[R-sig-ME] Connectedness of rows/columns of a matrix
Kevin Wright
kw.stat at gmail.com
Thu Jul 12 02:17:10 CEST 2012
Suppose I have data with two factors A and B that each have two
levels. If all combinations of the factors are observed, then an
incidence matrix showing combinations that are observed would look
like this:
b1 b2
a1 1 1
a2 1 1
If I then fit a (mixed) model like y ~ A + B, the effects are
generally estimable.
If, however, some combinations are not observed, so that the incidence
matrix looks like this:
b1 b2
a1 1 0
a2 0 1
then the A and B effects are aliased and non-estimable.
This is an extremely simple example, but sometimes when I am fitting
models which fail to converge, I dig into the data and find there is
not a connected path through the rows and columns of the incidence
matrix and (I assume) this is the cause of the non-estimability.
Two questions:
1. Is there a method to detect if the rows/columns of a matrix are
connected by at least one path through the matrix?
2. More generally, is there a measure of "connectedness" of the rows/columns?
3. Even more generally, what techniques do people use to diagnose
non-estimability?
Hope this is understandable and interesting.
Kevin Wright
--
Kevin Wright
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