Finds connected data set, i.e. connected rows and columns
of a numeric matrix M, that has the largest number of data entries.
Usage
maxConnectedSet(M)
Arguments
M
Numeric matrix with missing values considered as 0, or
a data frame. The data frame is internally converted to a matrix
and should have three columns (x, factor 1, factor 2) where
x are considered the entries of the matrix, rows correspond to
levels of factor 2 and columns correspond to levels of factor 1.
Details
In a two-way classification of linear models sometimes independent
sets of normal equations are obtained due to missing data in the
experiments design, i.e. the complete design matrix is not of full rank
and thus no solution can be found. However, solutions of the independent
sets of normal equations can still exist.
This phenomenon is called 'connectedness' of the data.
Especially in phenological analysis experimental designs are almost
always unbalanced because of missing data. Thus, when combined time
series are to be estimated, it is worth checking for and finding
connected data sets for which combined time series can then be estimated.
This can also be interpreted in the way that a prerequisite to obtain
a combined time series is to have overlapping time series.
Example (also see example data(Searle) from Searle (1997), page 324 and
example in 'connectedSets'):
In the following matrix dots represent missing values, X represent observations
and the lines join the connected sets:
Thus, in this matrix observations of rows 1, 5 and 7 or colums 1, 4 and 5 form
one connected set. Likewise observations of rows 2 and 6 (or columns 3 and 8)
and rows 3 and 4 (or columns 2, 6 and 7) form also connected sets, respectively.
Value
ms
maximal connected set as matrix or data frame, corresponding to the input.
maxl
Number of observations in the maximal connected data set.
nsets
Number of connected data sets.
lsets
Vector with number of observations in each connected data sets, i.e. lsets[i] is the number of observations in connected data set i.