pheno.lad.fit {pheno}

Fits a robust two-way linear model

Description

Fits a robust two-way linear model. The model assumes both factors (f1 and f2) to be fixed. Errors are assumed to be i.i.d. No general mean and sum of f2 is constrained to be zero.

Usage

pheno.lad.fit(D,limit=1000)

Arguments

D

Data frame with three columns (x, f1, f2) or a matrix where rows are ranks of factor f1 levels and columns are ranks of factor f2 levels and missing values are assumed to be NA or 0.

limit

Integer that determines which algorithm to use (see Details).

Details

The function minimizes the least absolute deviations (LAD or L1 norm) of the residuals of a two-way linear model. This function is basically a wrapper for the rq.fit() or rq.fit.sfn() functions of the quantreg package, respectively, adapted for the estimation of combined phenological time series. Depending on the size of the problem length(x)<=limit either the rq.fit() function using the Barrodale-Roberts algorithm is used or (length(x)>1000) the corresponding dense matrix implementation with rq.fit.sfn() using the Interior-Point method. In phenological applications, x should be the julian day of observation of a certain phase, factor f1 should be the observation year and factor f2 should be a station-id. For efficiency reasons, the linear model is calcualted for treatment contrasts and the constraint that the sum of f2 is zero, is adjusted afterwards. Note that the input data is sorted before fitting, such that subsequent analyses using the input data should be done using the sorted output data frame.

Value

f1

Estimated parameters of factor f1, in phenology this is precisely the combined time series.

f1.lev

Levels of f1. Should be the same order as f1.

f2

Estimated parameters of factor f2, in phenology these are precisely the station effects.

f2.lev

Levels of f2. Should be the same order as f2.

resid

Residuals

ierr

For length(x) > 1000 this is the return error code of rq.fit.sfn()

D

The input as ordered data frame, ordered first by f2 then by f1

fit

The fitted rq.fit model object.

Author(s)

Joerg Schaber

References

Rousseeuw PJ, Leroy AM (1987) 'Robust estimation and outlier detection'. Wiley. Schaber J, Badeck F-W (2002) 'Evaluation of methods for the combination of phenological time series and outlier detection'. Tree Physiology 22:973-982

See Also

rq.fit rq.fit.sfn

Examples

	data(DWD)
	R <- pheno.lad.fit(DWD)				# robust parameter estimation
	plot(levels(factor(R$D[[2]])),R$p1,type="l")	# plot combined time series
	R$D[R$resid >= 30,]				# observation whose residuals
							# are > 30 days (outliers)