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    $\begingroup$ Thanks, guys. I'm glad this came together well; this is actually a good example of how you can learn things on CV by answering questions, as well as asking & reading others' answers: I knew this information beforehand, but not quite well enough that I could just write it out cold. So I actually spent some time going through my old texts to figure out how to organize the material & put it forward clearly, & in the process solidified these ideas for myself. $\endgroup$ Commented Jun 22, 2012 at 18:18
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    $\begingroup$ @gung Thanks for this explanation, it is one of the clearest descriptions of GLMs in general that I have come across. $\endgroup$ Commented Sep 27, 2012 at 23:35
  • $\begingroup$ @whuber "When the response variable is not normally distributed (for example, if your response variable is binary) this approach [standard OLS] may no longer be valid." I'm sorry to bother you (again!) with this, but I find this bit confusing. I understand that there are no unconditional distributional assumptions on the dependent variable in OLS. Does this quote mean to imply that since the response is so wildly non-normal (i.e. a binary variable) that its conditional distribution given $X$ (and hence the distribution of the residuals) cannot possibly approach normality? $\endgroup$ Commented Mar 27, 2014 at 9:45
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    $\begingroup$ @landroni, you may want to ask a new question for this. In short, if your response is binary, the conditional distribution of Y given X=xi cannot possibly approach normality; it will always be binomial. The distribution of the raw residuals will also never approach normality. They will always be pi & (1-pi). The sampling distribution of the conditional mean of Y given X=xi (ie, pi) will approach normality, though. $\endgroup$ Commented Mar 27, 2014 at 13:41
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    $\begingroup$ I share somewhat of landroni's concern: after all, a normally distributed outcome non-normally distributed residuals, and a non-normally distributed outcome may have normally distributed residuals. The issue with the outcome seems to be less about its distribution per se, than its range. $\endgroup$ Commented Jul 23, 2014 at 20:47