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Generalized Additive Models

T. Hastie, R. Tibshirani
Published 1990 · Mathematics

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Likelihood-based regression models such as the normal linear regression model and the linear logistic model, assume a linear (or some other parametric) form for the covariates X1, X2, *--, Xp. We introduce the class of generalized additive models which replaces the linear form E fjXj by a sum of smooth functions E sj(Xj). The sj(.)'s are unspecified functions that are estimated using a scatterplot smoother, in an iterative procedure we call the local scoring algorithm. The technique is applicable to any likelihood-based regression model: the class of generalized linear models contains many of these. In this class the linear predictor q = E fjXj is replaced by the additive predictor E sj(Xj); hence, the name generalized additive models. We illustrate the technique with binary response and survival data. In both cases, the method proves to be useful in uncovering nonlinear covariate effects. It has the advantage of being completely auto- matic, i.e., no "detective work" is needed on the part of the statistician. As a theoretical underpinning, the technique is viewed as an empirical method of maximizing the expected log likelihood, or equivalently, of minimizing the Kullback-Leibler distance to the true model.
This paper references
10.1093/BIOMET/69.3.521
Regression with censored data
R. G. Miller (1982)
10.1080/00401706.1984.10487961
The Monotone Smoothing of Scatterplots
J. Friedman (1984)
10.1214/AOS/1176349940
The Dimensionality Reduction Principle for Generalized Additive Models
C. J. Stone (1986)
10.1111/J.2517-6161.1980.TB01109.X
Regression Models for Ordinal Data
P. McCullagh (1980)
10.1007/BF02293871
The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features
F. Young (1978)
10.1007/978-1-4615-7070-7_6
Semi-Parametric Generalized Linear Models.
P. Green (1985)
10.1080/03610927508827223
A completely automatic french curve: fitting spline functions by cross validation
G. Wahba (1975)
10.1080/01621459.1985.10478157
Estimating Optimal Transformations for Multiple Regression and Correlation.
L. Breiman (1985)
10.1080/01621459.1979.10481038
Robust Locally Weighted Regression and Smoothing Scatterplots
W. S. Cleveland (1979)
10.1080/01621459.1984.10477062
Graphical Methods for Assessing Logistic Regression Models
J. M. Landwehr (1984)
10.1007/978-1-4615-7070-7_8
Generalized Additive Models: Some Applications
T. Hastie (1987)
10.1214/AOS/1176343887
Discussion: Consistent Nonparametric Regression
P. Bickel (1977)
10.21236/ada119814
Smoothing of Scatterplots
J. Friedman (1982)
10.1080/01621459.1981.10477729
Projection Pursuit Regression
J. Friedman (1981)
10.1080/01621459.1986.10478243
Automatic Smoothing of Regression Functions in Generalized Linear Models
F. O'Sullivan (1986)
10.1007/978-1-4612-4380-9_37
Regression Models and Life-Tables
D. Cox (1972)
10.2307/2288339
Graphical Methods for Assessing Logistic Regression Models: Rejoinder
J. M. Landwehr (1984)
10.2307/2531415
Generalized Linear Models
P. McCullagh (1983)
10.21236/ada148833
Principal Curves and Surfaces
T. Hastie (1984)
10.1007/BF02162161
Smoothing by spline functions
Christian H. Reinsch (1967)
10.2307/2344614
Generalized Linear Models
J. Nelder (1972)



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C. Beale (2010)
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S. L. Ho (2012)
10.1051/proc/201448005
Emulators for stochastic simulation codes
V. Moutoussamy (2014)
10.1007/s10742-016-0160-x
A comparison of care management delivery models on the trajectories of medical costs among patients with chronic diseases: 4-year follow-up results
Hsiu-Ching Chang (2016)
10.1002/cjs.11313
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J. Taylor (2018)
10.1016/J.FORECO.2018.03.016
National-scale assessment of forest site productivity in Spain
Daniel Moreno-Fernández (2018)
10.1002/FOR.1027
A semiparametric method for predicting bankruptcy
R. Hwang (2007)
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Raphaelle Momal (2019)
Wildlife Picture Index- Implementation Manual Version 1.0
T. O'brien (2010)
Differential association of the codon 72 p53 and GSTM1 polymorphisms on histological subtype of non-small cell lung carcinoma.
G. Liu (2001)
10.1001/JAMA.288.8.980
Inflammatory biomarkers, hormone replacement therapy, and incident coronary heart disease: prospective analysis from the Women's Health Initiative observational study.
A. Pradhan (2002)
10.1109/SMC.2015.280
Predicting Nocturnal Hypoglycemia Using a Non-parametric Insulin Action Model
F. Ståhl (2015)
10.1016/j.envsoft.2015.11.004
A GUI platform for uncertainty quantification of complex dynamical models
Chen Wang (2016)
10.1007/s00376-015-5115-6
Temporal statistical downscaling of precipitation and temperature forecasts using a stochastic weather generator
Yongku Kim (2015)
Multi-objective ROC learning for classification
Andrew R. J. Clark (2011)
10.5109/12706
ADAPTIVE LEARNING MACHINES FOR NONLINEAR CLASSIFICATION AND BAYESIAN INFORMATION CRITERIA
T. Ando (2004)
10.1098/rspb.2005.3184
From patterns to processes and back: analysing density-dependent responses to an abiotic stressor by statistical and mechanistic modelling
S. Jannicke Moe (2005)
10.1016/j.csda.2004.10.011
Generalized structured additive regression based on Bayesian P-splines
Andreas Brezger (2006)
Component selection and smoothing in smoothing spline analysis of variance models -- COSSO
Y. Lin (2003)
10.1016/J.BIOCON.2012.07.012
A field test of acoustic deterrent devices used to reduce interactions between bottlenose dolphins and a coastal gillnet fishery
Danielle M. Waples (2013)
10.1111/J.2517-6161.1996.TB02080.X
Regression Shrinkage and Selection via the Lasso
R. Tibshirani (1996)
Title The spatial distribution of known predictors of autism spectrum disorders impacts geographic variability in prevalence in central North Carolina Permalink
K. Hoffman (2012)
10.1007/BF00942175
Analyzing preventive trials with generalized additive models
C. H. Brown (1993)
10.1177/096228029500400305
Trees and splines in survival analysis
O. Intrator (1995)
Eastern cooperative group trial of interferon gamma in metastatic melanoma: an innovative study design.
J. Schiller (1996)
10.13097/archive-ouverte/unige:83060
Robust penalized M-estimators for generalized linear and additive models
A. Medina (2016)
On Continuous Optimization Methods in Data Mining — Cluster Analysis , Classification and Regression — Provided for Decision Support and Other Applications
Tatiana Tchemisova (2008)
10.1002/(SICI)1099-095X(200001/02)11:1<63::AID-ENV381>3.0.CO;2-Q
Methodologic issues in linking aggregated environmental and health data.
Markku Mikael Nurminen (2000)
Female wage profiles: An additive mixed model approach to employment breaks due to childcare
Torben Kuhlenkasper (2010)
Title Generalized Varying-Coefficient Models Permalink
J. Fan (1999)
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