Difference between revisions of "Generalized linear model"
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Y = b<sub>0</sub> + b<sub>1</sub>X<sub>1</sub> + b<sub>2</sub>X<sub>2</sub> + ... + b<sub>k</sub>X<sub>k</sub> | Y = b<sub>0</sub> + b<sub>1</sub>X<sub>1</sub> + b<sub>2</sub>X<sub>2</sub> + ... + b<sub>k</sub>X<sub>k</sub> | ||
| − | In this [[equation]] b<sub>0</sub> is the [[regression analysis|regression]] [[coefficient]] for the intercept and the b<sub>i</sub> values are the regression | + | In this [[equation]] b<sub>0</sub> is the [[regression analysis|regression]] [[coefficient]] for the intercept and the b<sub>i</sub> values are the regression coefficients (for variables 1 through k) computed from the [[data]]."<ref>[http://www.statsoft.com/textbook/generalized-linear-models/ Generalized Linear Models]</ref> |
Whereas in classical linear models the variable Y is assumed to follow a normal distribution, generalized linear models consider more general distributions, such as a Poisson or a multinomial distribution, and are therefore applicable to a wider field of problems. | Whereas in classical linear models the variable Y is assumed to follow a normal distribution, generalized linear models consider more general distributions, such as a Poisson or a multinomial distribution, and are therefore applicable to a wider field of problems. | ||
Revision as of 19:29, January 3, 2012
The website statsoft.com offers this explanation of the generalized linear model:
"The Generalized Linear Model (GLZ) is a generalization of the general linear model (see, e.g., the General Linear Models, Multiple Regression, and ANOVA/MANOVA topics). In its simplest form, a linear model specifies the (linear) relationship between a dependent (or response) variable Y, and a set of predictor variables, the X's, so that
Y = b0 + b1X1 + b2X2 + ... + bkXk
In this equation b0 is the regression coefficient for the intercept and the bi values are the regression coefficients (for variables 1 through k) computed from the data."[1]
Whereas in classical linear models the variable Y is assumed to follow a normal distribution, generalized linear models consider more general distributions, such as a Poisson or a multinomial distribution, and are therefore applicable to a wider field of problems.