Whether to use factor analysis based on binary multiple response data? I have a survey where I have asked people which type of computer games they enjoy and whether they consider themselves a hardcore gamer. I allowed people to select multiple genres, but now I am unsure what to do with my data.
I initially thought factor analysis, with the idea being if there were genres that belonged to a particular type, they would separate out and I would be able to see a pattern. However, since I have the data on whether they consider themselves hardcore or not, it seems like I should use it.
If I did use it, would it make sense to test each genre individually, e.g. RTS-hardcore vs. RTS-non-hardcore, or should I look into combinations of genres?

[EDIT] @Srikant: Yes, I was planning to make the answers binary. It didn't make sense to me to score different answers with values depending on say the number of genres somebody chose, because they might not necessarily play each game evenly, and I would have no way to determine what ratio of gameplay each genre had, so binary seemed the most fair to me.
@mbq & @chl: The aim is just to see if certain genres tend to be more "hardcore" than other genres. I was expecting to find RTS, MOBA and FPS to cluster towards hardcore seeing as they tend to have a higher learning curve than say music/rhythm games.
 A: The first step is to define your research question.
A few possible research questions given your data include:


*

*How can genres of video games be grouped into a smaller set?

*How are genres of video games or groups of genres related to self-identifying as a hard-core gamer?


Then, you could present a table of frequencies and percentages of genre by hard-core gamer status.
You could also divide the analysis into two steps:


*

*grouping types of video games; this could be done conceptually (e.g., based on prior knowledge of ways of grouping gaming genres) or using a data driven approach such as PCA, factor analysis (perhaps on tetrachoric correlations)

*examine differences in endorsement of video gram types across hard-core gamer category.


As mentioned by Brandon correspondence analysis would also be another nice option.
A: Correspondence analysis might be a good fit. Creating a graph that shows the relationship between Hard-Core gaming (or not) and the different types of games that they are playing. The result would be the ability to say with cautious confidence that Hard Core Gamers play a certain group of game types (or not). 
With respect to factor analysis, I would recommend reviewing some of the answers to a question I asked previously, just so you're clear on what your goal is: 
What are the differences between Factor Analysis and Principal Component Analysis?
Interpreting and creating correspondence analysis plots is discussed here (with examples on how to create the plots as well, pay strict attention to the differences in taking inference from horizontal and vertical axis distances) 
Interpreting 2D correspondence analysis plots
A: As an alternative to CA suggested by @Brandon, you could also try Multiple Correspondence Analysis which has the advantage of considering all types of games at the same time (unlike CA), which are probably scored as binary variable (in this case, the MCA solution will be close to the PCA one--factor scores and eigenvalues are linearly related). Basically this will give you an idea of how games group together, if any. At the same time, you can use your "hardcore gamer" status (yes/no) as an illustrative variable (i.e., this variable will not participate to the construction of the factorial axes), which will help you identifying how it related to these clusters of variables.
The FactoMineR R package offers all of what is needed for such kind of analysis, see MCA(). 
As you didn't say anything about your sample size, it's hard to suggest confirmatory or model-based approaches, like logistic regression or latent class regression. But you can look at Random Forests and try to identify the "best" variables that allow to predict your outcome with a minimal classification error rate (see the randomForest package).
