I am a PhD student in a quantitative social science field. For the first study of my dissertation, I was given the opportunity to ask some questions that could be applied to an ongoing survey. Affiliated researchers have already used some of this data for a short commentary/descriptive article, and there is interest to apply the data in a slightly different 'modelling' study.
However, the underlying study design leaves much to be desired. Although the sample is relatively large, it is a convenience sample from only a fraction of all possible survey sites in the population. There is no opportunity to expand the data collection process. The data itself is unlikely to have measurement error, but almost any estimate produced from the dataset is highly likely to suffer from sampling bias.
Nevertheless, I realize this is a somewhat 'common' situation graduate student find themselves in. There is active interest from the affiliated partners to carry out the study, the design isn't 'ideal', and there are logistical considerations of invested time (or as I see it, sunk cost fallacy).
While I have many questions, I think the most straightforward is: should I attempt to make 'lemonade out of lemons' or 'stand my ground' that such a modelling study would be inappropriate?
Other potential information:
- Supervisor is 'ardent' that such a study should be carried out
- I have sought out external input as to what methods would be 'most' appropriate, there are some that might be 'less' worrisome than others