Use lmsreg with a formula Object

DESCRIPTION:

Performs least median of squares regression. This is a method for the function lmsreg for formula objects.

USAGE:

lmsreg.formula(formula, data=<<see below>>, weights, subset=<<see below>>, 
               na.action=na.fail, model=F, x=F, y=F, nsamp="standard", 
               wt=T, diagnostic=F, quan=<<see below>>, mve=T) 

REQUIRED ARGUMENTS:

formula
a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right.

OPTIONAL ARGUMENTS:

data
a data frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases -- see below for details.
subset
expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector which is replicated to have length equal to the number of observations, a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.
na.action
a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.exclude, which deletes observations that contain one or more missing values.
model
logical flag: if TRUE, the model frame is returned in component model.
x
logical flag: if TRUE, the model matrix is returned in component x.
y
logical flag: if TRUE, the response is returned in component y.
nsamp
either a positive integer or the character strings "all" or "standard". If numeric, this specifies the number of non-singular random subsamples of the observations that are to be used. If nsamp="all", then all subsamples are to be found. Note that this can be a very large number even for quite small datasets. There are n-choose-p subsamples, where n is the number of observations and p is the number of explanatory variables. The default ( nsamp="standard") is to take all of the subsamples if there are less than 3000, and to find 3000 non-singular random samples otherwise.
diagnostic
logical flag: if TRUE and if p>1, resistant diagnostics are returned. p is the number of explanatory variables.
quan
the amount of observations that ought to be considered as a "half". The default value is floor(n/2) + floor((p+1)/2), where n is the number of observations and p is the number of explanatory variables.
mve
logical flag: if TRUE, cov.mve will be called on x. The results are needed in plot.lms for the diagnostic plot.

VALUE:

a list of class "lms" giving the solution. See the lms.object help file for details.

DETAILS:

The formula argument is passed around unevaluated ;that is, the variables mentioned in the formula will be defined when the model frame is computed, not when lmsreg is initially called. In particular, if data is given, all these names should generally be defined as variables in that data frame.

The subset argument, like the terms in formula, is evaluated in the context of the data frame, if present. The specific action of the argument is as follows: the model frame, including weights and subset, is computed on allthe rows, and then the appropriate subset is extracted. A variety of special cases make such an interpretation desirable (e.g., the use of lag or other functions that may need more than the data used in the fit to be fully defined). On the other hand, if you meant the subset to avoid computing undefined values or to escape warning messages, you may be surprised. For example, lmsreg(y ~ log(x), mydata, subset = x > 0) will still generate warnings from log. If this is a problem, do the subsetting on the data frame directly: lmsreg(y ~ log(x), mydata[,mydata$x > 0]) lmsreg.default is called when the model frame has been computed. See the lmsreg.default help file for details on the computational algorithm.

NAMES. Variables occurring in a formula are evaluated differently from arguments to S-PLUS functions, because the formula is an object that is passed around unevaluated from one function to another. The functions such as lmsreg.formula that finally arrange to evaluate the variables in the formula try to establish a context based on the data argument. (More precisely, the function model.frame.default does the actual evaluation, assuming that its caller behaves in the way described here.) If the data argument to lmsreg.formula is missing or is an object (typically, a data frame), then the local context for variable names is the frame of the function that called lmsreg.formula, or the top-level expression frame if the user called lmsreg.formula directly. Names in the formula can refer to variables in the local context as well as global variables or variables in the data object.

The data argument can also be a number, in which case that number defines the local context. This can arise, for example, if a function is written to call lmsreg.formula, perhaps in a loop, but the local context is definitely notthat function. In this case, the function can set data to sys.parent(), and the local context will be the next function up the calling stack. See the second example below. A numeric value for data can also be supplied if a local context is being explicitly created by a call to new.frame. Notice that supplying data as a number implies that this is the onlylocal context; local variables in any other function will not be available when the model frame is evaluated. This is potentially subtle. Fortunately, it is not something the ordinary user of lmsreg.formula needs to worry about. It is relevant for those writing functions that call lmsreg.formula or other such model-fitting functions.

REFERENCES:

Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association , 79, 871-88.

Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection. New York: Wiley.

SEE ALSO:

, , , , , , .

EXAMPLES:

lmsreg(ozone~wind+radiation+temperature, nsamp="all", data=air) 
stacklms <- lmsreg(stack.loss~stack.x, nsamp="all") 

# Reweighted least squares 
stackrls <- lm(stack.loss~stack.x, weights=as.logical(stacklms$lms.wt))