[R] re: patterns of missing data: determining monotonicity

[Peter Dalgaard]

Michael Friendly <friendly at yorku.ca> writes:

> [Sorry for the re-post; my examples got garbled in the original cut/paste.]

I don't know about then but they sure are now!
 
> Here is a problem that perhaps someone out here has an idea about.  It
> vaguely reminds me of something
> I've seen before, but can't place.  Can anyone help?
> 
> For multiple imputation, there are simpler methods available if  the
> patterns of missing data are 'monotone' ---
> if Vj is missing then all variables Vk, k>j are also missing, vs. more
> complex methods required when the patterns are not monotone.  The
> problem is to determine if, for a collection of variables, there is an
> ordering of them with a monotone
> missing data pattern, or, if not, what the longest monotone sequence
> is.

Here's my take - no idea about implementation though.

You need to draw a directed graph.  Nodes are 1...n and the rule is
that if Vk is missing in a pattern, you draw an arrow from each j for
which Vj is nonmissing, to k. If this graph has no cycles, the
collection of patterns is monotone and there is a straightforward
method of putting them in order (pick a node with no ancestors,
remove it from the graph, repeat). A longest monotone sequence is
obtained by finding a maximal cycle-free subgraph. So it all reduces
to graph theory. 

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907