I am maximizing the log-likelihood function for a generalized linear model without using per-written functions like glm
due to the form of the model I have. So to maximize the log-likelihood, I am using the optim
function. That works fine. But how can I double check if the estimated parameters are actually occurring at the global maximum and not at a local maximum? Is there any method that guarantees the global maximum?
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1There is no universal method for all functions, so the more you can say about your function and its domain of definition, the stronger the answers will be. (At one extreme, when the log-likelihood is convex and is defined over a convex region, any local maximum will be a global maximum; at another extreme, almost nothing can be said about discontinuous functions or even continuous functions with non-compact domains.) For functions that are sufficiently smooth, plotting is usually worthwhile, as exemplified by the discussion at http://stats.stackexchange.com/a/7629. – whuber May 12 '14 at 18:24