Generalized additive models for longitudinal data

by Kiros Berhane

Publisher: University of Toronto, Department of Statistics in [Toronto, Ont

Written in English
Published: Pages: 21 Downloads: 899
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Subjects:

  • Linear models (Statistics),
  • Multivariate analysis.

Edition Notes

StatementKiros Berhane and Robert Tibshirani.
SeriesTechnical report series / University of Toronto, Department of statistics -- no. 9311, July 28, 1993, Technical report (University of Toronto. Dept. of Statistics) -- no. 9311
ContributionsTibshirani, Robert.
Classifications
LC ClassificationsQA278.2 .B47 1993
The Physical Object
Pagination21 p. :
Number of Pages21
ID Numbers
Open LibraryOL14752891M

  DOI link for Generalized Additive Models. Generalized Additive Models book. By T.J. Hastie. Edition 1st Edition. First Published eBook Published 19 October Pub. location New York. This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods. Abstract: We propose a comprehensive framework for additive regression models for non-Gaussian functional responses, allowing for multiple (par-tially) nested or crossed functional random e ects with exible correlation structures for, e.g., spatial, temporal, or longitudinal functional data as well.   Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data Raymond Carroll, Arnab Maity, Enno Mammen, and Kyusang Yu Raymond Carroll, Department of Statistics, TAMU, Texas A&M University, College Station, Texas , USA, Email: @llorrac, Telephone The GRATIS paper is accepted in Statistical Analysis and Data Mining J The DeepTCN paper is accepted in Neurocomputing Ma Generalized Linear Models, spring.

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. I am trying fit a generalized additive mixed model (GAMM) to longitudinal neuroanatomic data using the mgcv package in R. Some individuals have only two time points, while others have up to eight.   Although antedependence models are particularly useful for modeling longitudinal data that exhibit serial correlation, few books adequately cover these models. By gathering results scattered throughout the literature, Antedependence Models for Longitudinal Data offers a convenient, systematic way to learn about antedependence models. Another example of generalized linear models includes Poisson regression which models count data using the Poisson distribution. The link is typically the logarithm, the canonical link. as occurs for example in longitudinal studies and clustered designs: Generalized estimating equations Generalized Additive Models.

We propose a comprehensive framework for additive regression models for non-Gaussian functional responses, allowing for multiple (partially) nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data as well as linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the. Generalized Linear Models Meets: T/TH (Old Chem ) Instructor: David Dunson Old Chemistry, [email protected] Teaching Assistant: Eric Vance Old Chemistry, [email protected] idea, there are major challenges for estimating the additive model for dependent data. Until only very recently, Carroll et al. [2] gave the first contribution on the partly linear additive model for longitudinal/clustered data, focusing on a simple setup of the problem, where there is the same. Repeated Measures and Longitudinal Data Longitudinal Data Repeated Measures Multiple Response Multilevel Models Additive Models Modeling Ozone Concentration Additive Models Using mgcv Generalized Additive Models Alternating Conditional Expectations Additivity and Variance Stabilization Generalized Additive Mixed Models Multivariate Adaptive.

Generalized additive models for longitudinal data by Kiros Berhane Download PDF EPUB FB2

After their graduation this highly acclaimed book came out explaining both the theory and pratice of generalized additive models in a clear and concise way.

Generalized additive models are similar to generalized linear models in their additive structure but the form of the additive functions is much more by: Generalized additive models for longitudinal data We introduce a class of models for longitudinal data by extending the generalized estimating equations approach of Liang and Zeger () to incorporate the flexibility of nonparametric smoothing.

The algorithm provides a unified estimation procedure for marginal distributions from the Cited by:   1. Introduction. Generalized additive partial linear models (GAPLM) for correlated data (see, for instance, Wang et al. (), Lian et al. (), Manghi et al. ()) comprise an important approach for modeling clustered, repeated measurement and longitudinal models have the feature of jointly modeling the mean structure by parametric and nonparametric components, with the Cited by: 1.

Downloadable (with restrictions). Statistical procedures are proposed in generalized additive partial linear models (GAPLM) for analyzing correlated data.

A reweighed iterative process based on the backfitting algorithm is derived for the parameter estimation from a penalized GEE. Discussions on the inferential aspects of GAPLM, particularly on the asymptotic properties of the former Cited by: 1. additive model for dependent data.

Until only very recently, Carroll et al. () gave the first contribution on the partly linear additive model for longitudinal/clustered data, fo-cusing on a simple setup of the problem, where there is the same number of observations per subject/cluster, and the identity link function is used.

Unfortunately, this method only considered continuous responses with longitudinal data, and cannot deal directly with discrete longitudinal data, such as a generalized varying coefficient model.

Variable selection for longitudinal generalized varying coefficient models has only been sparsely studied. Saturation for degree-two splines requires the solution extrapolates as a constant beyond the range of the data. This along with an additive model formulation leads to a convex path algorithm for variable selection and smoothing with generalized additive models.

JMLR 18(), sis of longitudinal data in linear models. An incomplete list of recent work on the quantile regression for longitudinal data include Yin and Cai (), Tang and Leng (),FuandWang(),Fuetal.()andLuandFan().However,allthe above authors only considered linear models.

Thus, quantile PLAMs have not been. A GAM is a GLM in which the linear predictor is given by a user-specified sum of smooth functions of the covariates plus a conventional parametric component of.

Many data in the environmental sciences do not fit simple linear models and are best described by “wiggly models”, also known as Generalised Additive Models (GAMs). Let’s start with a famous tweet by one Gavin Simpson, which amounts to: 1. GAMs are just GLMs 2. GAMs fit wiggly terms 3. use + s(x) not x in your syntax 4.

use method = "REML". Hence as the plot shows that the output of lm() function is also similar and does not makes a difference if we use gam() or lm() to fit Generalized Additive produce exactly same results.

Conclusion. Generalized Additive Models are a very nice and effective way of fitting Linear Models which depends on some smooth and flexible Non linear functions fitted on some. ginal framework for the generalized additive model for corre lated data.

Section 3 introduces a penalized quadratic inference function method for simultaneous estimation and variable se lection of marginal generalized additive models.

Asymptotic theories are developed and issues for implementation are dis cussed. Classical categorical regression models such as the multinomial logit and proportional odds models are shown to be readily handled by the vector generalized linear and additive model (VGLM/VGAM.

Cantoni, E. Robust inference based on quasi-likelihoods for generalized linear models and longitudinal data. Proceedings of the International Conference on Robust Statistics Generalized Nonlinear Models Hastie, T., and Tibshirani, R.

Generalized Additive Models. Encyclopedia of Statistical Science, Wiley. (Postscript). In this paper, we consider the problem of variable selection and model detection in additive models with longitudinal data. Our approach is based on spline approximation for the components aided by two Smoothly Clipped Absolute Deviation (SCAD) penalty terms.

It can perform model selection (finding both zero and linear components) and estimation simultaneously. function; Xue, Qu and Zhou () proposed model selection of marginal generalized additive model analysis for correlated data.

However, the aforementioned work all assume that the dimension of predictors is xed. Some of these work only apply to continuous outcome data.

For correlated discrete outcome data, the joint likelihood function does. Ma, S. () Two-step Spline Estimating Equations for Generalized Additive Partially Linear Models with Large Cluster Sizes.

A nnals of Statistics, 40(6), or (PDF file) Ma, S., Yang, L. and Carroll, R. () Simultaneous Confidence Band for Sparse Longitudinal Regression. Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which.

idea, there are major challenges for estimating the additive model for dependent data. Until only very recently, Carroll et al. [2] gave the first contribution on the partly linear additive model for longitudinal/clustered data, focusing on a simple setup of the problem, where there is the same.

Generalized additive models are based on the additivity assumption INTRODUCTION The input data set to the initial DATA step is the longitudinal data set containing observations.

There are 6 variables in the data set: SUBJ_NO = subject number VISIT = visit number. We extend the GRC model to include both time-varying coefficient covariates and additive nonparametric covariates. We apply the proposed models and methods to a longitudinal binary data.

for longitudinal data, crossed random effects, smoothing of spatial count data, generalized additive models, generalized geostatistical models, additive models with interactions, varying coefficient models and various combinations of these (Wand, ).

Section 2 lays out notation for general design GLMMs and gives several im-portant examples. this paper, we propose generalized additive mixed models (GAMMs), which are an additive extension of generalized linear mixed models in the spirit of Hastie and Tibshirani ().

This new class of models uses additive nonparametric functions to model covariate effects while accounting for overdispersion and correlation by adding random effects. A generalized additive model is a generalized linear model with a linear predictor involving a sum of smooth functions of covariates.

This chapter illustrates how generalized additive models (GAMs) can be represented using basis expansions for each smooth, each with an associated penalty controlling function smoothness.

An introduction to modeling longitudinal data with generalized additive models: applications to single-case designs. Sullivan KJ(1), Shadish WR(1), Steiner PM(2).

Author information: (1)School of Social Sciences, Humanities and Arts. (2)Department of Educational Psychology, University of Wisconsin- Cited by: Generalized additive models: weeks Longitudinal and Grouped Data: weeks Background About the Course: Semiparametric Regression refers to a field of statistics the produces flexible models that allow for general regressions to take on many shapes.

From the book “Regression is. Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family.

This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs. additive model for dependent data. Until only very recently, Carroll et al. [2] gave the first contribution on the partly linear additive model for longitudinal/clustered data, fo-cusing on a simple setup of the problem, where there is the same number of observations.

Cited by: Shujie Ma, "Estimation and inference in functional single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pagesYang & Chaohui Guo & Jing Lv, "Variable selection for generalized varying coefficient models with longitudinal data," Statistical Papers, Springer, vol.

57(1. Statistical inference of additive models with longitudinal data has also been considered by some authors. By extending the generalized estimating equations approach, studied the estimation of additive model with [2] longitudinal data.

focuses on a nonparametric additive time[3] -varying regression model for longitudinal data. Yang, M., Xue, L., and Yang, L. (), "Variable selection for additive model via cumulative ratios of empirical strengths total," Journal of Nonparametric Statistics, 3, Instructional and Departmental Activities.

ST Generalized Regression Models II; ST Advanced Theory of Statistics II; ST Advanced Theory of Statistics III.Thus, generalized additive models can be applied to a much wider range of data analysis problems.

Like generalized linear models, generalized additive models consist of a random component, an additive component, and a link function relating the two components. The response, the random component, is assumed to have exponential family density.

Joint Models for Longitudinal and Time-to-Event Data: With Applications in R provides a full treatment of random effects joint models for longitudinal and time-to-event outcomes that can be utilized to analyze such data.

The content is primarily explanatory, focusing on applications of joint modeling, but sufficient mathematical details are Reviews: 1.