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How well does logistic regression behave with a large number of predictor variables that are all binary?

So say p > 1000 (number of predictors) and the Range(p) = 0 or 1

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    $\begingroup$ I guess it would work to some extend, probably also depending on how balanced your outcomes are. But why don't you give a bit of info as to why you'd do this i the first place as opposed to use a more suitable model? $\endgroup$
    – sheß
    May 10, 2016 at 17:25
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    $\begingroup$ Why wouldn't logistic regression work in this case? There is no assumption on the predictors in the logistic regression model, they are just known constants? $\endgroup$ May 10, 2016 at 17:27
  • $\begingroup$ @kjetilbhalvorsen, that's what I thought but then the other commenter seems to be saying that logistic regression may not be the best suited? $\endgroup$ May 10, 2016 at 17:28
  • $\begingroup$ @sheß well I have a binary classification problem where all my predictors (several thousand) are all binary ... thoughts? $\endgroup$ May 10, 2016 at 17:29
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    $\begingroup$ As long as p < n you should be fine. Your model will be something like $\log{\frac{\mu_0}{\mu_0+\mu_1}}=x\beta$. In fact, the results will be exactly the same as if you passed your data in a grouped form BUT you cannot use the deviance to assess your model fit. You can use the LRT, but not the deviance. $\endgroup$ May 10, 2016 at 17:44

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