I can achieve this task, but I feel like there must be a \"best\" (slickest, most compact, clearest-code, fastest?) way of doing it and have not figured it out so far ...
(I voted for Joshua's.) Here's an Hmisc::summary.formula solution. The advantage of this for me is that it is well integrated with the Hmisc::latex output "channel".
summary(y ~ interaction(f3,f2,f1), data=d, method="response",
fun=function(y) c(mean.y=mean(y) ,var.y=var(y) ))
#-----output----------
y N=108
+-----------------------+-------+---+---------+-----------+
| | |N |mean.y |var.y |
+-----------------------+-------+---+---------+-----------+
|interaction(f3, f2, f1)|I.a.A | 4|0.6502307|0.095379578|
| |II.a.A | 4|0.4876630|0.110796695|
snipped output to show the latex -> PDF -> png output: