Comparison of general and generalized linear models
Encyclopedia
| General linear model General linear model The general linear model is a statistical linear model.It may be written aswhere Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors or... |
Generalized linear model Generalized linear model In statistics, the generalized linear model is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to... |
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| Typical estimation method | Least squares Least squares The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every... , best linear unbiased prediction Best linear unbiased prediction In statistics, best linear unbiased prediction is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term "best linear unbiased predictor" seems not to have been used until 1962... |
Maximum likelihood Maximum likelihood In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters.... or Bayesian Bayesian probability Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is... |
| Special cases | ANOVA, ANCOVA ANCOVA In statistics, analysis of covariance is a general linear model with a continuous outcome variable and two or more predictor variables where at least one is continuous and at least one is categorical . ANCOVA is a merger of ANOVA and regression for continuous variables... , MANOVA MANOVA Multivariate analysis of variance is a generalized form of univariate analysis of variance . It is used when there are two or more dependent variables. It helps to answer : 1. do changes in the independent variable have significant effects on the dependent variables; 2. what are the interactions... , MANCOVA MANCOVA Multivariate analysis of covariance is an extension of analysis of covariance methods to cover cases where there is more than one dependent variable and where the dependent variables cannot simply be combined.... , ordinary linear regression Linear regression In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression... , mixed model Mixed model A mixed model is a statistical model containing both fixed effects and random effects, that is mixed effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences.... , t-test, F-test F-test An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.It is most often used when comparing statistical models that have been fit to a data set, in order to identify the model that best fits the population from which the data were sampled. ... |
general linear model General linear model The general linear model is a statistical linear model.It may be written aswhere Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors or... , logistic regression Logistic regression In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial regression... , Poisson regression Poisson regression In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown... |
| Function in R R (programming language) R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis.... |
lm | glm |
| Function in Matlab | mvregress | glmfit |
| Procedure in SAS SAS System SAS is an integrated system of software products provided by SAS Institute Inc. that enables programmers to perform:* retrieval, management, and mining* report writing and graphics* statistical analysis... |
PROC GLM, PROC MIXED | PROC GENMOD (PROC LOGISTIC for logistic regression Logistic regression In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial regression... only) |