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 <[EMAIL PROTECTED]> To: Dean Lee <[EMAIL PROTECTED]> CC: [EMAIL PROTECTED] 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
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