# How to use optim in R

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A friend of mine asked me the other day how she could use the function `optim`

in R to fit data. Of course there are functions for fitting data in R and I wrote about this earlier. However, she wanted to understand how to do this from scratch using `optim`

.

The function `optim`

provides algorithms for general purpose optimisations and the documentation is perfectly reasonable, but I remember that it took me a little while to get my head around how to pass data and parameters to `optim`

. Thus, here are two simple examples.

I start with a linear regression by minimising the residual sum of square and discuss how to carry out a maximum likelihood estimation in the second example.

### Minimise residual sum of squares

I start with an x-y data set, which I believe has a linear relationship and therefore I'd like to fit y against x by minimising the residual sum of squares.

dat=data.frame(x=c(1,2,3,4,5,6), y=c(1,3,5,6,8,12))

Next, I create a function that calculates the residual sum of square of my data against a linear model with two parameter. Think of `y = par[1] + par[2] * x`

.

min.RSS <- function(data, par) { with(data, sum((par[1] + par[2] * x - y)^2)) }

Optim minimises a function by varying its parameters. The first argument of `optim`

are the parameters I'd like to vary, `par`

in this case; the second argument is the function to be minimised, `min.RSS`

. The tricky bit is to understand how to apply `optim`

to your data. The solution is the `...`

argument in `optim`

, which allows me to pass other arguments through to `min.RSS`

, here my data. Therefore I can use the following statement:

result <- optim(par = c(0, 1), min.RSS, data = dat) # I find the optimised parameters in result$par # the minimised RSS is stored in result$value result ## $par ## [1] -1.267 2.029 ## ## $value ## [1] 2.819 ## ## $counts ## function gradient ## 89 NA ## ## $convergence ## [1] 0 ## ## $message ## NULL

Let me plot the result:

plot(y ~ x, data = dat) abline(a = result$par[1], b = result$par[2], col = "red")

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