Dear S users, Sorry for the length of this message.
I have a problem where I am trying to find maximum
likelihood estimates: I have a variable with 10 different levels.
and a parameter correspond to each of the 10 levels.
We assume a LOGISTIC DISTRIBUTION, where the density
is given by f(x|mu b)=1/b * exp(-(x-mu)/b)/(1+exp(-(x-mu)/b))^2.
where mu=theta*phi, and theta is a known parameter vector, and
phi is 10 dimensional paramter. Also we assume a relationship
between the mean and variance, so that b=(3*a*(mu-mu0)/pi^2)^1/2.
where mu0 is a fixed constant., and a is an unknown paramter,
therefore we now have 11 parameters to estimate.
Each set of group can have the same parameter value in my data.
One more thing: The constribution to the likelihood depend on whether
or not x>c, or x<=c.
if x<=c, then the contribution to the likelihood is 1/1+exp(mu-c),
if x>c then the contribution is the above density evaluated at x.
Hence, I obtain the likelihood by taking the product over all
the above expressions.
My problem is that I can't seem to apply the nlmin function to
minimize the negative log-likelihood.
I have created a vector containing the parameter names (phi1-phi10)
But I am afraid I can't use Splus to compute the Likelihood, and then
minimize the -log-likelihood.
Any help will be greatly appreciated.
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