# Estimate Model Parameters Using Optimization This function estimates the parameters of a model by minimizing the negative log-likelihood function using the specified optimization method. It utilizes the `optim()` function in R, with the provided initial parameter values and gradient computation. The optimization method can be specified, with "BFGS" being the default. ```r estimate_parameters(initial_params = rep(0.01, 4), optimMethod = 'BFGS') ``` ## Arguments - `initial_params`: A numeric vector of initial parameter values to start the optimization. Default is a vector of four values, all set to 0.01. - `optimMethod`: A character string specifying the optimization method to use. The default is `"BFGS"`. See `?optim` for a list of available methods. ## Returns An `optim` object containing the optimization results, including the estimated parameters, value of the objective function at the optimum, and other optimization details. ## Details The `estimate_parameters` function performs parameter estimation by minimizing the negative log-likelihood function using the chosen optimization method. The function requires an initial guess for the parameters (a numeric vector) and will optimize the log-likelihood function. The optimization also takes into account the gradient of the log-likelihood function, which is computed using the `compute_grad` function. The result of the optimization is an object of class `optim` containing the estimated parameters and other details of the optimization process. The optimization method can be specified via the `optimMethod` argument. The default method is "BFGS", but any method supported by R's `optim()` function (such as "Nelder-Mead", "CG", etc.) can be used. ## Examples ```r library(cmpp) data("fertility_data") Nam <- names(fertility_data) fertility_data$Education datt <- make_Dummy(fertility_data, features = c("Education")) datt <- datt$New_Data datt['Primary_Secondary'] <- datt$`Education:2` datt['Higher_Education'] <- datt$`Education:3` datt$`Education:2` <- datt$`Education:3` <- NULL datt2 <- make_Dummy(datt, features = 'Event')$New_Data d1 <- datt2$`Event:2` d2 <- datt2$`Event:3` feat <- datt2[c('age', 'Primary_Secondary', 'Higher_Education')] |> data.matrix() timee <- datt2[['time']] Initialize(feat, timee, d1, d2, 1e-10) # Estimate model parameters using default initial values and the BFGS method result <- estimate_parameters() print(result) ``` ## See Also stats::optim for more details on optimization methods and usage.

estimate_parameters function