Sobel test with survey data I would like to ask if there is any problem / concern with Sobel test when I use survey data? In particular, I was using the web-based calculation tool here based on coefficients derived from regression analysis using survey command. I also hope to know if there is a good reference article about this. 
 A: From a mathematical standpoint, there's nothing wrong with doing a Sobel test with survey data (by the way, and slightly off-topic -- you should consider using a bootstrapping method to test your indirect effects instead of a Sobel test; bootstrapping methods are uniformly more powerful than Sobel tests).  The real question is what conclusions you would be able to draw from your Sobel test.
To get a clear sense of the problem, consider a simple study in which the researcher measures people's scores on a self-report measure of trait empathy and the amount of money these people donated to charitable causes within the last year.  Assuming that the researchers observed a relationship between trait empathy and donations, few people would make the mistake of concluding that trait empathy causes donations (i.e., empathy -> donations), since the people in the study were not randomized to their values of trait empathy.  Thus, it is possible that people who thought about their levels of donations reported higher levels of trait empathy (i.e., donations -> empathy) or that a third variable caused the observed values of both donations and empathy.
Let's now consider a study in which the researchers measured trait empathy, charitable donations, and positive emotions.  The researcher wishes to show that the experience of positive emotions mediates the link between trait empathy and charitable donations (i.e., that empathy -> positive emotions -> donations).  In order to convincingly establish mediation, we must show both that empathy -> positive emotions and that empathy -> donations.  However, because people were not randomized to their values of trait empathy, we cannot conclude that empathy caused either positive emotions or donations.
However, even if we had randomized people to their empathy scores, we would still not necessarily be able to conclude that positive emotions were a mediator for the empathy -> donations effect because, after people's assignment to their empathy scores, people were not randomized to their values of positive emotions.  Thus, even if we established a non-zero indirect effect, it is possible that, for example, an unobserved candidate mediator causes both positive emotions and donations, and it is this unobserved candidate mediator that creates the observed empathy -> positive emotions -> donations indirect effect (for more information about this problem, see some of the references added below).
In short, there is nothing wrong with doing a Sobel test or any other test of mediation with survey data.  However, just as when you examine simple bivariate relationships with survey data, such a test probably will not reveal much about causal mechanisms because the assumptions required to draw these conclusions are implausible at best.
I recommend reading some of the references below for more information about assumptions in mediation models.
Jo, B. (2008).  Causal inference in randomized experiments with mediational processes. Psychological Methods, 13, 314–336.
Imai, K., Keele, L., & Yamamoto, T. (2010). Identiﬁcation, inference and sensitivity
analysis for causal mediation eﬀects. Statistical Science, 25, 51-71.
Imai, K., Keele, L., Tingley, D., & Yamamoto T. (2011). Unpacking the black box of causality: Learning about causal mechanisms from experimental and observational studies. American Political Science Review, 105, 765-789.
