Table 1 Difference between linear model and generalized model
From: Survey on clinical prediction models for diabetes prediction
S. no | Simple linear model | Generalized linear models |
|---|---|---|
1 | μ = E(Y) = β0 + β1 * X1 + β2 * X2+ ··· + βn*Xn | g(μ) = β0 + β1 * X1 + β2 * X2+ ··· + βn*Xn |
2 | Target variable Y does not depend on the value of Y for any other record, only the predictors | Target variable Y does not depend on the value of Y for any other record, only the predictors |
3 | Y is normally distributed | Distribution of Y is a member of the exponential family of distributions(normal, Poisson, gamma, binomial, negative binomial, inverse Gaussian) |
4 | Mean of Y depends on the predictors, but all records have the same variance | Variance of Y is a function of the mean of Y |
5 | Y is related to predictors through simple linear function | g(μ) is linearly related to the predictors. The function g is called the link function |