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  1. PO
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    <p>One thing is how to convert your data. Another is why. From <code>?glm</code>: "[f]or binomial [...] famil[y] the response can [...] be specified as a factor (when the first level denotes failure and all others success) or as a two-column matrix with the columns giving the numbers of successes and failures.". The first way corresponds to your "R's glm wants a dataframe of 2046 rows each reporting a TRUE or FALSE conversion". The second way basically corresponds to the your original data set where the "successes" easily can be calculated from Rate and N. A third way would be to use the proportion of successes per treatment combination as response variable, in which case the number of trials must be supplied as the <code>weights</code> argument.</p> <pre><code>set.seed(1) # one row per observation df1 &lt;- data.frame(x = sample(c("yes", "no"), 40, replace = TRUE), y = sample(c("yes", "no"), 40, replace = TRUE), z = rbinom(n = 40, size = 1, prob = 0.5)) df1 library(plyr) # aggregated data with one row per treatment combination df2 &lt;- ddply(.data = df1, .variables = .(x, y), summarize, n = length(z), rate = sum(z)/n, success = n*rate, failure = n - success) df2 # three different ways to specify the models, # which all give the same parameter estimates for x, y and x*y mod1 &lt;- glm(z ~ x * y, data = df1, family = binomial) mod2 &lt;- glm(cbind(success, failure) ~ x * y, data = df2, family = binomial) mod3 &lt;- glm(rate ~ x * y, data = df2, weights = n, family = binomial) summary(mod1) summary(mod2) summary(mod3) </code></pre>
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    1. POElegantly convert rate summary rows into long binary-response rows?
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    1. USHenrik
    1. USHenrik
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    1. VO
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      1. VTUpMod
    1. COThe weights is a cool-looking approach, even simpler than the `cbind` solution, but I'm a little bit troubled that these apparently-equivalent approaches aren't turning in the same result. It's the same data in the same regression, isn't it? The *parameters* may be the same, but other values differ. For example, the complexity measure: look at `mod1$aic; mod2$aic; mod3$aic` and you'll see the long format is turning in a very different AIC.
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      1. USgwern
    2. CO@gwern, I'm sorry, but I don't understand what you mean by "it's the same data in the same regression". AIC values of the three models I present are not directly comparable, because they have different response variables and are fit using two different data sets.
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      1. USHenrik
    3. COAlright, then that's a problem: I don't see why 3 ostensibly equivalent approaches are using 'two different data sets'. If that's true, doesn't that seem like a big deal? I wouldn't use an algorithm that randomly made up data for no reason, why would I use data conversion commands that made up data...
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