I am not surprised that you are running into difficulties with this model estimation, since you are treating a constrained optimization problem as unconstrained one. It is not so easy to set constraints on the covariance matrix (i.e. positive definiteness). The is the beauty of the EM algorithm is that not only does it possess the ascent property (i.e. the likelihood is guaranteed to not decrease) for any starting value, but it also ensures that the constraints are automatically satisfied. Therefore, EM would be my preferred choice. Why do you not want to try that?
If you really want to use direct maximization, you could try to impose all the constraints on the parameters, including positive definiteness of covariance matrix, and solve the constrained optimization problem. R has two packages: "alabama" and "Rsolnp" that can handle nonlinear constraints. Ravi. -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of roach Sent: Thursday, October 21, 2010 10:24 PM To: r-help@r-project.org Subject: [R] Help: Maximum likelihood estimation I was trying to reproduce a result in a published journal, and I have come across some difficulties. I have the following equation, which is two equations combined together. http://r.789695.n4.nabble.com/file/n3006584/Screenshot.png where http://r.789695.n4.nabble.com/file/n3006584/Screenshot-1.png http://r.789695.n4.nabble.com/file/n3006584/Screenshot-2.png http://r.789695.n4.nabble.com/file/n3006584/Screenshot-3.png I[t] is unknown, but have the following distribution http://r.789695.n4.nabble.com/file/n3006584/Screenshot-4.png hence, the probability density function is http://r.789695.n4.nabble.com/file/n3006584/Screenshot-5.png and the likelihood function is http://r.789695.n4.nabble.com/file/n3006584/Screenshot-6.png It used Kiefer's E-M algorithm to estimate the problem. To simplify, first assume lamda is known. I multiply the matrix in the probability density function, and write it in a non-matrix form, and use the function optim() to estimate the maximum. but I got non-sensible estimates of the parameters, and got 39 warnings. the inverse of sigma is negative, and the warnings says that in log(det(sigma)): NaNs produced. What did I do wrong? Can anybody give me a hint? -- View this message in context: http://r.789695.n4.nabble.com/Help-Maximum-likelihood-estimation-tp3006584p3 006584.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.