I am currently in an assistant student research position (I am working directly with a, for sake of privacy, Dr. R, on developmental Toxicity Dose-Response Modeling simulation).
I am currently using R trying to maximize and estimate using the 'mle' function (maximum likelihood estimate). Having trouble with this question before I have asked questions on sister sites found here: Trouble With MLE!
The function with parameters I want to estimate is, $$L\varpropto \sum_{i=1}^g\sum_{j=1}^{m_i}\{\sum_{k=0}^{x_{ij} -1}log(\mu_i +k*\theta_i )+\sum_{k=0}^{n_{ij}-x_{ij}-1}log(1-\mu_i+k*\theta_i)-\sum_{k=0}^{n_{ij}-1}log(1+k*\theta_i)\}$$
where, $g, m_i, x_{ij},and \space n_{ij}$ are already known. This means the parameters i want to estimate and maximize are $\mu_1...\mu_g$ and $\theta_1...\theta_g$. I have initial values for both $\mu\space and\space\theta$.
My Question is:
What methods can I use to maximize and estimate these parameters? Though I have been using the mle function as shown in the above link, I was curious to see if there were other methods since I could not get the mle function to work.
The research i have done online points me to other statistical software or R, which i am obviously having trouble with. Any help would be appreciated!