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Version 5 (modified by Víctor de Buen Remiro, 14 years ago) (diff)

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  1. Package GrzLinModel
    1. Weighted Generalized Regresions
      1. Weighted Normal Regresion
      2. Weighted Poisson Regresion
      3. Weighted Qualitative Regresion

Package GrzLinModel

Max-likelihood and bayesian estimation of ​generalized linear models.

Weighted Generalized Regresions

Abstract class GrzLinModel::@WgtReg is the base to inherit weighted generalized linear regressions as poisson, binomial, normal or any other, given just the scalar link function g and the density function f .

In a weighted regression each row of input data has a distinct weight in the likelihood function. For example, it can be very usefull to handle with data extrated from an stratified sample.

Let be

  • X\in\mathbb{R}^{m\times n} the regression input matrix
  • w\in\mathbb{R}^{m} the vector of weights of each register
  • y\in\mathbb{R}^{m} the regression output matrix
  • \beta\in\mathbb{R}^{n} the regression coefficients
  • \eta=X\beta\in\mathbb{R}^{n} the linear prediction
  • g the link function
  • f the density function of a distribution of the ​exponential family

Then we purpose that the average of the output is the inverse of the link function applyied to the linear predictor

E\left[y\right]=\mu=g^{-1}\left(X\beta\right)

The density function becomes as a real valuated function of at least two parameters

f\left(y_{k};\mu_{k}\right)

the output y_k and the average

\mu_{k}=g^{-1}\left(\eta_{k}\right)=g^{-1}\left(x_{k}\beta\right)

for each row k=1 \dots n:

Weighted Normal Regresion

Is implemented in GrzLinModel::@WgtNormal There is a sample of use in test_0001/test.tol

Weighted Poisson Regresion

It will be implemented in GrzLinModel::@WgtPoisson but is not available yet.

Weighted Qualitative Regresion

For boolean and qualitative response outputs like logit or probit there is an specialization on package QltvRespModel