Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/GSest_multireg.R
Computes GS-Estimates of multivariate regression based on Tukey's biweight function.
1 2 3 4 5 6 |
formula |
an object of class |
data |
data frame from which variables specified in formula are to be taken. |
X |
a matrix or data frame containing the explanatory variables. |
Y |
a matrix or data frame containing the response variables. |
int |
logical: if |
bdp |
required breakdown point. Should have 0 < |
control |
a list with control parameters for tuning the computing algorithm, see |
na.action |
a function which indicates what should happen when the data contain NAs. Defaults to |
... |
allows for specifying control parameters directly instead of via |
Generalized S-estimators are defined by minimizing the determinant of a robust estimator of the scatter matrix of
the differences of the residuals. Hence, this procedure is intercept free and only gives an estimate for the slope matrix. To estimate
the intercept, we use the M-type estimator of location of Lopuhaa (1992) on the residuals with the residual scatter matrix
estimate of the residuals as a preliminary estimate. We use a fast algorithm similar to the one proposed by Salibian-Barrera
and Yohai (2006) for the regression case. See GScontrol
for the adjustable tuning parameters of this algorithm.
The returned object inherits from class mlm
such that the standard coef
, residuals
, fitted
and predict
functions can be used.
An object of class FRBmultireg
which extends class mlm
and contains at least the following components:
coefficients |
GS-estimates of the regression coefficients |
residuals |
the residuals, that is response minus fitted values |
fitted.values |
the fitted values. |
Sigma |
GS-estimate of the error covariance matrix |
Gamma |
GS-estimate of the error shape matrix |
scale |
GS-estimate of the size of the multivariate errors |
weights |
implicit weights corresponding to the GS-estimates (i.e. final weights in the RWLS procedure for the intercept estimate) |
outFlag |
outlier flags: 1 if the robust distance of the residual exceeds the .975 quantile of (the square root of) the chi-square distribution with degrees of freedom equal to the dimension of the responses; 0 otherwise |
b,c |
tuning parameters used in Tukey biweight loss function, as determined by |
method |
a list with following components: |
control |
a copy of the |
Ella Roelant, Gert Willems and Stefan Van Aelst
H.P. Lopuhaa (1992) Highly efficient estimators of multivariate location with high breakdown point. The Annals of Statistics, 20, 398-413.
E. Roelant, S. Van Aelst and C. Croux (2009) Multivariate Generalized S-estimators. Journal of Multivariate Analysis, 100, 876–887.
M. Salibian-Barrera and V. Yohai (2006) A fast algorithm for S-regression estimates. Journal of Computational and Graphical Statistics, 15, 414-427.
S. Van Aelst and G. Willems (2013). Fast and robust bootstrap for multivariate inference: The R package FRB. Journal of Statistical Software, 53(3), 1–32. URL: http://www.jstatsoft.org/v53/i03/.
diagplot.FRBmultireg
, FRBmultiregGS
, GSboot_multireg
, Sest_multireg
, GScontrol
1 2 3 4 5 6 | data(schooldata)
school.x <- data.matrix(schooldata[,1:5])
school.y <- data.matrix(schooldata[,6:8])
GSest <- GSest_multireg(school.x,school.y,nsamp=50)
# or using the formula interface
## Not run: GSests <- GSest_multireg(cbind(reading,mathematics,selfesteem)~., data=schooldata)
|
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