It can be impossible to identify any sampling error and create statistical inferences from the sample to the population.
Earl Babbie wrote an interesting book, The Practice of Social Research, when you can find a chapter devoted to "The Logic of Sampling". Namely, the snowball sampling technique is detailed in page 184.
I recommend that you turn to an excellent text on qualitative research such as Michael Quinn Patton's Qualitative Research and Evaluation Methods or Gretchen Rossman's Designing Qualitative Research for their discussions.
I just found this post that might be of your interest: http://research.boisestate.edu/compliance/institutional-review-board-irb-home/guidelines-for-researchers/guidelines-for-investigators-using-snowball-sampling-recruitment-methods/
Earl Babbie wrote an interesting book, The Practice of Social Research, when you can find a chapter devoted to "The Logic of Sampling". Namely, the snowball sampling technique is detailed in page 184.
The justification should be related to the research question under consideration. If for example you aim to do research on sensitive issues, such HIV Aids, drug abuse, prostitution, you might find it difficult to recruit respondents. In these cases snowball sampling would be justified because following a chain of referral would provide you with access to respondents you could not obtain through other methods. That said, as others have pointed out snowball sampling comes with its own collection of problems and woes. There are lots of good texts available to help you. I am partial to an 'old school' article by Patrick Biernacki & Dan Waldorf titled: Snowball Sampling: problems and techniques of chain referral sampling. In my experience snowballing has been primarily associated with qualitative research, if statistical inference is a central concern perhaps you should choose another data collection method.
Convience sampling is not free from problems either, but any good research methods book will provide you good arguments for making that choice. The research question remains at the center of any decision. Good luck!
I agree with Linda's answer: "the research question is at the center of any decision".
I would agree that the research question does matter but the study population of interest will also influence your decision to either use snow ball or other sampling method.
Most of this discussion concerns snowball sampling as a basis for purposive selection of participants in qualitative studies, but there is another more technical literature on snowball sampling.
In particular, the Wikipedia entry on snowball sampling contain several citations to articles about calculating the statistical properties of snow ball samples, starting with the work of Leo Goodman in the 1960's.
Most of this work relies on strong assumptions, however, such as a random sampling of the initial "seeds" and a further random sample of the names nominated by those first respondents.
In my view a lot of this justification can be developed if snowball sampling is used alongside another approach, such as for example purposive sampling. I wrote about it a while back.
https://researcholic.wordpress.com/2017/01/26/what-is-snowball-sampling/
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