
> Hello,
> 
> I am analyzing time-series data for multiple songbird species where
> data were collected at 3 point count stations within a stand (~150
> stations) visited twice a year and with multiple observers. Point
> count stations along seismic lines (10-12 stations/seismic line) were
> added three years after the start of the surveys with 10-12
> stations/seismic line which created an unbalanced design. I am using a
> linear mixed effects model in lme4 that includes year and visit (first
> or second visit to a sight) as fixed effects and observer and station
> nested within stand (or seismic line) (to account for spatial
> auto-correlation) as random variables. The full model includes a
> quadratic effect of year plus their interaction terms (several species
> have shown a quadratic response to budworm outbreak): 
> 
> lme1a<-lmer(Abundance ~ Yr + Yr2 + Seismic + Yr*Seismic + Yr2*Seismic
> + Visit + (1|Site/Station) + (1|Observer), data=CAWA, family =
> poisson(link=log))
> summary(lme1a)
> 
> Reduced models:
> lme2a<-lmer(Abundance ~ Yr + Seismic + Yr*Seismic + Visit +
> (1|Observer) + (1|Site/Station), data=CAWA, family =
> poisson(link=log))
> summary(lme2a)
> 
> lme3a<-lmer(Abundance ~ Yr + Yr2 + Visit + (1|Site/Station)+
> (1|Observer), data=CAWA, family = poisson(link=log))
> summary(lme3a)
> 
> lme4a <- lmer(Abundance ~ Yr + Visit + (1|Site/Station)+ (1|Observer),
> data=CAWA, family = poisson(link = log))
> summary(lme4a)
> 
> I initially included visit as a random effect but since there are only
> 2 levels in this parameter, made it a fixed effect. Doing this changes
> the parameter estimates for the fixed effects only slightly, including
> their AIC values (delta <0.5 in most cases) and has not changed their
> 'significance' (according to the Z-statistic).  
> 
> Based on AIC, the full model fits the data the best (although delta
> AIC for all models is <3). 
> 
>   AIC  BIC logLik deviance
>  1398 1458 -689.1     1378
> Random effects:
>  Groups       Name        Variance Std.Dev.
>  Station:Site (Intercept) 0.272577 0.52209 
>  Site         (Intercept) 2.922394 1.70950 
>  Observer     (Intercept) 0.045124 0.21242 
> Number of obs: 2807, groups: Station:Site, 242; Site, 65; Observer, 19
> 
> Fixed effects:
>              Estimate Std. Error z value Pr(>|z|)    
> (Intercept) -2.847531   0.316017  -9.011   <2e-16 ***
> Yr           0.127510   0.067730   1.883   0.0598 .  
> Yr2         -0.014141   0.006561  -2.155   0.0311 *  
> Seismic     -0.437059   1.263792  -0.346   0.7295    
> Visit       -0.201875   0.092130  -2.191   0.0284 *  
> Yr:Seismic  -0.159138   0.351301  -0.453   0.6506    
> Yr2:Seismic  0.024156   0.026194   0.922   0.3564    
> 
>       Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)  
> lme4a  6 1400.97 1436.61 -694.49                           
> lme3a  7 1401.86 1443.44 -693.93 1.1086      1    0.29238  
> lme2a  8 1398.46 1445.98 -691.23 5.4011      1    0.02012 *
> lme1a 10 1398.15 1457.54 -689.07 4.3172      2    0.11548 
> 
> Question #1: Because the parameter estimates change only slightly with
> the inclusion of visit as a fixed instead of a random effect, is this
> evidence that we could model visit as a random effect since visit is
> really a nuisance variable?
> 
> Question #2: I am interested only in knowing if the trend of a species
> is significant or if changes (slopes) in trends between seismic and
> non-seismic are different. To select models, I initially used AIC to
> select the most appropriate model and then reduced the fixed
> parameters in the model based on their Z-statistic (a la Zuur et al
> 2009) but have since read that that step-wise model selection is not
> appropriate for GLMM. I've also heard (without actually seeing any
> published reference) that model averaging can't be used with quadratic
> terms(?) and log likelihoods are anti-conservative.  Leaving variables
> in a model to predict trend that apparently have little effect on the
> results seems illogical in this case, particularly when no one model
> fits the data much 'better' than any other model. 
> 
Can anyone help me with understanding the most appropriate approach to
selecting a model/parameters with my data set/goals?

> (I've read and re-read multiple papers, books and threads on this
> mailing list but have they have only left me more confused!)
> 
> Thanks a lot for your help!
> 
> Kevin
> 
> 

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