maxConnectedSet: Maximal connected set in a matrix

Description

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

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 leve

Value

msmaximal connected set as matrix or data frame, corresponding to the input.
maxlNumber of observations in the maximal connected data set.
nsetsNumber of connected data sets.
lsetsVector with number of observations in each connected data sets, i.e. lsets[i] is the number of observations in connected data set i.

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:

: X___.___.___.___X . . . : $\mid$ : . . X___.___!___.___.___X : $\mid$ $\mid$ : . X___.___.___!___X___X ! : $\mid$ $\mid$ $\mid$ : . X___.___.___!___X___X ! : $\mid$ $\mid$ : . . . . X . . ! : $\mid$ $\mid$ : . . X___.___!___.___.___X : $\mid$ : . . . X___X . . . 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.

References

Searle (1997) 'Linear Models'. Wiley. page 318.

Examples

Run this code

data(Searle)
	maxConnectedSet(Searle)

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