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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