cubinf: Conditionally unbiased bounded influence estimates of...

In robcbi: Conditionally Unbiased Bounded Influence Estimates

Conditionally unbiased bounded influence estimates of discrete Generalized Linear Models

Description

Conditionally unbiased bounded influence estimates as described in Kuensch et al. (1989) in three special GLM cases: Bernoulli, Binomial, and Poisson distributed responses. The result is an object of class "cubinf".

Usage

cubinf(x, y, weights = NULL,  start=NULL, etastart=NULL, mustart=NULL,
       offset = NULL, family = binomial(), control = cubinf.control(...),  
       intercept = FALSE, ...)

Arguments

x	Vector or matrix of explanatory variable(s). Columns represent variables and rows are observations.
y	Vector of observed responses. In the case of Binomial responses, y is a two column matrix: the 1st column contains the number of successes, the 2nd column the number of failures. The Bernoulli case, is treated as a special Binomial case. However, the response y is a categorical variable (not a matrix with two colums) with two levels.
weights	Optional weigths for weighted regression. Components must be non negative integers.
start	Starting values for the parameters in the linear predictor. Not used but required for compatibility with the glm function.
etastart	Starting values for the linear predictor. Not used but required for compatibility with the glm function.
mustart	Starting values for the vector of means. Not used but required for compatibility with the glm function.
offset	Optional offset added to the linear predictor.
family	A family object. Only two options are available for cubinf: 'family=binomial()' and 'family=poisson()'.
control	A list of control parameters for the numerical algorithms. See cubinf.control for the possible control parameters and their defaults.
intercept	Logical flag: if TRUE, an intercept term is added to the model.
...	Further named control arguments as singular.ok or qr.out used in the case where the x matrix is singular.

Details

The initial values of the coefficients (theta), the matrix A and the bias correction c are computed using the ROBETH subroutine GINTAC (Marazzi, 1993). Then an initial covariance matrix (for the convergence criterion) is computed by means of the ROBETH subroutines GFEDCA and KTASKW. Finally, the main algorithm (subroutine GYMAIN) alternates between improving values of - theta, for fixed A and c (theta-step, subroutine GYTSTP), - c, for fixed theta and A (c-step, subroutine GYCSTP), - A, for fixed theta and c (A-step, subroutine GYASTP).

For the different available options see the function cubinf.control.

Value

A list with the following components:

coefficients	Coefficient estimates.
residuals	Working residuals.
rsdev	Deviance residuals.
fitted.values	Fitted values.
cov	Estimated covariance matrix of the coefficients.
rank	Rank of the model matrix.
df.residuals	Degrees of freedom in the residuals.
ci	Vector of final bias corrections.
A	Final value of the matrix A.
ai	Vector with components a_i=ufact/|Ax_i| (where x_i^T denotes the ith row of the model matrix)
converged	A logical value. FALSE if the maximum number of iterations was reached.
control	Control parameters.
prior.weights	Input vector w (when some of its components are different from 1).
family	The family object used in the call to cubinf 'ics=1' for the Bernoulli case. 'ics=2' for the Binomial case. 'ics=3' for the Poisson case.
linear.predictors	Components of the linear predictor (the model matrix multiplied by the coefficient vector).
iter	Number of iterations required in the main algorithm.
y	Coded value of the response.
gradient	Vector of the final unscaled negative gradient of the objective function.
inv.hessian	Vector of the final inverse of the Hessian matrix in compact storage mode.

References

Kuensch, H.R., Stefanski L.A., Carroll R.J. (1989). Conditionally unbiased bounded-influence estimation in general regression models, with application to generalized linear models. Journal of the American Statistical Association, 84, 460-466.

Marazzi, A. (1993). Algorithms, Routines, and S-functions for robust Statistics. Chapman and Hall, New York.

See Also

glm(..., method="cubinf"), cubinf.control

Examples

  library(robcbi)
  y <- c(5,10,15,20,30,40,60,80,100)
  x <- matrix(
	c(0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1),
    nrow=9,byrow=FALSE)
  z <- cubinf(x,y, family=poisson, control=list(ufact=3.2), intercept=TRUE)
  z$iter
  z$coeff
  z <- cubinf(x,y, family=poisson, control=list(ufact=30), intercept=TRUE)
  z$iter
  z$coeff

robcbi documentation built on Aug. 22, 2023, 1:06 a.m.