Dear R list,I'm trying to fit a generalized mixed model...all the factors are fixed effects (Abundance of species was hypothesized to be a function of fixed e	ffects, including time (2001 vs. 2012), summit, cardinal direction (N, S, W, E), and interactionsamong these and repeated measures on the same subject (polt id) is the only random effect. My data (Abundance) are counts and I used a Poisson distribution $ Abundance : int  14 5 34 14 0 8 7 13 9 35 ... $ time     : Factor w/ 2 levels "2001","2012": 2 2 2 2 2 2 2 2 2 2 ... $ summit   : Factor w/ 3 levels "FEM","MAC","MAM": 1 1 1 1 1 1 1 1 1 1 ... $ direction: Factor w/ 4 levels "E","N","S","W": 1 1 1 1 2 2 2 2 3 3 ... $ plot_id  : Factor w/ 48 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...I checked for data overdispersion by plotting group means against group variances (Bolker et al. 2009 supplementary materials).Since my data are overdispersed I fit the GLMM by maximum likelihood (glmmPQL function) (mean numberof counts per treatment combination is more than five)
I'm mainly interested  in the time effect and then in intercation with the others fixed effects
model1<-glmmPQL(Abundance~time*summit*direction, random = ~1|plot_id, data=endem, family="quasipoisson")model2<-glmmPQL(Abundance~time+summit+direction, random = ~1|plot_id, data=endem, family="quasipoisson")
For Model 1 only summit shows a significant effects 
By removing the interaction (direction*time, summit*time, direction*summit and direction*summit*time) terms (model2) time and summit show significant effects
How should I choose the best model?
Thanks in advanced
Ludovico
                                                                                                                                
Ludovico
Frate

PhD student (University of Molise - Italy)
Environmetrics Lab
http://www.distat.unimol.it/STAT/environmetrica/organico/collaboratori/ludovico-frate-1
Department of Biosciences and Territory - DiBT
Università del Molise.
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E-mail ludovico.frate@unimol.it
ludovicofrate@hotmail.it
 		 	   		  
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