slm function

Fit a linear regression model using sparse matrix algebra

This is a function to illustrate the use of sparse linear algebra to solve a linear least squares problem using Cholesky decomposition. The syntax and output attempt to emulate lm() but may fail to do so fully satisfactorily. Ideally, this would eventually become a method for lm. The main obstacle to this step is that it would be necessary to have a model.matrix function that returned an object in sparse csr form. For the present, the objects represented in the formula must be in dense form. If the user wishes to specify fitting with a design matrix that is already in sparse form, then the lower level function slm.fit() should be used.

slm(formula, data, weights, na.action, method = "csr", contrasts = NULL, ...)

Arguments

• formula: a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right. As in lm(), the response variable in the formula can be matrix valued.
• 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.
• weights: vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous.
• 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.omit, which deletes observations that contain one or more missing values.
• method: there is only one method based on Cholesky factorization
• contrasts: a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels.
• ...: additional arguments for the fitting routines

Returns

A list of class slm consisting of: - coefficients: estimated coefficients

• chol: cholesky object from fitting

• residuals: residuals

• fitted: fitted values

• terms: terms

• call: call

...

References

Koenker, R and Ng, P. (2002). SparseM: A Sparse Matrix Package for ,

http://www.econ.uiuc.edu/~roger/research/home.html

Author(s)

Roger Koenker

See Also

slm.methods for methods summary, print, fitted, residuals and coef associated with class slm, and slm.fit for lower level fitting functions. The latter functions are of special interest if you would like to pass a sparse form of the design matrix directly to the fitting process.

Examples

data(lsq)
X <- model.matrix(lsq) #extract the design matrix
y <- model.response(lsq) # extract the rhs
X1 <- as.matrix(X)
slm.time <- system.time(slm(y~X1-1) -> slm.o) # pretty fast
lm.time <- system.time(lm(y~X1-1) -> lm.o) # very slow
cat("slm time =",slm.time,"\n")
cat("slm Results: Reported Coefficients Truncated to 5  ","\n")
sum.slm <- summary(slm.o)
sum.slm$coef <- sum.slm$coef[1:5,]
sum.slm
cat("lm time =",lm.time,"\n")
cat("lm Results: Reported Coefficients Truncated to 5  ","\n")
sum.lm <- summary(lm.o)
sum.lm$coef <- sum.lm$coef[1:5,]
sum.lm