How to define function arguments based on data.frame columns (R)? - r

Question

I have a script that runs maximum likelihood estimation for a linear model. The model has several variables and I need to vary them occasionally, maybe add or drop some. The usual way to define the likelihood function is like this:
LL <- function(beta0, beta1, beta2, mu, sigma){
R = y - beta0*X$x0 + beta1*X$x1 + beta2*X$x2
R = dnorm(R, mu, sigma, log = T)
-sum(R)
}
I have dependent variable in vector y and covariates in data.frame X:
X <- data.frame(x0 = 1, x1 = runif(100), x2 = runif(100)*2)
y <- X$x0 + X$x1 + X$x2 + rnorm(100)
Now the amount of variables is subject to change by application and I need to reformulate the function so that it will take as many covariates as there are columns in the data.frame X. I was already able to reformulate this to a more general form:
cols <- 0:(ncol(X)-1)
betas <- paste0("beta", cols)
eqR <- paste0("y - ", paste0(betas, "*X$x", cols, collapse = " - "))
LL <- function(beta0, beta1, beta2, mu, sigma){
R = as.formula(eqR)
R = dnorm(R, mu, sigma, log = T)
-sum(R)
}
I'm still struggling to find a way to dynamically define the function so that it would take the same number of beta arguments as there are columns in the covariate matrix. Ellipsis is perhaps useful here? I also tried with do.call:
LL <- function(betas, mu, sigma){
R <- do.call(dnorm(as.formula(eqR), mu, sigma, log = T), betas)
-sum(R)
}
That doesn't work when you fit the model, which has another stumbling block in the list of initial values:
require(stats4)
fit <- mle(LL, start = list(beta0 = 0, beta1 = 0, beta2 = 0, mu = 0, sigma = 1))
Any ideas for this?
EDIT:
I made some advance with bbmle package:
require(bbmle)
dfModel <- cbind(y, X)
cols <- 0:(ncol(X)-1)
betas <-paste0("beta",cols)
betaList <- as.list(rep(0), length(betas)))
names(betaList) <- betas
initList <- c(betaList, mu = 0, sigma = 1)
fitML <- mle2(mu ~ dnorm(mean = y - beta0*x0 - beta1*x1 - beta2*x2, sd = sigma),
start = initList,
data = dfModel)
The above example works. But when I try to define the function beforehand with as.formula, I can't get it working. So the following does not work.
eqR <- paste0("y - ", paste0(betas, "*x", cols, collapse = " - "))
fitML <- mle2(mu ~ dnorm(mean = as.formula(eqR), sd = sigma),
start = initList,
data = dfModel)
The error message is:
Error in eval(expr, envir, enclos) : object 'beta0' not found
I suspect that this might have something to do with scoping - conflict between dnorm and as.formula? I just can't find workaround for that.

Answer 1

Try this:
betas = c(0,0,0)
X <- data.frame(x0 = 1, x1 = runif(100), x2 = runif(100)*2)
y <- apply(X,1,sum) + rnorm(100)
where betas is (b0, b1, b2, ...etc) and its length must be equal to the number of columns of X.
Since X could have a different number of columns y should be defined as above.
Your LL function should change to:
LL <- function(betas, mu, sigma){
R = y - as.matrix(X) %*% as.matrix(betas)
R = dnorm(R, mu, sigma, log = T)
-sum(R)
}
where %*% is the matrix product. This is the same as doing b[1]*X[,1] + b[2]*X[,2] + b[3]*X[,3] + ... + b[n]*X[,n]
With these changes, you could have data frame X with any number of columns, betas an array of the same length as columns of X.
I hope I understood what you needed.