loessfit: Univariate Lowess With Prior Weights
In limma: Linear Models for Microarray Data

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Univariate locally weighted linear regression allowing for prior weights. Returns fitted values and residuals.

1 2	loessFit(y, x, weights=NULL, span=0.3, iterations=4L, min.weight=1e-5, max.weight=1e5, equal.weights.as.null=TRUE, method="weightedLowess")

`y`	numeric vector of response values. Missing values are allowed.
`x`	numeric vector of predictor values Missing values are allowed.
`weights`	numeric vector of non-negative prior weights. Missing values are treated as zero.
`span`	positive numeric value between 0 and 1 specifying proportion of data to be used in the local regression moving window. Larger numbers give smoother fits.
`iterations`	number of local regression fits. Values greater than 1 produce robust fits.
`min.weight`	minimum weight. Any lower weights will be reset.
`max.weight`	maximum weight. Any higher weights will be reset.
`equal.weights.as.null`	should equal weights be treated as if weights were `NULL`, so that `lowess` is called? Applies even if all weights are all zero.
`method`	method used for weighted lowess. Possibilities are `"weightedLowess"`, `"loess"` or `"locfit"`.

This function is essentially a wrapper function for lowess and weightedLowess with added error checking. The idea is to provide the classic univariate lowess algorithm of Cleveland (1979) but allowing for prior weights and missing values.

The venerable lowess code is fast, uses little memory and has an accurate interpolation scheme, so it is an advantage to use it when prior weights are not needed. This functions calls lowess when weights=NULL, but returns values in original rather than sorted order and allows missing values. The treatment of missing values is analogous to na.exclude.

By default, weights that are all equal (even all zero) are treated as if they were NULL, so lowess is called in this case also.

When unequal weights are provided, this function calls weightedLowess by default, although two other possibilities are also provided. weightedLowess implements a similar algorithm to lowess except that it uses the prior weights both in the local regressions and in determining which other observations to include in the local neighbourhood of each observation.

Two alternative algorithms for weighted lowess curve fitting are provided as options. If method="loess", then a call is made to loess(y~x,weights=weights,span=span,degree=1,family="symmetric",...). This method differs from weightedLowess in that the prior weights are ignored when determining the neighbourhood of each observation.

If method="locfit", then repeated calls are made to locfit:::locfit.raw with deg=1. In principle, this is similar to "loess", but "locfit" makes some approximations and is very much faster and uses much less memory than "loess" for long data vectors.

The arguments span and iterations here have the same meaning as for weightedLowess and loess. span is equivalent to the argument f of lowess while iterations is equivalent to iter+1 for lowess. It gives the total number of fits rather than the number of robustifying fits.

When there are insufficient observations to estimate the loess curve, loessFit returns a linear regression fit. This mimics the behavior of lowess but not that of loess or locfit.raw.

A list with components

`fitted`	numeric vector of same length as `y` giving the loess fit
`residuals`	numeric vector of same length as `x` giving residuals from the fit

With unequal weights, "loess" was the default method prior to limma version 3.17.25. The default was changed to "locfit" in limma 3.17.25, and then to "weightedLowess" in limma 3.19.16. "weightedLowess" will potentially give somewhat different results to the older algorithms because the local neighbourhood of each observation is determined differently (more carefully).

Gordon Smyth

Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74, 829-836.

If weights=NULL, this function calls lowess. Otherwise it calls weightedLowess, locfit.raw or loess. See the help pages of those functions for references and credits.

Compare with loess in the stats package.

See 05.Normalization for an outline of the limma package normalization functions.

x <- (1:100)/101
y <- sin(2*pi*x)+rnorm(100,sd=0.4)
out <- loessFit(y,x)
plot(x,y)
lines(x,out$fitted,col="red")

# Example using weights

y <- x-0.5
w <- rep(c(0,1),50)
y[w==0] <- rnorm(50,sd=0.1)
pch <- ifelse(w>0,16,1)
plot(x,y,pch=pch)
out <- loessFit(y,x,weights=w)
lines(x,out$fitted,col="red")