[R] How to improve the "OPTIM" results

[kathie]

Dear R users,

I used to "OPTIM" to minimize the obj. function below.  Even though I used
the true parameter values as initial values, the results are not very good.

How could I improve my results?  Any suggestion will be greatly appreciated.

Regards,

Kathryn Lord

#------------------------------------------------------------------------------------------

x = c(0.35938587,  0.34889725,  0.20577608,  0.15298888, -4.24741146,
-1.32943326,
        0.29082527, -2.38156942, -6.62584473, -0.22596237,  6.97893687, 
0.22001081,
       -1.39729222, -5.17860124,  0.52456484,  0.46791660,  0.03065136, 
0.32155177,
       -1.12530013,  0.02608057, -0.22323154,  3.30955460,  0.54653982, 
0.29403011,
        0.47769874,  2.42216260,  3.93518355,  0.23237890,  0.09647044,
-0.48768933,
        0.37736377,  0.43739341, -0.02416010,  4.02788119,  0.07320802,
-0.29393054,
        0.25184609,  0.76044448, -3.34121918,  1.16028677, -0.60352008,
-2.86454069,
       -0.84411691,  0.24841071, -0.11764954,  5.92662106,  1.03932953,
-6.21987657,
       -0.54763352,  0.20263192)                         # data

theta0= c(log(2),0,c(0,-.3,.3),log(c(10,.05,.05)))  # initial value(In fact,
true parameter value)
n = length(x)

fr2 = function(theta)
{	
	a1 = theta[1]; a2 = theta[2]
	mu1 = theta[3]; mu2 = theta[4]; mu3 = theta[5]
	g1 = theta[6]; g2 = theta[7]; g3 = theta[8]
	
	w1=exp(a1)/(1+exp(a1)+exp(a2))
	w2=exp(a2)/(1+exp(a1)+exp(a2))
	w3=1-w1-w2

	obj =((w1^2)/(2*sqrt(exp(g1)*pi)) 
         +  (w2^2)/(2*sqrt(exp(g2)*pi))
         +  (w3^2)/(2*sqrt(exp(g2)*pi))

	 +  2*w1*w2*dnorm((mu1-mu2)/sqrt(exp(g1)+exp(g2)))/sqrt(exp(g1)+exp(g2))
         + 
2*w1*w3*dnorm((mu1-mu3)/sqrt(exp(g1)+exp(g3)))/sqrt(exp(g1)+exp(g3))
         + 
2*w2*w3*dnorm((mu2-mu3)/sqrt(exp(g2)+exp(g3)))/sqrt(exp(g2)+exp(g3))

         -  (2/n)*(sum(w1*dnorm((x-mu1)/sqrt(exp(g1)))/sqrt(exp(g1)) 
                     + w2*dnorm((x-mu2)/sqrt(exp(g2)))/sqrt(exp(g2))
                     + w3*dnorm((x-mu3)/sqrt(exp(g3)))/sqrt(exp(g3)) )))

	return(obj)
}

optim(theta0, fr2, method=BFGS", control = list (fnscale=10,
parscale=c(.01,.01,.01,.01,.01,1,1,1), maxit=100000))

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