> Dear Frank,

> thanks for your suggestions! I still have some questions:

I though that autocorrelated / autoregressive residuals inflate p- 
values, thus insignificant variables become significant, not the other  
way around?
Did I get it right? You suggest to use in the second step a GLS or  
mixed model (where I included AR1 correlation structure), where only  
those variables are included that have been significant in the first  
step?
I tried both ways: your 2-step approach as well as the GLS/mixed model  
as in your second step but with a full model (including all  
covariates) and then do the model selection. The results where the  
same. So why is it not ok to use a full GLS/mixed model followed by  
the model selection in the first place?

I still do not understand the difference between an AR1 model where  
other covariates are included as well (e.g. by using the arima()  
function) and a model where I included an AR1 correlation structure  
(by using e.g. gls() or lme() )

Is there any book where I can find out more about this matter?

Thanks again,
Saskia
>
>
> ------------------------------
>
> Message: 4
> Date: Thu, 11 Nov 2010 16:26:21 +0200
> From: Frank Berninger <frankberninger@gmail.com>
> To: r-sig-ecology@r-project.org
> Subject: [R-sig-eco] Autoregressive modelling
> Message-ID: <4CDBFD0D.7030806@gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> Dear Saskia,
>
> 1) Autoregressive residuals (for stationary AR processes) do not bias
> your estimates but will bias your confidence intervals. (Unfortunately
> mostly making significant variables insignificant). If the AR model  
> for
> your residuals is not stationary you are in statistical trouble.
>
> 2) I think that there are different ways of proceeding. The most
> conservative way would be to do a two stage process: (A) first you
> identify your model (using detrended dependent and independent
> variables). The variables that are significant are thereafter used in
> the second stage. (B) You build the model using the variables found in
> A. This can be done in using gls (nlme package) or mixed models. That
> model the autocovariance structure.
>
> Some people do not do A but use a gls model directly. I think in the
> case of strong trends in the data (both X and Y) A could be  
> insightful.
> On the other hand the identification might fail for variables that
> increase evenly with a strong time trend without much variation in the
> rate of increase.
>
> Frank
>
>
>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Wed, 10 Nov 2010 13:56:33 +0100
>> From: Saskia Otto<Saskia.Otto@uni-hamburg.de>
>> To: r-sig-ecology@r-project.org
>> Subject: [R-sig-eco] handling autocorrelation in regression data
>> Message-ID:<4CDA9681.4080405@uni-hamburg.de>
>> Content-Type: text/plain
>>
>> Dear list members,
>>
>> to identify the drivers of a temporal trend in fish abundance, I  
>> applied
>> a linear regression including several covariates in the full model:
>> Abun_t ~ b_0 + b_1 *cov1_t + b_2 *cov2_t + ... + e_t , where t
>> represents the year.
>>
>> The problem is that the residuals of the full model show strong
>> autocorrelation (order 1 autoregressive (AR(1) ) errors), thus  
>> violating
>> the independence assumptions.
>> My question is now: what can I do alternatively?
>> Since I want to model explicitly the trend, I do not want to  
>> detrend the
>> time series.
>> Should I fit an autoregressive time series model where I include  
>> other
>> covariates as well:
>> Abun_t ~ b_0 + b_1 *Abund_t-1 + _b_2 *cov1_t + b_3 *cov2_t +...+  
>> e_t ?
>> Can I do this using the lm() function:lm(Abun_t ~ Abund_t-1 +  
>> cov1_t +
>> cov2_t + ...)
>> or do I have to use the function arima(): arima(Abund _t , order =
>> c(1,0,0), xreg = cbind(cov1,cov2,...) )  ?
>>
>> What is the difference between an AR1 model (by using for instance  
>> the
>> arima function where I define only the AR order) and the gls()  
>> function
>> where I include an AR1 correlation structure:
>> gls(Abun_t ~ cov1_t + cov2_t + ..., correlation = corAR1(form =~ 1 |
>> Year) )  ?
>>
>> To me it seems quite similar, but I only came across literature that
>> dealt with either one of these approaches.
>>
>> I would be glad if someone of you could help me out and get things
>> clearer on this issue.
>>
>> Thanks a lot in advance!
>> Saskia
>>
>>
>
>


Saskia A. Otto

Mail: Saskia.Otto@uni-hamburg.de
Phone: +49(0)40-42838 6648
Hamburg University
Institute for Hydrobiology and Fisheries Science
Grosse Elbstrasse 133
22767 Hamburg
Germany




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