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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