I have a function that I am currently using very inefficiently. The following are needed to illustrate the problem:

set.seed(12345)
dat <- matrix(sample(c(0,1), 110, replace = TRUE), nrow = 11, ncol=10)
mis <- sample(1:110, 5)
dat[mis] <- NA
theta <- rnorm(11)
b_vector <- runif(10, -4,4)
empty <- which(is.na(t(dat)))

So, I have a matrix (dat) with some values within the matrix missing. In my real world problem, the matrix is huge, and most values are missing. The function in question is called derivs() and is below. But, let me step through the inefficient portions.

First, I create a matrix of some predicted probabilities as:

rasch <- function(theta,b) 1/ (1 + exp(b-theta))
mat <- apply(as.matrix(theta), 1, rasch, b_vector)

However, I only need those predicted probabilities in places where the data are not missing. So, the next step in the function is

mat[empty] <- NA

which manually places NAs in places where the data are missing (notice the matrix 'mat' is the transpose of the data matrix and so I get the empty positions from the transpose of dat).

Afterwards, the function computes the gradient and hessians needed to complete the MLE estimation.

All of this works in the sense that it yields the correct answers for my problem. But, the glaring problem is that I create predicted probabilities for every cell in 'mat' when in many cases they are not needed. I end up replacing those values with NAs. In my real world problem, this is horribly inefficient and slow.

My question is then is there a way to use apply such that is computes the necessary predicted probabilities only when the data are not missing to yield the matrix 'mat'. My desired end result is the matrix 'mat' created after the manually placing the NAs in the appropriate cells.

Thanks
Harold


derivs <- function(dat, b_vector, theta){
                                mat <- apply(as.matrix(theta), 1, rasch, b_vector)
                                mat[empty] <- NA
                                gradient <- -(colSums(dat, na.rm = TRUE) - rowSums(mat, na.rm = TRUE))
                                hessian <-  -(rowSums(mat * (1-mat), na.rm = TRUE))
                                list('gradient' = gradient, 'hessian' = hessian)
                }



> sessionInfo()
R version 2.10.1 (2009-12-14)
i386-pc-mingw32

locale:
[1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United States.1252    LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                           LC_TIME=English_United States.1252

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached):
[1] tools_2.10.1
>

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