Function within Function in R

You might want to have a look at the R scoping rules. In particular, there's no reason to expect that variables you define in a function are visible in other functions.

You might be confused because the global environment (i.e. the top-level outside all functions) is an exception from this rule. I'm not going to go into your other questions, but let me note that the entire script looks very messed up to me - i.e. M1 to M3 are essentially one function, and the wad of copy/paste in get.f is definitely terrible. Whatever it is that you're trying to do can definitely be written in a less convoluted way.

Let's have a look at the Ms first - why not one function with a parameter? Including the solution to your scope problem, that makes two parameters -

M <- function(sampleData, offset) { 
    a1 = sampleData[,c(2:5,7,9)] + offset
    b1 = sampleData[,c(2:4,6,8,7)] + offset
    c1 = b1+a1
    list(a1=a1,b1=b1,c1=c1)
}

If you insist on defining aliases, you can also do something like

M1 <- function(sampleData) M(sampleData, 0) 
M2 <- function(sampleData) M(sampleData, 2) 
M3 <- function(sampleData) M(sampleData, 8) 

This is already less repetitive, but ideally you want the computer to do the repetition for you (DRY!):

offsets <- c(0,2,8)
Models <- sapply(offsets, FUN=function(offset) function(sampleData) M(sampleData, offset))

Looking at get.f, it's not quite clear what you're trying to do - you're trying to fit something and collect something from the results, but the part about Model$cof refers to an undefined variable (your Model just has a1,b1 and c1 entries). Assuming you want to actually collect cof and discarding the interim code, get.f probably looks like this:

M <- function(sampleData, offset) { 
    a1 = sampleData[,c(2:5,7,9)] + offset
    b1 = sampleData[,c(2:4,6,8,7)] + offset
    c1 = b1+a1
    list(a1=a1,b1=b1,c1=c1)
}

get.f <- function(asim,Model,M){
    sse <-c()
    for(i in 1:asim){
        set.seed(i)
        Samdat <- dat[sample(1:nrow(dat),nrow(dat),replace=T),]
        Y <- Samdat[,1]
        model <- Model()
        if(M==1){
            a2 <- model$a1
            b2 <- model$b1
            c2 <- model$c1
            s<- a2+b2+c2
            fit <- lm(Y~s)
            cof <- sum(summary(fit)$coef[,1])
            sse <-c(sse,cof)
        }
        else if(M==2){
            a2 <- model$a1
            b2 <- model$b1
            c2 <- model$c1
            s<- c2+12
            fit <- lm(Y~s)
            cof <- sum(summary(fit)$coef[,1])
            sse <-c(sse,cof)
        }
        else {
            a2 <- model$a1
            b2 <- model$b1
            c2 <- model$c1
            s<- c2+a2
            fit <- lm(Y~s)
            cof <- sum(summary(fit)$coef[,1])
            sse <-c(sse,cof)
        }
    }
    return(sse)
}


get.f(10,Model=M1,M=1) 
get.f(10,Model=M2,M=2)
get.f(10,Model=M3,M=3)

That's still terribly repetitive, so why don't we think about it for a minute? All you're doing with your samples is to calculate one column from them to use in your fit. I don't see why you need to do the calculation in an M function and then do the extraction of the single value in get.f (dependent on which particular M you were using) - this seems indicative that the extraction should much rather be part of M... but if you need to keep them separate, okay, let's use separate extraction functions. Still comes in under half of your code size in reasonably-written R:

# Set up test data
dat <-  cbind(Y=rnorm(20),rnorm(20),runif(20),rexp(20),rnorm(20),runif(20), rexp(20),rnorm(20),runif(20),rexp(20))
nam <- paste("v",1:9,sep="")
colnames(dat) <- c("Y",nam)

# calculate a1..c1 from a sample
M <- function(sampleData, offset) { 
    a1 = sampleData[,c(2:5,7,9)] + offset
    b1 = sampleData[,c(2:4,6,8,7)] + offset
    c1 = b1+a1
    list(a1=a1,b1=b1,c1=c1)
}

# create a fixed-offset model from the variable offset model by fixing offset
makeModel <- function(offset) function(sampleData) M(sampleData, offset)   

# run model against asim subsamples of data and collect coefficients
get.f <- function(asim,model,expected) 
    sapply(1:asim,  function (i){
        set.seed(i)
        Samdat <- dat[sample(1:nrow(dat),nrow(dat),replace=T),]
        Y <- Samdat[,1]
        s <- expected(model(Samdat))
        fit <- lm(Y~s)
        sum(summary(fit)$coef[,1])
    })

# list of models to run and how to extract the expectation values from the model reslts
todo <- list(
        list(model=makeModel(0), expected=function(data) data$a1+data$b1+data$c1),
        list(model=makeModel(2), expected=function(data) data$c1+12),
        list(model=makeModel(8), expected=function(data) data$c1+data$a1))

sapply(todo, function(l) { get.f(10, l$model, l$expected)})