R help - Oct 2011 - sum of functions

Dear all,

I would like to create a code for semiparametric Klein and Spady's
estimator. For that I created a function that provides the log-likelihood
function for each observation (so it is a function of betas and i, where i
denotes the observation). Now, in order to maximize the log-likelihood
function, I have to sum these log-likelihood functions for each i and so to
get another function that is a function only of betas and so to maximize it
through maxLik for instance. Is that possible? 

In order to be more clear I give an example of how it could be:

Prob1	 <- function(b, i)
g.yj(b,y=1,h.np,i)/(g.yj(b,y=1,h.np,i)+g.yj(b,y=0,h.np,i))
loglik.i<- function(b, i) Y[i,]*log(Prob1(b,i))+(1-Y[i,])*log(1-Prob1(b,i))

where b denotes the betas, i the observations, Y is the response vector and
g.yj(b,1,h.np,i) a function that I created previously, Prob1(b,i) is a
function that gives the conditional probability for observation i and
loglik.i(b,i) is function that gives the log-likelihood for observation i.

How can I sum the loglik.i(b,i) for each i and remain as a function of b
ONLY in order to maximize it???

For exemple this could be done manually by
loglik<- function(b)
loglik.i(b,1)+loglik.i(b,2)+loglik.i(b,3)+?.+loglik.i(b,N)

but how can I do it automatically for all observations?

Thank you

Dimitris



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On 6 October 2011 16:20, Dimitris.Kapetanakis
<dimitrios.kapetanakis at gmail.com> wrote:
> Dear all,
>
> I would like to create a code for semiparametric Klein and Spady's
> estimator. For that I created a function that provides the log-likelihood
> function for each observation (so it is a function of betas and i, where i
> denotes the observation). Now, in order to maximize the log-likelihood
> function, I have to sum these log-likelihood functions for each i and so to
> get another function that is a function only of betas and so to maximize it
> through maxLik for instance. Is that possible?
>
> In order to be more clear I give an example of how it could be:
>
> Prob1 ? ?<- function(b, i)
> g.yj(b,y=1,h.np,i)/(g.yj(b,y=1,h.np,i)+g.yj(b,y=0,h.np,i))
> loglik.i<- function(b, i)
Y[i,]*log(Prob1(b,i))+(1-Y[i,])*log(1-Prob1(b,i))
>
> where b denotes the betas, i the observations, Y is the response vector and
> g.yj(b,1,h.np,i) a function that I created previously, Prob1(b,i) is a
> function that gives the conditional probability for observation i and
> loglik.i(b,i) is function that gives the log-likelihood for observation i.
>
> How can I sum the loglik.i(b,i) for each i and remain as a function of b
> ONLY in order to maximize it???
>
> For exemple this could be done manually by
> loglik<- function(b)
> loglik.i(b,1)+loglik.i(b,2)+loglik.i(b,3)+?.+loglik.i(b,N)
>
> but how can I do it automatically for all observations?
loglik <- function(b) sapply( 1:N, loglik.i, b = b )

Please note that logLik( b ) returns a *vector* of the likelihood
contributions of each observation. maxLik() takes the sum of the
elements of this vector automatically. If logLik( b ) returns a vector
of the likelihood contributions of each observation (rather than just
the sum), the BHHH optimisation method can be used.

/Arne

-- 
Arne Henningsen
http://www.arne-henningsen.name