I have a function f_2 and need to minimize it's parameters by nlminb in order to estimate log likelihood (that is the objective in nlminb output). There is one constrain I want to add (u1+u2+u3+u4+u5+u6+u7+u8+u9)==1 or sum of the parameters to be equal 1. My code is below:
f_2<-function(par){
u1<-par[1]
u2<-par[2]
u3<-par[3]
u4<-par[4]
u5<-par[5]
u6<-par[6]
u7<-par[7]
u8<-par[8]
u9<-par[9]
u1+u2+u3+u4+u5+u6+u7+u8+u9==1
-(n1_2*log(u1/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+n2_2*log(u2/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+
n3_2*log(u3/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+n4_2*log(u4/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+
n5_2*log(u5/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+n6_2*log(u6/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+
n7_2*log(u7/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+n8_2*log(u8/(u1+u2+u3+u4+u5+u6+u7+u8+u9))+
n9_2*log(u9/(u1+u2+u3+u4+u5+u6+u7+u8+u9)))
}
z1_2<-nlminb(c(1,1,1,1,1,1,1,1,1),f_2, lower = 0.0001, upper = Inf)
My output is
$par
[1] 0.57573059 1.62807832 2.99217185 0.01711788 0.01621807 0.60546191 0.39102822 0.03153362 0.19371337
. As you see the constrain for the sum of parameters to be 1 is just ignored. It is important to set up this constrain to be able to compare par for different models. I understand that I can do that manually but want to find out the way to make it in coding. Could you, please, help me solve this issue and to make constrain to be applied? Thank you!
