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I've collected some survey data on homeless individuals, surveying their drug use, education level, age, gender etc. I hope to run a logistic regression to see how impactful homelessness (+other dependent variables) are on the likelihood a child uses drugs.

DrugUser= B0 + B1Homeless + B3X3 + ... + u

However, due to the constraints of the study I was not able to survey randomly, only surveying those individuals who came into a homeless shelter (A convenience sample?). Hence the majority of the sample were made up of homeless people. Does this mean that any results I get for B1 would be spurious, as almost all of the sample is of homeless children and not a randomised sample of the population?

Therefore, is there anyway I can measure the effect of homelessness on drug use considering the quality of the data?

If not, could I still accurately measure the effects of the other variables on the likelihood an individual takes drugs that are not made bias by this convenience sample (like age, gender etc.)?

Is there any way I can use survey data like this to run a logistic regression at all?

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  • $\begingroup$ Even with a random sample you won't be able to measure any (causal!) effect with a simple logistic regression (e.g. you won't be able to tell if drug use leads to homelessness or vice versa). $\endgroup$
    – oW_
    Dec 12, 2022 at 23:26
  • $\begingroup$ I see, I'm still quite new to this so that's useful to know. What else is needed to be able to measure a causal effect (if any)? $\endgroup$
    – JS Holding
    Dec 13, 2022 at 15:48

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You can model survey data with logistic regression. A survey at best can provide evidence for correlation, never causation. The validity of the correlation is a result of the survey methodology and subsequent analysis.

There is a decision to be made on how to handle inference on the parameters. In other words, how far do the conclusions extend?

The most conservative approach would be to treat the results as summary statistics of the empirical sample. A step further would assume that the results are representative of other "individuals who came into a homeless shelter". An additional extension would be to apply the results to other homeless individuals that did not seek shelter.

Ultimately, it is a subjective decision.

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  • $\begingroup$ Thanks Brian, I have also conducted interviews in a longer format, collecting qualitative on the issue of homeless drug use. Lets say I find a statistically significant parameter for homelessness' effect on drug use, by combining it with this qualitative data would that be enough to infer causation? (assuming of course the qualitative data backs up the stat significant parameter instead of discounting it). I also know you said its subjective but I'd still value your opinion. Cheers $\endgroup$
    – JS Holding
    Dec 13, 2022 at 16:03
  • $\begingroup$ Surveys can never infer causation. There is no type of statistics that can help. $\endgroup$ Dec 13, 2022 at 16:28

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