Paired contrasts/Multi comp: glht to test for differences of differences (nb glmm) - Do I use an interaction model for the matrix? I am struggling with paired contrasts of linear models. I want to test for the differences of differences, and I am not sure if I have to use my original model or the interaction model to build the matrix. I thought it should be the same, but my results are (slighlty) different.
My data:
I want to test the influence of burns on animal abundance. I've got data from 3 periods (Period: before, post1 and post2). I have one burn and one control site (treatment: pburn & control).
I am using a nb glmm
mod7 <- glmmadmb(abundance ~ Period*treatment,random = ~ 1|trap, family = "nbinom", data = Spall)

Estimate Std. Error z value Pr(>|z|)    
(Intercept)                   2.942      0.306    9.62   <2e-16 ***
Periodpost1                  -0.903      0.427   -2.11    0.034 *  
Periodpost2                  -0.247      0.417   -0.59    0.553    
treatmentpburn               -0.704      0.450   -1.56    0.118    
Periodpost1:treatmentpburn   -0.421      0.633   -0.66    0.506    
Periodpost2:treatmentpburn    1.173      0.592    1.98    0.047 *  
  ---

with
head(SPall)
 abundance treatment Period trap species          int
1         2     pburn before   t1    both pburn.before
2        24     pburn before   t2    both pburn.before
3         1     pburn before   t3    both pburn.before
4         8     pburn before   t4    both pburn.before

I want to do a pairwise test, tesing for the differences of differences (If the changes between control.before and control.post1 are different to the changes between pburn.before and pburn.post1 for example)
But I am really confused about whether I should use my original model, or an interaction model to build the matrix....
Original model matrix
(comparing differences between control.before&control.post1 VS pburn.before&pburn.post1)
BP1 <-matrix(c(1,-1,0,0,0,0),1)
PBBP1 <- matrix(c(1,-1,0,1,-1,0),1)
BP1 <- CBP1-PBBP1
CP <- glht(mod7, linfc=BP1)
summary (CP)

Linear Hypotheses:
       Estimate Std. Error z value Pr(>|z|)
1 == 0   0.2832     0.7429   0.381    0.703

#interaction model

SPall$int <- with(SPall, interaction(treatment, Period, drop = TRUE))
mod.int <- glmmadmb(abundance ~ 0 + int, random = ~ 1|trap, family="nbinom", data = SPall)

With the interaction model matrix
CBP1 <-matrix(c(1,0,-1,0,0,0),1)
PBBP1 <- matrix(c(0,1,0,-1,0,0),1)
BP1 <- CBP1-PBBP1  
CP <- glht(mod.int, linfc=BP1)  

summary (CP)

Linear Hypotheses:
      Estimate Std. Error z value Pr(>|z|)
1 == 0  -0.4211     0.6333  -0.665    0.506

I am wondering if anyone can help me. I am pretty new to all this, so I am hoping I didn't do anything wrong.
 A: I think you definitely should include the interaction in the model if you want to test an interaction contrast. Otherwise, it doesn't make sense because any interaction contrast would be estimated as zero (unless you make a mistake somewhere).
An easy way to create and test interaction contrasts is to use the lsmeans package (available from CRAN). But do not use that constructed int factor -- use the earlier model mod7 that has treatment and Period in there explicitly:
library("lsmeans")
mod.lsm <- lsmeans(mod7, ~ treatment * Period)
mod.lsm     # display the cell means
contrast(mod.lsm, "dunnett", interaction = TRUE, adjust = "none")
coef(.Last.value)

The 4th statement above shows the interaction contrasts along with their standard errors, t ratios, and unadjusted P values. The interaction contrast coefficients are obtained as the products of the contrast coefficients suggested in the row labels. The last statement may be used in case you are in doubt about what those coefficients are. But since the Dunnett contrasts compare each level with the first level, the resulting interaction contrasts are differences of differences.
