Hello all,

I am a Master's student seeking help to run a mixed effects model with a post-hoc (Tukey) analysis on my thesis data.  I am having difficulty setting contrasts for the post-hoc analysis so that it only compares 3 specific interactions (REF vs TRT @PRE), (REF vs TRT @WK4), and (REF vs TRT @WK8).

I need to compare enzyme activity (APA) from periphyton on rocks in a reference (REF) and treatment (TRT) "reach" of a stream.  I have 3 "stations" within each reach (UP, MID, DWN) where 4 replicate rocks were collected, and I have 3 "time" points to observe differences due to the treatment (PRE, WK4, WK8). Thus, 48 samples total.  I have set up a mixed effects model using "reach" and "time" as the fixed effects and "station" as the random effect.

My mixed effects model was run as follows using the "nlme" package:
lme(APA~1+Time+Reach+Time*Reach, random=~1|Station, method="REML", data=apa3)

Here is the output:
Linear mixed-effects model fit by REML
 Data: apa3
        AIC      BIC   logLik
  -302.3262 -284.809 159.1631

Random effects:
 Formula: ~1 | Station
         (Intercept)   Residual
StdDev: 3.833552e-07 0.01938121

Fixed effects: APA ~ 1 + Time + Reach + Time * Reach
                        Value   Std.Error DF   t-value p-value
(Intercept)       0.028333333 0.005594873 64  5.064160  0.0000
TimeWK4          -0.003333333 0.007912346 64 -0.421283  0.6750
TimeWK8          -0.003333333 0.007912346 64 -0.421283  0.6750
ReachTRT          0.003333333 0.007912346 64  0.421283  0.6750
TimeWK4:ReachTRT  0.023333333 0.011189747 64  2.085242  0.0410
TimeWK8:ReachTRT  0.025833333 0.011189747 64  2.308661  0.0242
 Correlation:
                 (Intr) TimWK4 TimWK8 RchTRT TWK4:R
TimeWK4          -0.707
TimeWK8          -0.707  0.500
ReachTRT         -0.707  0.500  0.500
TimeWK4:ReachTRT  0.500 -0.707 -0.354 -0.707
TimeWK8:ReachTRT  0.500 -0.354 -0.707 -0.707  0.500

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-2.14984854 -0.73094850 -0.08599394  0.42996971  2.36483339

Number of Observations: 72
Number of Groups: 3

>From this output, I gathered that there was a significant interaction between Reach and Time.

The issue I am attempting to address is the manner in which I setup a post-hoc test comparing only the two reaches on one specific time point.  We are not interested in comparing, for instance, REF@WK4 to TRT@WK8, but only (REF & TRT @PRE), (REF & TRT @WK4), and (REF & TRT @WK8).  I have been attempting to set up this comparison using glht in the "multcomp" package, but cannot figure out how to prepare a contrast statement with these interactions only.

Anyone who can set up an interaction contrast statement, please help.

Thank you,
Alyse

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