Binary Data with repetitions Why is Binomial data called Binary Data with repetitions? This is in context of Logistic Regression, where the response variable has a binomial distribution.
 A: It is not. Such description would be ambiguous and misleading. You must have in mind models for binary data with repeated measurements (e.g. as on those slides), then you would have "binary data with repetitions". Otherwise, there is nothing "repeated" in binomial data, so calling standard binomial data (counts of "successes") like this would not make any sense. You could argue that binomial data is about $n$ trials, so the trials are repeated, but the same would be true for hypergeometric, or geometric distributions etc.
A: It is presumably in the sense that one $Y \sim \text{Bin}(n, \pi)$ random variable is the same thing as $n$ i.i.d. $Y_i \sim \text{Bernoulli}(\pi)$ for $i=1,\ldots,n$ (aka binary) random variables.
It is perhaps not such a good name, as one could get confused with the setting, where the same individual has a binary response measured at different times (which are correlated) with potentially different expected proportions. In that case treating the dependent binary random variables as independent random variables would be inappropriate.
