Hey all, what tools can one use on data that has so many missing values?
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Consultant  Rescuer of Doomed Projects; Solver of Impossible Problems; Inspired by Sharing How to Do It AllDavid,
You made a comment above " If you're talking about more than half the data set, then you may be out of luck."
It really depends on what the data are and how the missing data are "missing." You can get good usable estimates with 100% of the data missing if you have the right kind of data and the right kind of "missing." It is all in the formulation of the likelihood.
Mark Powell 
Consultant  Rescuer of Doomed Projects; Solver of Impossible Problems; Inspired by Sharing How to Do It AllDavid,
Let me correct myself, you can always do a prior predictive estimate without any data at all, even without any missing data.
Mark Powell 
Scientist at JOANNEUM RESEARCH Forschungsgesellschaft mbHI like the R package VIM: Visualization and Imputation of Missing Values (http://cran.rproject.org/web/packages/VIM/index.html). Especially the graphics can really help on understanding the structure of missing values. The package also comes with an optional graphical user interface.
There are also some good manuals and explanations around in the web (e.g. http://www.unece.org/fileadmin/DAM/stats/documents/ece/ces/ge.44/2014/mtg1/Topic_5_Austria.pdf). 
Research and Data Analytics SpecialistBtw, do any you have any sources to recommend on missing (at random) data in directed social network? Thanks.
Gelman et al, "Bayesian Data Analysis," also has a great chapter on missing data, and will be consistent with the references David recommended.
Mark Powell
I usually just go to Amazon.com. All of the references suggested by me and David are available there.
Mark Powell
http://www.stat.columbia.edu/~gelman/arm/missing.pdf
You could check also "The BUGS Book" by Lunn et al ( http://www.amazon.co.uk/BUGSBookPracticalIntroductionStatistical/dp/1584888490/ ) it also gives some hints on missing data in Bayesian approach.