I am trying to use speedglm to achieve a faster GLM estimation than glm, but why it is even slower?
set.seed(0)
n=1e3
p=1e3
x=matrix(runif(n*p),nrow=n)
y=sample(0:1,n,replace = T)
ptm <- proc.time()
fit=glm(y~x,family=binomial())
print(proc.time() - ptm)
# user system elapsed
# 10.71 0.07 10.78
library(speedglm)
ptm <- proc.time()
fit=speedglm(y~x,family=binomial())
print(proc.time() - ptm)
# user system elapsed
# 15.11 0.12 15.25
The efficiency of speedglm over glm, is the way it reduces the n * pmodel matrix to a p * p matrix. However, if you have n = p, there is no effective reduction. What you really want to check, is the n >> p case.
More insight form computational complexity, in each iteration of Fisher scoring.
glm using QR factorization for a n * p matrix takes 2np^2 - (2/3)p^3 FLOP, while speedglm forming matrix cross product of a n * p matrix, followed by a QR factorization of a p * p matrix, involves np^2 + (4/3)p^3 FLOP. So as n >> p, speedglm only has half the computation amount of glm. Furthermore, the blocking, caching strategy used by speedglm gives better use of computer hardware, giving high performance.
If you have n = p, you immediately see that glm takes (4/3)p^3 FLOP, but speedglm takes p^3 + (4/3)p^3 FLOP, more expensive! In fact, the matrix cross product becomes a shear overhead in this case!
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