Fits a two-way linear mixed model.
The model assumes the first factor f1 to be fixed and the second factor f2 to
be random. Errors are assumed to be i.i.d. No general mean and sum of
f2 is constrained to be zero.
Usage
pheno.mlm.fit(D)
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 set to 0.
Details
This function is basically a wrapper for the lme() function of
the nlme package, adapted for the estimation of combined
phenological time series. Estimation method: restricted maximum likelihood (REML)
In phenological application, 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.
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
fixed
Estimated fixed effects, in phenology this is precisely the combined time series.
fixed.lev
Levels of fixed effects. Should be the same order as fixed effects.
random
Estimated random effects, in phenology these are the station effects.
random.lev
Levels of random effects. Should be the same order as random effects.
SEf1
Standard error group f1, i.e. square root of variance component fixed effect.
SEf2
Standard error group f2, i.e. square root of variance component random effect.
lclf
Lower 95 percent confidence limit of fixed effects.
uclf
Upper 95 percent confidence limit of fixed effects.
D
The input as ordered data frame, ordered first by f2 then by f1
fit
The fitted lme model object.
Author(s)
Joerg Schaber
References
Searle (1997) 'Linear Models'. 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
lme
Examples
data(DWD)
R <- pheno.mlm.fit(DWD) # parameter estimation
plot(levels(factor(DWD[[2]])),R$fixed,type="l") # plot combined time series
tr <- lm(R$fixed~rank(levels(factor(DWD[[2]])))) # trend estimation
summary(tr)$coef[2] # slope of trend
summary(tr)$coef[4] # standard error of trend
providing 
.