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I would like to minimize the mean squared error (the mse() in the hydroGOF Package might be used) between modeled and observed spreads. The function is defined as:

    KV_CDS <- function(Lambda, s, sigma_S){
     KV_CDS = (Lambda * (1 + s)) / exp(-s * sigma_S) - Lambda^2)
}

The goal is to minimize mse between KV_CDS and C by leaving Lambda a free parameter in the KV_CDS function.

df <- data.frame(C=c(1,1,1,2,2,3,4),
                 Lambda=c(0.5),s=c(1:7),
                 sigma_S=c(0.5,0.4,0.3,0.7,0.4,0.5,0.8),
                 d=c(20,30,40,50,60,70,80), 
                 sigma_B=0.3, t=5, Rec=0.5, r=0.05)
New2R
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  • Can you clarify your question a bit? A function of a function is just a function that is the composition of the two functions. What is c/C? It's kind of hard to decipher what is fixed and what is a parameter from all the code you posted. – Andrew Mao Feb 28 '13 at 18:37
  • I want to minimize the MSE but the free Parameter is Lambda in the KV_CDS function. All the other Parameters are fixed. It is easy in Excel using the Solver, but my data is pretty large, so I try to avoid the Solver. c is the dataframe, and C are observations I want to fit the model to. I will rename c to df to make it more readable. The function KV_PS and C_G are only help functions to solve the target function. Sorry, for the confusing display. – New2R Feb 28 '13 at 19:08
  • I see you've added the question about applying `TestMSE` by ID. I'd suggest that you ask it as a separate question, which would get it more attention. – Simon Mar 01 '13 at 19:51

2 Answers2

2

You'll need to write a function to minimise that calculates the mean squared error for this particular case, e.g.:

calcMSE <- function (Lambda) 
{
        d <- df # best not to use -df- as a variable because of confusion with
                # degrees of freedom
        err <- d$C - KV_CDS(Lambda, d$s, d$sigma_S, d$d, d$sigma_B, d$t, d$Rec, d$r)
        sum(err^2) / length(err)
}

... and then you can use optimize(), like this for instance (you need to specify the range of possible values for Lambda -- incidentally not an ideal name because it implies that it could be a function when it is actually just a variable):

optimize(calcMSE,c(0,1))

I couldn't do the complete test because I didn't have pbivnorm installed but this ought to do it for you.

Simon
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  • Thanks for your idea Simon, but I always receive "invalid function value in 'optimize'". What could be possibly wrong, the value cant be zero otherwise the function errors. So I scalled `optimize(calcMSE,lower=0.1, upper=1.5)` and also tried `optimize(calcMSE,c(0.1,1.5))`, but the error message remains. – New2R Mar 01 '13 at 10:46
  • @New2R -- my mistake. `err^2 / length(err)`, as I had originally written it, was returning the vector of squared errors, each divided by the length of `err`. I should have been returning the sum of `err^2` divided by the length of `err`. I've edited my answer accordingly. – Simon Mar 01 '13 at 19:47
1

Thanks to you Simon, I came to a solution:

  d <- df

  TestMSE <- function(LR)
    {

     D <- KV_CDS(LR, d$s, d$sigma_s, d$D, d$sigma_B, d$t, d$Rec, d$r)
      mse(d$C, D)
     }

  optimize(TestMSE,lower = 0.1, upper =1.5)

or: 

TestMSE2 <- function(LR)
    {
 D <- KV_CDS(LR, d$s, d$sigma_s, d$D, d$sigma_B, d$t, d$Rec, d$r)
      mean((d$C- D)^2)
     }

  optimize(TestMSE2,lower = 0.1, upper =1.5)

Thanks for your help guys!

New2R
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