[R-sig-ME] Confidence intervals in GAMM4

[Highland Statistics Ltd]

> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 11 Jun 2013 09:02:22 -0300
> From: Rodrigo Tardin <rhtardin at gmail.com>
> To: Gavin Simpson <gavin.simpson at ucl.ac.uk>
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] Confidence intervals in GAMM4
> Message-ID:
> 	<CAE5HZZKkEmyCYre6NgJb3fciLX5pA8ZwkhaAuaXTR4=htY2ZWw at mail.gmail.com>
> Content-Type: text/plain
>
> Hi Gavin and other member of the list
>
> Thanks a lot for your response. You are right about the correlation
> structure. I was not aware, thank you.
> One other question that may look like very basic:
> Without the correlation structure (that as you said, does not exist in
> GAMM4 or lme4) in the mixed model, does it account for autocorrelation or
> no, without any specification of correlation structure it does not account
> for autcorrelation in the residuals. Because my data do have a problem of
> autocorrelation on the residuals.

Hello,
Here is an alternative (and probably the only) approach:

1. Write your smoother as X * beta + Z * b (e.g. using an O'Sullivan spline)
2. Add more covariates to your predictor function (if needed)
3. Add random effects to the predictor function, and also an 
auto-regressive correlation structure on the residuals in the predictor 
function.
4. Put the whole thing in JAGS and let it run for a while

Plenty of papers are available for step 1...see for example:

ON SEMIPARAMETRIC REGRESSION WITH O’SULLIVAN PENALIZED SPLINES
M. P. WAND AND J. T. ORMEROD

They also provide R code for such smoothers. No need to dive into the 
underlying stats.


Steps 3 & 4 are described in our upcoming book
'Beginner's Guide to GLM & GLMM with R"
Zuur, Hilbe, Ieno

available next week

Other smoother options are described in 'A Beginner's Guide to GAM', 
Zuur (2012)
Or in Wood (2006), or Ruppert et al. (2003). Plus a whole bunch of 
papers from Wand.


Alain
> Thanks in advance
> Rodrigo




-- 

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


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