# Gaussian quadrature for bivariate normal distribution

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## Gaussian quadrature for bivariate normal distribution

 This post was updated on . Dear R Users I am maximizing  a likelihood function it has two two correlated random effects which follows bivariate normal distribution. To get the marginal distribution I want to integrate out with respect to these two correlated random effects. Does any body know how can I implement gaussian quadrature to approximate this integral. Thanks for taking time
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## Re: Maximization problem in the optim function

 What distribution's log-likelihood are you using? If sigma is supposed to be square-rooted, you may have to put a constraint or use of abs() might suffice -- though, admittedly I'm not sure what that will do to convergence behavior -- but it's hard to help without seeing the function at hand. Michael On Wed, Mar 14, 2012 at 6:57 PM, Niroshan <[hidden email]> wrote: > Dear R Users > > > I am maximizing a user defined log likelihood function. It includes variance > parameter (sigma). I used R function optim with BFGS maximization method. > However, it stops before the solution saying “sqrt(sigma): NaNs produced” > Could anybody know a proper transformation for sigma which can be passed in > the function?  For the correlation parameter I used Fishers’ transformation > so it didn’t give any problems. I know we can use ‘L-BFGS-B’ method instead > of ‘BFGS’. However, it produces some non sensible estimates. > > Thanks for taking time > > > -- > View this message in context: http://r.789695.n4.nabble.com/Maximization-problem-in-the-optim-function-tp4473408p4473408.html> Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > [hidden email] 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. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.