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Topic: Generalized linear model

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Linear model

	Generalized linear model - Wikipedia, the free encyclopedia
		Error distributions from the exponential family, besides the normal distribution are permitted.
		As in the notation of other regression models such as the General linear model, X is the design matrix, and β is a matrix containing parameters that must be estimated.
		Generalized linear models include, as special cases, ordinary linear regression, logistic regression, Poisson regression, and several other interesting models.
	en.wikipedia.org /wiki/Generalized_linear_model (215 words)

	MA3201 Generalized Linear Models
		The aim of covering the theory for the generalized linear model is to understand the extension of the theory to cover log-linear models for the analysis of counts and proportions and linear logistic regression models for binary data.
		Students should be able to understand the theory of the generalized linear model and be able to understand how to use GLIM to analyse data with the generalized linear model.
		Students will be able to assess the fit of a log-linear model using change in deviance, knowledge of the theory of the general linear model, and the ability to use GLIM to analyse data with the generalized linear model.
	www.mcs.le.ac.uk /Modules/MA/MA3201.html (639 words)

	PlanetMath: generalized linear model
		Given a random vector, or the response variable, Y, a generalized linear model, or GLM for short, is a statistical model
		GLM is a direct generalization of the general linear model, which includes linear regression models, ANOVA and ANCOVA.
		This is version 10 of generalized linear model, born on 2004-07-27, modified 2004-11-04.
	planetmath.org /encyclopedia/LinkFunction.html (305 words)

	Linear model - Wikipedia, the free encyclopedia
		The general linear model (or multivariate regression model) is a linear model with multiple measurements per object.
		ANOVA, or analysis of variance, is historically a precursor to the development of linear models.
		Here the model parameters themselves are not computed, but X column contributions and their significance are identified using the ratios of within-group variances to the error variance and applying the F test.
	en.wikipedia.org /wiki/Linear_model (300 words)

	General Linear Models (GLM)
		Linear combinations of responses reflecting a repeated measure effect (for example, the difference of responses on a measure under differing conditions) can be constructed and tested for significance using either the univariate or multivariate approach to analyzing repeated measures in the general linear model.
		In using the general linear model, one must keep in mind that finding a particular arbitrary solution to the normal equations is primarily a means to the end of accounting for responses on the dependent variables, and not necessarily an end in itself.
		The general implication of the theory of estimability of linear functions is that hypotheses which cannot be expressed as linear combinations of the rows of X (i.e., the combinations of observed levels of the categorical predictor variables) are not estimable, and therefore cannot be tested.
	www.statsoft.com /textbook/stglm.html (13045 words)

	MC361 Generalized Linear Models
		With a suitable choice of link function and error structure it is possible to cover, within a general framework, a number of techniques for analysing data: linear modelling of continuous variables, log-linear modelling for the analysis of counts and proportions and linear logistic regression modelling for binary data.
		It is possible to associate confidence intervals to estimates or predictions obtained from the model and assign p-values to hypotheses to be tested.
		The analysis of the model is based on the deviance which offers a method for assessing the acceptability of any proposed model.
	www.mcs.le.ac.uk /Modules/Modules01-02/node61.html (666 words)

	[No title]
		The general linear model is a generalization of the linear regression model, such that effects can be tested (1) for categorical predictor variables, as well as for effects for continuous predictor variables and (2) in designs with multiple dependent variables as well as in designs with a single dependent variable.
		Generalized Additive Models are generalizations of generalized linear models.
		In generalized additive models, the linear function of the predictor values is replaced by an unspecified (non-parametric) function, obtained by applying a scatterplot smoother to the scatterplot of partial residuals (for the transformed dependent variable values).
	www.statsoft.com /textbook/glosf.html (3048 words)

	What is a Generalized Linear Model?
		For example, the mean of a measured proportion is between 0 and 1, but the linear predictor of the mean in a traditional linear model is not restricted to this range.
		A generalized linear model extends the traditional linear model and is, therefore, applicable to a wider range of data analysis problems.
		As in the case of traditional linear models, fitted generalized linear models can be summarized through statistics such as parameter estimates, their standard errors, and goodness-of-fit statistics.
	www.sfu.ca /sasdoc/sashtml/stat/chap29/sect2.htm (412 words)

	PlanetMath: deviance
		to be served as a base model in case when more than one models are being assessed.
		are the null model and the saturated model.
		Cross-references: degrees, statistic, hypothesis testing, distribution, regression models, squares, sum, residual, maximum likelihood estimate, observations, independent, identity, general linear model, normal, vector, MLE, log-likelihood function, outcome, base, difference, link function, mean, model, one way, explanatory variable, response variable, generalized linear model
	planetmath.org /encyclopedia/Deviance.html (294 words)

	S archive: Double generalized linear model object
		, since it consists of two coupled generalized linear models, one for the mean and one for the dispersion.
		The responses for this model are the deviance components from the original generalized linear model.
		The prior weights are 1 and the dispersion or scale of this model is 2.
	www.statsci.org /s/dglmobj.html (175 words)

	Analyzing Linear and Nonlinear systems
		Thus, the "general" in General Regression Models refers both to the use of the general linear model, and to the fact that unlike most other stepwise regression programs, GRM is not limited to the analysis of designs that contain only continuous predictor variables.
		The General Regression Models (GRM) module offers all standard and unique results options described in the context of the GLM module in the previous section (including desirability profiling, predicted and residual statistics for the computation or training sample, cross-validation or verification sample, and prediction sample; tests of assumptions, means plots, etc.).
		Generalized linear models make it possible to flexibly search for linear and nonlinear relationships between a continuous, or binomial, multinomial, or ordinal multinomial categorical response variable and categorical or continuous predictor variables.
	www.statsoft.nl /products/visual.html (2619 words)

	Generalized Linear Models: Selected Bibliography
		This is a very idiosyncratic of bibliography of some of the recent generalized linear model literature.
		Glms assume a response distribution which is a linear exponential family plus a dispersion parameter.
		Gilmour, A. R., Anderson, R. D., and Rae, A. The analysis of binomial data by a generalized linear mixed model.
	www.statsci.org /glm/bibliog.html (2204 words)

	Generalized Linear Models
		A wide variety of models with a categorical response is a typical (althgough not the only one!) example, where the assumption of normality cannot be accepted as reasonable.
		In this course we study generalized linear models, where the response variables are allowed to be non-normal.
		We start from the general theory of generalazied linear models, extending the corresponding results for standard linear regression, and then consider the most useful particular cases in more details.
	www.math.tau.ac.il /~felix/Genlin.html (533 words)

	Statistics.com Courses: Generalized Linear Models (Site not responding. Last check: 2007-10-22)
		Generalized Linear Models is a unified method used to extend the general linear model, or ordinary least squares (OLS) regression, to incorporate responses other than normal.
		GLM models are all members of the exponential family of distributions, and allow the modeling of responses, or dependent variables, that take the form of counts, proportions, dichotomies (1/0), positive continuous values, as well as values that follow the normal Gaussian distribution.
		Each type of GLM model will be addressed, with separate discussion sections being given to continuous response and to discrete response data situations.
	www.statistics.com /content/courses/glm (933 words)

	Generalized Linear Models (GLZ)
		This chapter describes the use of the generalized linear model for analyzing linear and non-linear effects of continuous and categorical predictor variables on a discrete or continuous dependent variable.
		Discussion of the ways in which the linear regression model is extended by the general linear model can be found in the General Linear Models chapter.
		The generalized linear model can be used to predict responses both for dependent variables with discrete distributions and for dependent variables which are nonlinearly related to the predictors.
	www.rrz.uni-hamburg.de /RRZ/Software/Statistica/Handbuch/stglz.html (4230 words)

	Generalized linear measurement error models
		Three new commands are available for Stata 8 to fit generalized linear models when one or more covariates are measured with error.
		Regression calibration was suggested as a general approach by Carroll and Stefanski (1990) and Gleser (1990).
		Forthcoming from StataPress is Generalized Linear Measurement Error Models in Stata by R. Carroll, J. Hardin, and H. Schmiediche.
	www.stata.com /merror (1168 words)

	R: Analysis of Deviance for Generalized Linear Model Fits (Site not responding. Last check: 2007-10-22)
		That is, the reductions in the residual deviance as each term of the formula is added in turn are given in as the rows of a table, plus the residual deviances themselves.
		For all but the first model, the change in degrees of freedom and deviance is also given.
		Mallows' Cp statistic is the residual deviance plus twice the estimate of sigma^2 times the residual degrees of freedom, which is closely related to AIC (and a multiple of it if the dispersion is known).
	www.ualberta.ca /CNS/RESEARCH/Rdoc/R/library/base/html/anova.glm.html (275 words)

	R: Accessing Generalized Linear Model Fits (Site not responding. Last check: 2007-10-22)
		The partial residuals are a matrix of working residuals, with each column formed by omitting a term from the model.
		Chapter 6 of Statistical Models in S eds J. Chambers and T. Hastie, Wadsworth and Brooks/Cole.
		McCullagh P. and Nelder, J. Generalized Linear Models.
	www.ma.hw.ac.uk /ams/Rhelp/library/stats/html/glm.summaries.html (144 words)

	MODEL
		Add/delete an observation to/from a general linear regression model
		Estimates of parameters of a general linear regression model for given constraints
		Estimate of an estimable function for a general linear regression model
	www.uni-regensburg.de /EDV/Unix_Workstations/Linux/Software/nagbib/NAGdoc/cl/html/indexes/kwic/model.html (204 words)

	Jeff Gill: Homepage (Site not responding. Last check: 2007-10-22)
		My research applies Bayesian modeling and data analysis (decision theory, testing, model selection, elicited priors) to questions in general social science quantitative methodology, American political behavior and institutions, focusing on Congress, the bureaucracy, and voters, using computationally intensive tools (Monte Carlo methods, MCMC, stochastic optimization, non-parametrics).
		Gauss Code for the Schnabel-Eskow generalized Cholesky Decomposition, R version, and Some R routines for checking/running.
		GLMLAB: A Generalized Linear Model Package for MATLAB by Peter Dunn at the Department of Mathematics and Computing, University of Southern Queensland (Australia).
	psblade.ucdavis.edu (1265 words)

	Testing the Generalized Linear Regression Model Driver (Site not responding. Last check: 2007-10-22)
		The driver routine for the generalized linear regression model is
		On each iteration of the innermost loop, matrices 16#16 and 97#97 are generated and used to test the GLM driver routine.
		Please note that the block size NB is not an input test parameter since the GLM problem is solved by calling GQR factorization.
	www.netlib.org /lapack/lawn41/node90.html (191 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		% demgmm1 - Demonstrate density modelling with a Gaussian mixture model.
		% demgmm3 - Demonstrate density modelling with a Gaussian mixture model.
		% demgmm5 - Demonstrate density modelling with a PPCA mixture model.
	www.cis.upenn.edu /~ungar/KDD/FullBNT/netlab/Contents.m (1541 words)

	Publications and Technical Reports
		1996-2 Bayesian probit modeling of binary repeated measures data with an application to a cross-over trial (with Sid Chib).
		1995-1 Bayesian residual analysis for binary response regression models (with Sid Chib).
		1983-3 Models for reflecting prior beliefs of association in contingency tables (with A. Gupta).
	bayes.bgsu.edu /papers/papers.html (1088 words)

	Generalized Linear Models (Site not responding. Last check: 2007-10-22)
		Generalized linear models assume that the response y
		has a distribution from the exponential family (normal, inverse Gaussian, gamma, Poisson, binomial) and a function can be used to link the expected response mean and a linear function of the X effects.
		The design matrix is generated the same way as for linear models.
	www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/insight/chap39/sect3.htm (128 words)

	Publications
		Beretvas, S.N., Meyers, J.L., and Leite, W.L. A reliability generalization study of the Marlowe-Crowne Social Desirability Scale, Educational and Psychological Measurement, 6(4), 570-589.
		Beretvas, S.N. and Williams, N.J. The use of hierarchical generalized linear model for item dimensionality assessment.
		The cross-classified multilevel measurement model: An explanation and demonstration, Journal of Applied Measurement.
	www.pearsonedmeasurement.com /research/publications.htm (906 words)

	R: Digamma generalized linear model family (Site not responding. Last check: 2007-10-22)
		Produces a Digamma generalized linear model family object.
		This family is useful for dispersion modelling with gamma generalized linear models.
		produces a glm family object, which is a list of functions and expressions used by
	www.stat.ucl.ac.be /ISdidactique/Rhelp/library/statmod/html/digammaf.html (303 words)

	Amazon.ca: Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models: ... (Site not responding. Last check: 2007-10-22)
		This modern statistics text discusses the extension of the linear model through the regression model.
		It extensively addresses the generalized linear model, GLM diagnostics, generalized linear mixed models, trees, and the use of neural networks in the field of statistics.
		It discusses the regression model in three forms: through the use of dummy variables for qualitative predictors, by allowing transformation of variables as in the Box-Cox transformation, and the use of weights that allow heterogeneous error structures and the exclusion of outliers.
	www.amazon.ca /exec/obidos/ASIN/158488424X (289 words)

	ERRORS (Site not responding. Last check: 2007-10-22)
		Fits a generalized linear model with binomial errors
		Estimates and standard errors of parameters of a general linear model for given constraints
		Analysis of variance, general row and column design, treatment means and standard errors
	www.nag.co.uk /numeric/cl/manual/xhtml/indexes/kwic/cl_errors.xml (67 words)

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