prms: Partial robust M regression

In sprm: Sparse and Non-Sparse Partial Robust M Regression and Classification

Description

Partial robust M regression for models with univariate response. This method for dimension reduction and regression analysis yields estimates with a partial least squares alike interpretability that are robust to both vertical outliers and leverage points.

Usage

prms(formula, data, a, fun = "Hampel", probp1 = 0.95, hampelp2 = 0.975, 
hampelp3 = 0.999, center = "median", scale = "qn", usesvd = FALSE, 
numit = 100, prec = 0.01)

Arguments

formula	an object of class formula.
data	a data frame or list which contains the variables given in formula.
a	the number of PRMS components to be estimated in the model.
fun	an internal weighting function for case weights. Choices are "Hampel" (preferred), "Huber" or "Fair".
probp1	the 1-alpha value at which to set the first outlier cutoff for the weighting function.
hampelp2	the 1-alpha values for second cutoff. Only applies to fun="Hampel".
hampelp3	the 1-alpha values for third cutoff. Only applies to fun="Hampel".
center	type of centering of the data in form of a string that matches an R function, e.g. "mean" or "median".
scale	type of scaling for the data in form of a string that matches an R function, e.g. "sd" or "qn" or alternatively "no" for no scaling.
usesvd	logical, default is FALSE. If TRUE singular value decomposition is performed.
numit	the number of maximal iterations for the convergence of the coefficient estimates.
prec	a value for the precision of estimation of the coefficients.

Details

The NIPLS algorithm combined with weighted regression is used for the model estimation.

a is the number of components in the model. Note that it is not possible to simply reduce the number of weighting vectors to obtain a model with a smaller number of components. Each model has to be estimated separately due to its dependence on robust case weights.

Value

prms returns an object of class prm.

Functions summary, predict and plot are available. Also the generic functions coefficients, fitted.values and residuals can be used to extract the corresponding elements from the prm object.

coefficients	vector of coefficients of the weighted regression model.
intercept	intercept of weighted regression model.
wy	the case weights in the y space.
wt	the case weights in the score space.
w	the overall case weights used for weighted regression (depending on the weight function). w=wy*wt.
scores	the matrix of scores.

R	Direction vectors (or weighting vectors or rotation matrix) to obtain the scores. scores=Xs%*%R.
loadings	the matrix of loadings.
fitted.values	the vector of estimated response values.
residuals	vector of residuals, true response minus estimated response.
coefficients.scaled	vector of coefficients of the weighted regression model with scaled data.
intercept.scaled	intercept of weighted regression model with scaled data.
YMeans	value used internally to center response.
XMean	vector used internally to center data.
Xscales	vector used internally to scale data.
Yscales	value used internally to scale response.
Yvar	percentage of contribution for each component to the explanation of the variance of the response.
Xvar	percentage of contribution for each component to the explanation of the variance of the variables.
inputs	list of inputs: parameters, data and scaled data.

Author(s)

Sven Serneels, BASF Corp and Irene Hoffmann

References

Hoffmann, I., Serneels, S., Filzmoser, P., Croux, C. (2015). Sparse partial robust M regression. Chemometrics and Intelligent Laboratory Systems, 149, 50-59.

Serneels, S., Croux, C., Filzmoser, P., Van Espen, P.J. (2005). Partial Robust M-Regression. Chemometrics and Intelligent Laboratory Systems, 79, 55-64.

See Also

prmsCV, plot.prm, biplot.prm, predict.prm, sprms

Examples

set.seed(5023)
U <- c(rep(2,20), rep(5,30))
X <- replicate(6, U+rnorm(50))
beta <- c(rep(1, 3), rep(-1,3))
e <- c(rnorm(45,0,1.5),rnorm(5,-20,1))
y <- X%*%beta + e
d <- as.data.frame(X)
d$y <- y
mod <- prms(y~., data=d, a=2, fun="Hampel")
summary(mod)

Example output

Loading required package: ggplot2
Partial M-robust regression 
 Number of components:  2
 weight function:  Hampel with cutoff 0.95 0.975 0.999

Percentage of explained variance
                              X        y
With  1  component(s): 55.03667 24.25559
With  2  component(s): 75.00504 69.97580

sprm documentation built on May 2, 2019, 9:57 a.m.