Chapter Contents |
Previous |
Next |
Fit Analyses |
In parametric regression, the linear model is given by
Let W be an n×n diagonal matrix consisting of weights w_{1}>0, w_{2}>0, ..., and w_{n}>0 for the observations, and let W^{1/2} be an n×n diagonal matrix with diagonal elements w_{1}^{1/2}, w_{2}^{1/2}, ..., and w_{n}^{1/2}.
The weighted fit analysis is equivalent to the usual (unweighted) fit analysis of the transformed model
The estimate of is then given by
For nonparametric weighted regression, the minimizing criterion in spline estimation is given by
In kernel estimation, individual weights are
For generalized linear models, the function for binomial distribution with m_{i} trials in the ith observation, for other distributions. The function is used to compute the likelihood function and the diagonal matrices W_{o} and W_{e}.
The individual deviance contribution d_{i} is obtained by multiplying the weight w_{i} by the unweighted deviance contribution. The deviance is the sum of these weighted deviance contributions.
The Pearson statistic is
Chapter Contents |
Previous |
Next |
Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.