fsdaR (version 0.4-9)

fsreg: fsreg: an automatic outlier detection procedure in linear regression

Description

An automatic outlier detection procedure in linear regression

Usage

fsreg(x, …) 
# S3 method for formula
fsreg(formula, data, subset, weights, na.action,
       model = TRUE, x.ret = FALSE, y.ret = FALSE,
       contrasts = NULL, offset, …)
# S3 method for default
fsreg(x, y, bsb, intercept = TRUE, 
        family = c("homo", "hetero", "bayes"),
		method = c("FS", "S", "MM", "LTS", "LMS"),
        monitoring = FALSE, control, 
        …)

Arguments

formula

a formula of the form y ~ x1 + x2 + ....

data

data frame from which variables specified in formula are to be taken.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. NOT USED YET.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The “factory-fresh” default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

model, x.ret, y.ret

logicals indicating if the model frame, the model matrix and the response are to be returned, respectively.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. An offset term can be included in the formula instead or as well, and if both are specified their sum is used.

family

family of robust regression models, can be 'homo' for homoscedastic (same variance) regression model, 'hetero' for heteroskedastic regression model or 'bayes' Bayesian linear regression. The default is family='homo' for homoscedastic regression model.

method

robust regression estimation model, can be 'FS' for Forward search, 'S' for S regression, 'MM' for MM regression, 'LMS' or 'LTS'. The default is method='FS' for forward search estimation.

monitoring

wheather to perform monitoring for several quantities in each step of the forward search or for series of values of the breakdown point in case of S estimates or for series of values of the efficiency in case of MM estimates. Deafault is monitoring=FALSE.

y

Response variable. Vector. Response variable, specified as a vector of length n, where n is the number of observations. Each entry in y is the response for the corresponding row of X. Missing values (NA's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

x

Predictor variables. Matrix. Matrix of explanatory variables (also called 'regressors') of dimension n x (p-1) where p denotes the number of explanatory variables including the intercept. Rows of X represent observations, and columns represent variables. By default, there is a constant term in the model, unless you explicitly remove it using input option intercept=FALSE, so do not include a column of 1s in X. Missing values (NA's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

bsb

Initial subset - vector of indices. If bsb=0 (default) then the procedure starts with p units randomly chosen. If bsb is not 0 the search will start with m0=length(bsb).

intercept

Indicator for constant term. Scalar. If intercept=TRUE, a model with constant term will be fitted (default), else, no constant term will be included.

control

A control object (SS) containing estimation options. If the control object is supplied, the parameters from it will be used. If parameters are passed also in the invocation statement, they will override the corresponding elements of the control object.

…

potential further arguments passed to lower level functions.

Value

Depending on the input parameters family and method, one of the following objects will be returned:

1. fsr.object

2. sreg.object

3. mmreg.object

4. fsdalms.object

5. fsdalts.object

6. fsreda.object

7. sregeda.object

8. mmregeda.object

References

Riani, M., Atkinson A.C., Cerioli A. (2009). Finding an unknown number of multivariate outliers. Journal of the Royal Statistical Society Series B, Vol. 71, pp. 201-221.

Examples

# NOT RUN {
    
# }
# NOT RUN {
    n <- 200
    p <- 3
    
    X <- matrix(data=rnorm(n*p), nrow=n, ncol=p)
    y <- matrix(data=rnorm(n*1), nrow=n, ncol=1)
    (out = fsreg(X, y))

    ## Now we use the formula interface:
    (out1 = fsreg(y~X, control=FSR_control(plot=FALSE)))

    ## Or use the variables in a data frame
    (out2 = fsreg(Y~., data=hbk, control=FSR_control(plot=FALSE)))

    ## let us compare to the LTS solution
    (out3 = ltsReg(Y~., data=hbk))
    
    ## Now compute the model without intercept
    (out4 = fsreg(Y~.-1, data=hbk, control=FSR_control(plot=FALSE)))
    
    ## And compare again with the LTS solution
    (out5 = ltsReg(Y~.-1, data=hbk))

    ## using default (optional arguments)        
    (out6 = fsreg(Y~.-1, data=hbk, control=FSR_control(plot=FALSE, nsamp=1500, h=50)))
    
# }