GLM模型1.pptVIP

2010-4-15 广义线性模型Generalized linear model 明确两个概念： 线性模型（linear model），也称经典线性模型（classical linear model）或一般线性模型（general linear model, GLM）。 广义线性模型（generalized linear model，GENMOD）是一般线性模型的直接推广，由Nelder Wedderburn(1972)首先提出。 SAS软件中的PROC GLM： PROC GLM analyzes data within the framework of general linear models. PROC GLM handles models relating one or several continuous dependent variables to one or several independent variables. The independent variables may be either classification variables or continuous variables. Thus, the GLM procedure can be used for many different analyses, including simple regression multiple regression analysis of variance (ANOVA), especially for unbalanced data analysis of covariance response-surface models (响应面模型) weighted regression polynomial regression (多项式回归) partial correlation multivariate analysis of variance (MANOVA) repeated measures analysis of variance SAS软件中的PROC GENMOD： The GENMOD Procedure The GENMOD procedure fits generalized linear models. The class of generalized linear models is an extension of traditional linear models that allows the mean of a population to depend on a linear predictor through a nonlinear link function and allows the response probability distribution to be any member of an exponential family of distributions. Many widely used statistical models are generalized linear models. These include classical linear models with normal errors, logistic and probit models for binary data, and log-linear models for multinomial data. Many other useful statistical models can be formulated as generalized linear models by the selection of an appropriate link function and response probability distribution. 一、何为“广义线性模型”？ 广义线性模型（generalized linear model）由Nelder Wedderburn(1972)首先提出，是一般线性模型的直接推广，它使因变量的总体均值通过一个非线性连接函数（link function）而依赖于线性预测值，同时还允许响应概率分布为指数分布族中的任何一员。许多广泛应用的统计模型均属于广义线性模型，如logistic回归模型、Probit回归模型、Poisson回归模型、负二项回归模型等。 指数分布族的概率密度（概率函数）可表示为： 何为“广义线性模型”？(续) 一个广义线性模型包括以下三个组成部分： （1）线性成分