Topic

# Linear model

About: Linear model is a(n) research topic. Over the lifetime, 19008 publication(s) have been published within this topic receiving 1054229 citation(s). The topic is also known as: linear models.

##### Papers
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Book
01 Jan 1983-
TL;DR: In this Section: 1. Multivariate Statistics: Why? and 2. A Guide to Statistical Techniques: Using the Book Research Questions and Associated Techniques.

53,012 citations

Journal ArticleDOI
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

36,018 citations

Book
Peter McCullagh1, John A. NelderInstitutions (1)
01 Jan 1983-
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).

23,204 citations

Book
Christopher M. Bishop1Institutions (1)
17 Aug 2006-
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

22,762 citations

Journal ArticleDOI
Kung Yee Liang1, Scott L. Zeger1Institutions (1)
01 Apr 1986-Biometrika
Abstract: SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.

16,152 citations

##### Network Information
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##### Performance
###### Metrics
No. of papers in the topic in previous years
YearPapers
202215
2021676
2020748
2019759
2018694
2017775

###### Top Attributes

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Topic's top 5 most impactful authors

Hua Liang

27 papers, 865 citations

Joseph W. McKean

25 papers, 1.1K citations

Peter Bühlmann

23 papers, 3.7K citations

Raymond J. Carroll

23 papers, 1.2K citations

Daniel Gianola

20 papers, 1.3K citations