Dear R users,
I am using the function "constrOptim" to minimize the -1*log-likelihood
where \beta_i>=0 i=1,...,p and \beta_0 is unconstrained.
I construct u_i as
0 0 0 ... 0
0 1 0 ... 0
0 0 1 ... 0
. . . ... 0
. . . ... 0
. . . ... 0
0 0 0 ... 1
and c_i as (-1,0,...,0).
Then whatever value \beta_0 takes, the first value of u_i%*%theta_i is
always zero, which automatically is larger than -1. That is how I construct
u_i and c_i.
contrOptim returns the barrier.value. I am wondering whether the value
corresponds to -1*\mu*(\sum_{i=1}^p log(\hat{\beta_i}-0)+\log(1)).
I need to get the information matrix which also takes into account the
additional barrier term so I need to figure out what the value of \mu is.
Assuming what I wrote down above is right, I obtain \mu as
-1*barrier.value/(log(\beta_1)+...+log(\beta_p)).
I would be extremely grateful if anyone checks whether my ways to construct
u_i and c_i and to obtain \mu in the barrier term are right.
Thanks!
Minsun
constrOptim(beta,fr_general,score_single_parameter,ui=rbind(rep(0,dim(x)[2]+1),cbind(rep(0,dim(x)[2]),diag(1,nrow=dim(x)[2]))),ci=c(-1,rep(0,dim(x)[2])),hessian=TRUE,
method="BFGS")
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