implementation. It explains robust optimization in these models in terms of both the theory and methodology. In this context it studies R(C)MARS results with different uncertainty scenarios for a numerical example. Lastly, the book demonstrates the implementation of the method in a number of applications from the financial, energy, and environmental sectors, and provides an outlook on future research.
Author: Richard B. DarlingtonPublish On: 2016-09-27
The user of linear spline regression chooses the values of the regressor X but not
the Y values that define the “joints” in a spline model. In Figure 12.9, these are
marked J1, J2, and J3. These could be chosen after examining a scatterplot, ...
Author: Richard B. Darlington
Publisher: Guilford Publications
ISBN: 9781462521135
Category: Social Science
Page: 661
View: 257
Ephasizing conceptual understanding over mathematics, this user-friendly text introduces linear regression analysis to students and researchers across the social, behavioral, consumer, and health sciences. Coverage includes model construction and estimation, quantification and measurement of multivariate and partial associations, statistical control, group comparisons, moderation analysis, mediation and path analysis, and regression diagnostics, among other important topics. Engaging worked-through examples demonstrate each technique, accompanied by helpful advice and cautions. The use of SPSS, SAS, and STATA is emphasized, with an appendix on regression analysis using R. The companion website (www.afhayes.com) provides datasets for the book's examples as well as the RLM macro for SPSS and SAS. Pedagogical Features: *Chapters include SPSS, SAS, or STATA code pertinent to the analyses described, with each distinctively formatted for easy identification. *An appendix documents the RLM macro, which facilitates computations for estimating and probing interactions, dominance analysis, heteroscedasticity-consistent standard errors, and linear spline regression, among other analyses. *Students are guided to practice what they learn in each chapter using datasets provided online. *Addresses topics not usually covered, such as ways to measure a variable?s importance, coding systems for representing categorical variables, causation, and myths about testing interaction.
Author: Frank E. Harrell , Jr.Publish On: 2015-08-14
Parametric splines are piecewise polynomials and can be fitted using any
existing regression program after the constructed predictors are computed. Spline regression is equally suitable to multiple linear regression, survival models, and ...
Author: Frank E. Harrell , Jr.
Publisher: Springer
ISBN: 9783319194257
Category: Mathematics
Page: 582
View: 262
This highly anticipated second edition features new chapters and sections, 225 new references, and comprehensive R software. In keeping with the previous edition, this book is about the art and science of data analysis and predictive modelling, which entails choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasises problem solving strategies that address the many issues arising when developing multi-variable models using real data and not standard textbook examples. Regression Modelling Strategies presents full-scale case studies of non-trivial data-sets instead of over-simplified illustrations of each method. These case studies use freely available R functions that make the multiple imputation, model building, validation and interpretation tasks described in the book relatively easy to do. Most of the methods in this text apply to all regression models, but special emphasis is given to multiple regression using generalised least squares for longitudinal data, the binary logistic model, models for ordinal responses, parametric survival regression models and the Cox semi parametric survival model. A new emphasis is given to the robust analysis of continuous dependent variables using ordinal regression. As in the first edition, this text is intended for Masters' or PhD. level graduate students who have had a general introductory probability and statistics course and who are well versed in ordinary multiple regression and intermediate algebra. The book will also serve as a reference for data analysts and statistical methodologists, as it contains an up-to-date survey and bibliography of modern statistical modelling techniques.
Table 6.5 OLS regression with linear and natural splines (Example 2: Working
hours) Linear splines Natural splines M1 M2 M3 M4 M5 age: Spline 1 –0.198 –
0.881 0.229∗ –0.043 –0.088 (0.193) (0.682) (0.091) (0.134) (0.165) Spline 2 ...
Author: Henning Best
Publisher: SAGE
ISBN: 9781473908352
Category: Reference
Page: 424
View: 643
'The editors of the new SAGE Handbook of Regression Analysis and Causal Inference have assembled a wide-ranging, high-quality, and timely collection of articles on topics of central importance to quantitative social research, many written by leaders in the field. Everyone engaged in statistical analysis of social-science data will find something of interest in this book.' - John Fox, Professor, Department of Sociology, McMaster University 'The authors do a great job in explaining the various statistical methods in a clear and simple way - focussing on fundamental understanding, interpretation of results, and practical application - yet being precise in their exposition.' - Ben Jann, Executive Director, Institute of Sociology, University of Bern 'Best and Wolf have put together a powerful collection, especially valuable in its separate discussions of uses for both cross-sectional and panel data analysis.' -Tom Smith, Senior Fellow, NORC, University of Chicago Edited and written by a team of leading international social scientists, this Handbook provides a comprehensive introduction to multivariate methods. The Handbook focuses on regression analysis of cross-sectional and longitudinal data with an emphasis on causal analysis, thereby covering a large number of different techniques including selection models, complex samples, and regression discontinuities. Each Part starts with a non-mathematical introduction to the method covered in that section, giving readers a basic knowledge of the method’s logic, scope and unique features. Next, the mathematical and statistical basis of each method is presented along with advanced aspects. Using real-world data from the European Social Survey (ESS) and the Socio-Economic Panel (GSOEP), the book provides a comprehensive discussion of each method’s application, making this an ideal text for PhD students and researchers embarking on their own data analysis.
Parametric splines are piecewise polynomials and can be fitted using any
existing regression program after the constructed predictors are computed. Spline regression is equally suitable to multiple linear regression, survival models, and ...
Author: Frank E. Harrell
Publisher: Springer Science & Business Media
ISBN: 9781475734621
Category: Mathematics
Page: 572
View: 224
Many texts are excellent sources of knowledge about individual statistical tools, but the art of data analysis is about choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for dealing with nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. This text realistically deals with model uncertainty and its effects on inference to achieve "safe data mining".
This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and ...
Author: Randall L. Eubank
Publisher: CRC Press
ISBN: 9781482273144
Category: Mathematics
Page: 360
View: 697
Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.
In this thesis , we study the applications of free - knot spline in two nonlinear regression models with multiple responses : ( 1 ) Self - modeling nonlinear
regression – Repeated measurements are observed at consecutive times ( or
ages ) for a ...
This dissertation investigates the use of multivariate adaptive regression splines (MARS), due to Friedman, for nonlinear regression modeling and analysis of time series systems.
This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear.
Author: George J. Knafl
Publisher: Springer
ISBN: 9783319339467
Category: Medical
Page: 372
View: 524
This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the standard, logistic, and Poisson regression contexts with continuous, discrete, and counts outcomes, respectively, either univariate or multivariate. The book also provides a comparison of adaptive modeling to generalized additive modeling (GAM) and multiple adaptive regression splines (MARS) for univariate outcomes. The authors have created customized SAS macros for use in conducting adaptive regression modeling. These macros and code for conducting the analyses discussed in the book are available through the first author's website and online via the book’s Springer website. Detailed descriptions of how to use these macros and interpret their output appear throughout the book. These methods can be implemented using other programs.
Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, t
Author: Yuedong Wang
Publisher: CRC Press
ISBN: 9781420077568
Category: Mathematics
Page: 384
View: 488
A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, thin-plate, L-, and partial splines, as well as more advanced models, such as smoothing spline ANOVA, extended and generalized smoothing spline ANOVA, vector spline, nonparametric nonlinear regression, semiparametric regression, and semiparametric mixed-effects models. It also presents methods for model selection and inference. The book provides unified frameworks for estimation, inference, and software implementation by using the general forms of nonparametric/semiparametric, linear/nonlinear, and fixed/mixed smoothing spline models. The theory of reproducing kernel Hilbert space (RKHS) is used to present various smoothing spline models in a unified fashion. Although this approach can be technical and difficult, the author makes the advanced smoothing spline methodology based on RKHS accessible to practitioners and students. He offers a gentle introduction to RKHS, keeps theory at a minimum level, and explains how RKHS can be used to construct spline models. Smoothing Splines offers a balanced mix of methodology, computation, implementation, software, and applications. It uses R to perform all data analyses and includes a host of real data examples from astronomy, economics, medicine, and meteorology. The codes for all examples, along with related developments, can be found on the book’s web page.
Failure time analysis is a form of regression analysis where the time until an
event occurs is of interest. The event is generically referred to as failure in this
thesis, the observational units are referred to as individuals. Unlike most
regression ...
Author: Matthias Kaeding
Publisher: Springer
ISBN: 9783658083939
Category: Mathematics
Page: 110
View: 839
Matthias Kaeding discusses Bayesian methods for analyzing discrete and continuous failure times where the effect of time and/or covariates is modeled via P-splines and additional basic function expansions, allowing the replacement of linear effects by more general functions. The MCMC methodology for these models is presented in a unified framework and applied on data sets. Among others, existing algorithms for the grouped Cox and the piecewise exponential model under interval censoring are combined with a data augmentation step for the applications. The author shows that the resulting Gibbs sampler works well for the grouped Cox and is merely adequate for the piecewise exponential model.
NONLINEAR MODELING OF MULTIVARIATE AND CATEGORICAL TIME
SERIES USING MULTIVARIATE ADAPTIVE REGRESSION SPLINES PETER
A W LEWIS Department of Operations Research , Naval Postgraduate School
Monterey ...
Author: Howell Tong
Publisher: World Scientific
ISBN: 9810213530
Category: Mathematics
Page: 223
View: 425
This volume is the first in the new series Nonlinear Time Series and Chaos. The general aim of the series is to provide a bridge between the two communities by inviting prominent researchers in their respective fields to give a systematic account of their chosen topics, starting at the beginning and ending with the latest state. It is hoped that researchers in both communities will find the topics relevant and thought provoking. In this volume, the first chapter, written by Professor Colleen Cutler, is a comprehensive account of the theory and estimation of fractal dimension, a topic of central importance in dynamical systems, which has recently attracted the attention of the statisticians. As it is natural to study a stochastic dynamical system within the framework of Markov chains, it is therefore relevant to study their limiting behaviour. The second chapter, written by Professor Kung-Sik Chan, reviews some limit theorems of Markov chains and illustrates their relevance to chaos. The next three chapters are concerned with specific models. Briefly, Chapter Three by Professor Peter Lewis and Dr Bonnie Ray and Chapter Four by Professor Peter Brockwell generalise the class of self-exciting threshold autoregressive models in different directions. In Chapter Three, the new and powerful methodology of multivariate adaptive regression splines (MARS) is adapted to time series data. Its versatility is illustrated by reference to the very interesting and complex sea surface temperature data. Chapter Four exploits the greater tractability of continuous-time Markov approach to discrete-time data. The approach is particularly relevant to irregularly sampled data. The concluding chapter, by Professor Pham Dinh Tuan, is likely to be the most definitive account of bilinear models in discrete time to date.
as a basis function in a combined substantive-empirical approach that uses re-
gression splines as the other basis ... which use the parametric regression models of Chapter 4 or the nonparametric regression models of this chapter, are
...
Author: Tze Leung Lai
Publisher: Springer Science & Business Media
ISBN: 9780387778266
Category: Business & Economics
Page: 356
View: 764
The idea of writing this bookarosein 2000when the ?rst author wasassigned to teach the required course STATS 240 (Statistical Methods in Finance) in the new M. S. program in ?nancial mathematics at Stanford, which is an interdisciplinary program that aims to provide a master’s-level education in applied mathematics, statistics, computing, ?nance, and economics. Students in the programhad di?erent backgroundsin statistics. Some had only taken a basic course in statistical inference, while others had taken a broad spectrum of M. S. - and Ph. D. -level statistics courses. On the other hand, all of them had already taken required core courses in investment theory and derivative pricing, and STATS 240 was supposed to link the theory and pricing formulas to real-world data and pricing or investment strategies. Besides students in theprogram,thecoursealso attractedmanystudentsfromother departments in the university, further increasing the heterogeneity of students, as many of them had a strong background in mathematical and statistical modeling from the mathematical, physical, and engineering sciences but no previous experience in ?nance. To address the diversity in background but common strong interest in the subject and in a potential career as a “quant” in the ?nancialindustry,thecoursematerialwascarefullychosennotonlytopresent basic statistical methods of importance to quantitative ?nance but also to summarize domain knowledge in ?nance and show how it can be combined with statistical modeling in ?nancial analysis and decision making. The course material evolved over the years, especially after the second author helped as the head TA during the years 2004 and 2005.
An introductory guide to smoothing techniques, semiparametric estimators, and their related methods, this book describes the methodology via a selection of carefully explained examples and data sets.
Author: Luke John Keele
Publisher: John Wiley & Sons
ISBN: 0470998121
Category: Mathematics
Page: 230
View: 585
An introductory guide to smoothing techniques, semiparametric estimators, and their related methods, this book describes the methodology via a selection of carefully explained examples and data sets. It also demonstrates the potential of these techniques using detailed empirical examples drawn from the social and political sciences. Each chapter includes exercises and examples and there is a supplementary website containing all the datasets used, as well as computer code, allowing readers to replicate every analysis reported in the book. Includes software for implementing the methods in S-Plus and R.
... ( 2 ) The Overfitting Is Based on Spline Functions The spline regression model
differs from the piecewise linear regression model mainly by the fact that in the
spline case adjacent regression lines ( and its derivatives ) are required to
intersect ...
Author: Peter Hackl
Publisher: Vandehoeck & Rupprecht
ISBN: STANFORD:36105038907957
Category: Regression analysis
Page: 132
View: 490
Techniques for testing the constancy of regression relation-ships over time: a survey; The MOSUM thecniques; Comparison of the MOSUM techniques with other test procedures; Sequencial test procedures; A consumption function.
... provided a mathematically gentler introduction to the field through regression models that are largely univariate. Much has happened in the past decade, and
more has been done with the penalty method than just regression. In this book.
Author: Chong Gu
Publisher: Springer Science & Business Media
ISBN: 0387953531
Category: Mathematics
Page: 289
View: 778
Smoothing methods are an active area of research. In this book, the author presents a comprehensive treatment of penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored life time data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source clone of the popular S/S- PLUS language.
