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I have a large nonrandom sample and a small random sample from the same population. I wish to control the first by the second. In particular, I want to estimate both a linear regression and a binary logistic model with the larger sample but using the corresponding models obtained based on the smaller. Any ideas?

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  • $\begingroup$ This question is too vague to be answerable, except generically to remind you that inference from a "nonrandom sample" can be problematic and depends critically on all the details and context of the sampling process. If you could be more specific and explain what you by "evaluate its properties" and "relevance of inference," then perhaps we could venture useful answers. $\endgroup$
    – whuber
    Aug 4 at 16:14
  • $\begingroup$ Thanks. I want to use the random sample for estimating regression models. Then, I would like to use these models to somehow control the corresponding models for a much larger nonrandom sample. $\endgroup$
    – fernando
    Aug 5 at 17:05
  • $\begingroup$ Could you please explain what you mean by "somehow control"? $\endgroup$
    – whuber
    Aug 5 at 19:08
  • $\begingroup$ OK. I am aware of the limitations of the analysis when the sampling is nonrandom. My question is if there is a way to improve the analysis if a smaller random sample is also drawn form the same population. For example, would it be ok to consider the final choice of regressors for the model estimated with the random sample (after excluding variables with nonsignificant coefficients) as the relevant for the model based on the nonrandom one? If so, why? $\endgroup$
    – fernando
    2 days ago
  • $\begingroup$ There are so many things to consider that it won't work to ask this question generically. Why not describe the situation you actually face? $\endgroup$
    – whuber
    2 days ago

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