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I am currently using the Laplace approximation to fit some geostatistical models for binomial data. Regarding parameters estimation I do not have any problem. I can easily implement the Laplace approximation and get my estimates.

But when it comes to obtain the standard errors I am puzzled about how I can derive the hessian of my objective function, hence the Fisher information. I tried to derive this analytically but it seems very laborious and tedious. Is there any reference about this or someone has a solution?

kjetil b halvorsen
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Emanuele Giorgi
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  • Welcome to the site, @Emanuele Giorgi! You can refer to "Maximum Likelihood for Generalized Linear Models With Nested Random Effects via High-Order, Multivariate Laplace Approximation" by RAUDENBUSMH, YANG, and YOSEF (2000). Also, the `glmer()` in `R` package `lme4` uses Laplacian approximation in default. – Randel Jan 29 '14 at 17:01
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    Can you just use a finite-difference approximation to get a good-enough estimate of the hessian ... ? – Ben Bolker Jan 29 '14 at 23:46
  • You should really give some more details, like the exact method you are using (or at least a reference) – kjetil b halvorsen Nov 19 '14 at 11:17

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