title: Error with post hoc tests in ANCOVA with factorial design
body: <p>Does anyone know how to do post hoc tests in an ANCOVA model with a factorial design?</p>
  
  <p>I have two vectors consisting of 23 baseline values (covariate) and 23 values after treatment (dependent variable) and I have two factors with both two levels. I created an ANCOVA model and calculated the adjusted means, standard errors and confidence intervals. Example:</p>
  
  <pre><code>library(effects)
  
  baseline = c(0.7672,1.846,0.6487,0.4517,0.5599,0.2255,0.5946,1.435,0.5374,0.4901,1.258,0.5445,1.078,1.142,0.5,1.044,0.7824,1.059,0.6802,0.8003,0.5547,1.003,0.9213)
  after_treatment = c(0.4222,1.442,0.8436,0.5544,0.8818,0.08789,0.6291,1.23,0.4093,0.7828,-0.04061,0.8686,0.8525,0.8036,0.3758,0.8531,0.2897,0.8127,1.213,0.05276,0.7364,1.001,0.8974)
  
  age = factor(c(rep(c("Young","Old"),11),"Young")) 
  treatment = factor(c(rep("Drug",12),rep("Placebo",11)))
  
  ANC = aov(after_treatment ~ baseline + treatment*age)
  
  effect_treatage = effect("treatment*age",ANC)
  data.frame(effect_treatage)
  
    treatment   age       fit        se     lower     upper
  1      Drug   Old 0.8232137 0.1455190 0.5174897 1.1289377
  2   Placebo   Old 0.6168641 0.1643178 0.2716452 0.9620831
  3      Drug Young 0.5689036 0.1469175 0.2602413 0.8775659
  4   Placebo Young 0.7603360 0.1462715 0.4530309 1.0676410
  </code></pre>
  
  <p>Now I want test if there is a difference between the adjusted means of</p>
  
  <p>Young-Placebo:Young-Drug<br>
  Old-Placebo:Old-Drug<br>
  Young-Placebo:Old-Drug<br>
  Old-Placebo:Young-Drug  </p>
  
  <p>So I tried:</p>
  
  <pre><code>library(multcomp)
  pH = glht(ANC, linfct = mcp(treatment*age="Tukey"))
  # Error: unexpected '=' in "ph = glht(ANC_nback, linfct = mcp(treat*age="
  </code></pre>
  
  <p>And:</p>
  
  <pre><code>pH = TukeyHSD(ANC)
  # Error in rep.int(n, length(means)) : unimplemented type 'NULL' in 'rep3'
  # In addition: Warning message:
  # In replications(paste("~", xx), data = mf) : non-factors ignored: baseline
  </code></pre>
  
  <p>Does anyone know how to resolve this?</p>
  
  <p>Many thanks!</p>
  
  <p>PS for more info see </p>
  
  <p><a href="https://stackoverflow.com/questions/23496230/r-how-to-graphically-plot-adjusted-means-se-ci-ancova">R: How to graphically plot adjusted means, SE, CI ANCOVA</a></p>