[R] Comparison: glm() vs. bigglm()

[Peter Dalgaard]

Benilton Carvalho wrote:
> Hi,
>
> Until now, I thought that the results of glm() and bigglm() would  
> coincide. Probably a naive assumption?
>
> Anyways, I've been using bigglm() on some datasets I have available.  
> One of the sets has >15M observations.
>
> I have 3 continuous predictors (A, B, C) and a binary outcome (Y).  
> And tried the following:
>
> m1 <- bigglm(Y~A+B+C, family=binomial(), data=dataset1, chunksize=10e6)
> m2 <- bigglm(Y~A*B+C, family=binomial(), data=dataset1, chunksize=10e6)
> imp <- m1$deviance-m2$deviance
>
> For my surprise "imp" was negative.
>
> I then tried the same models, using glm() instead... and as I  
> expected, "imp" was positive.
>
> I also noticed differences on the coefficients estimated by glm() and  
> bigglm() - small differences, though, and CIs for the coefficients (a  
> given coefficient compared across methods) overlap.
>
> Are such incrongruences expected? What can I use to check for  
> convergence with bigglm(), as this might be one plausible cause for a  
> negative difference on the deviances?
>   
It doesn't sound right, but I cannot reproduce your problem on a similar
sized problem (it pretty much killed my machine...). Some observations:

A: You do realize that you are only using 1.5 chunks? (15M vs. 10e6
chunksize)

B: Deviance changes are O(1) under the null hypothesis but the deviances
themselves are O(N). In a smaller variant (N=1e5), I got

> m1$deviance
[1] 138626.4
> m2$deviance
[1] 138626.4
> m2$deviance - m1$deviance
[1] -0.05865785

This does leave some scope for roundoff to creep in. You may want to
play with a lower setting of tol=...

-- 
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