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r - Function to count NA values at each level of a factor

I have this dataframe:

set.seed(50)
data <- data.frame(age=c(rep("juv", 10), rep("ad", 10)),
                   sex=c(rep("m", 10), rep("f", 10)),
                   size=c(rep("large", 10), rep("small", 10)),
                   length=rnorm(20),
                   width=rnorm(20),
                   height=rnorm(20))

data$length[sample(1:20, size=8, replace=F)] <- NA
data$width[sample(1:20, size=8, replace=F)] <- NA
data$height[sample(1:20, size=8, replace=F)] <- NA

   age sex  size      length       width      height
1  juv   m large          NA -0.34992735  0.10955641
2  juv   m large -0.84160374          NA -0.41341885
3  juv   m large  0.03299794 -1.58987765          NA
4  juv   m large          NA          NA          NA
5  juv   m large -1.72760411          NA  0.09534935
6  juv   m large -0.27786453  2.66763339  0.49988990
7  juv   m large          NA          NA          NA
8  juv   m large -0.59091244 -0.36212039 -1.65840096
9  juv   m large          NA  0.56874633          NA
10 juv   m large          NA  0.02867454 -0.49068623
11  ad   f small  0.29520677  0.19902339          NA
12  ad   f small  0.55475223 -0.85142228  0.33763747
13  ad   f small          NA          NA -1.96590570
14  ad   f small  0.19573384  0.59724896 -2.32077461
15  ad   f small -0.45554055 -1.09604786          NA
16  ad   f small -0.36285547  0.01909655  1.16695158
17  ad   f small -0.15681338          NA          NA
18  ad   f small          NA          NA          NA
19  ad   f small          NA  0.40618657 -1.33263085
20  ad   f small -0.32342568          NA -0.13883976

I'm trying to make a function that counts the number of NA values of each of length, width and height at each level of the three factors in the dataframe. I've tried this:

 exploreMissingValues <- function(dataframe, factors, variables){
  library(plyr)
  Variables <- list(variables)

  llply(Variables, function(x) ddply(dataframe, .(factors), 
                                     summarise, 
                                     number.of.NA=length(x[is.na(x)])))  
}

exploreMissingValues(data, 
                     c("age", "sex", "size"), 
                     c("length", "width", "height"))

...but this gives an error. How can I get this function to return number of NA values at each level of the dataframe?

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Looking for something like this...???

library(doBy)
summaryBy(length+width+height~age+sex+size,
          data=data,
          FUN=function(x) sum(is.na(x)),
          keep.names=TRUE)
  age sex  size length width height
1  ad   f small      3     4      4
2 juv   m large      5     4      4

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