R help - May 2004 - questions about optim

Hi,
I am trying to do parameter estimation with optim, but I can't get it to 
work quite right-- I have an equation X = Y where X is a gaussian, Y is a 
multinomial distribution, and I am trying to estimate the probabilities of 
Y( the mean and sd of X are known ), Theta1, Theta2, Theta3, and Theta4; I 
do not know how I can specify the constraint that Theta1 + Theta2 + Theta3 + 
Theta4 = 1 in optim. Is there another method/package that I should use for 
this?
Also, I wonder if there's a more elegant way to code this equation in R; 
right now my function looks something like Y/rnorm( 10000, mean, sd), and I 
try to maximize it to 1; is it possible to "plug" the entire gaussian(
instead of using rnorm ) into the equation? Thanks.

Regards,

-Dean

1.  Have you considered parameterizing the problem in terms of 
(Theta1, Theta2, Theta3), and then computing Theta4 <- 
(1-Theta1-Theta2-Theta3) in the function you ask "optim" to optimize? 

      2.  Beyond this, I don't understand what you are trying to do.  Do 
you want to estimate a multinomial approximation to a normal 
distribution?  If yes, are you given the mean and standard deviation of 
the normal distribution PLUS the break points?  If yes, then what about 
the following: 

 > Breaks <- 1:3
 > Mean <- 0
 > Sd <- 1
 > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
 > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
 > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
 > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
 > Breaks <- 1:3
 > Mean <- 0
 > Sd <- 1
 > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
 > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
 > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
 > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
 > Theta1;Theta2;Theta3;Theta4
[1] 0.8413447
[1] 0.1359051
[1] 0.862745
[1] 0.001349898
 
       hope this helps.  spencer graves

Dean Lee wrote:
> Hi,
> I am trying to do parameter estimation with optim, but I can't get it 
> to work quite right-- I have an equation X = Y where X is a gaussian, 
> Y is a multinomial distribution, and I am trying to estimate the 
> probabilities of Y( the mean and sd of X are known ), Theta1, Theta2, 
> Theta3, and Theta4; I do not know how I can specify the constraint 
> that Theta1 + Theta2 + Theta3 + Theta4 = 1 in optim. Is there another 
> method/package that I should use for this?
> Also, I wonder if there's a more elegant way to code this equation in 
> R; right now my function looks something like Y/rnorm( 10000, mean, 
> sd), and I try to maximize it to 1; is it possible to "plug" the 
> entire gaussian( instead of using rnorm ) into the equation? Thanks.
>
> Regards,
>
> -Dean
>
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> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html

Hi Spencer,
Thanks for the reply.

1) When I was playing with optim before sometimes the probabilities came up 
to be negative. I am not sure what I did before, but now it seems to work 
correctly after I specify the lower and upper bounds on the Thetas using the 
L-BFGS-B method in optim.

2) No the break points are not given. But yes, I am trying to estimate a 
multinomial to a normal; sorry I wasn't being clear. What are some of the 
approaches that I can try in this case? Thanks.

Regards,

-Dean




>From: Spencer Graves <spencer.graves at pdf.com>
>To: Dean Lee <deanylee at hotmail.com>
>CC: r-help at stat.math.ethz.ch
>Subject: Re: [R] questions about optim
>Date: Sat, 15 May 2004 13:38:38 -0700
>
>      1.  Have you considered parameterizing the problem in terms of 
>(Theta1, Theta2, Theta3), and then computing Theta4 <- 
>(1-Theta1-Theta2-Theta3) in the function you ask "optim" to
optimize?
>
>      2.  Beyond this, I don't understand what you are trying to do.  Do
>you want to estimate a multinomial approximation to a normal distribution?  
>If yes, are you given the mean and standard deviation of the normal 
>distribution PLUS the break points?  If yes, then what about the following:
>
> > Breaks <- 1:3
> > Mean <- 0
> > Sd <- 1
> > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
> > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
> > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
> > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
> > Breaks <- 1:3
> > Mean <- 0
> > Sd <- 1
> > Theta1 <- pnorm((Breaks[1]-Mean)/Sd)
> > Theta2 <- (pnorm((Breaks[2]-Mean)/Sd)-Theta1)
> > Theta3 <- (pnorm((Breaks[3]-Mean)/Sd)-Theta2)
> > Theta4 <- pnorm((Breaks[3]-Mean)/Sd, lower.tail=FALSE)
> > Theta1;Theta2;Theta3;Theta4
>[1] 0.8413447
>[1] 0.1359051
>[1] 0.862745
>[1] 0.001349898
>
>       hope this helps.  spencer graves