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A friend of mine asked me the other day how she could use the function **mages' blog**, and kindly contributed to R-bloggers)`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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