[R] ANCOVA post-hoc test

[peter dalgaard]

Inline below

On Feb 12, 2012, at 13:39 , Evagelopoulos Thanasis wrote:
[...]
> 
> Because there exist significantly different regression slopes, I did a post hoc test with glht() to find out between which samplings:
> 
>> summary(glht(mod, linfct=mcp(sampling="Tukey")))
> 

I believe this compares the intercepts, not slopes. Slope differences are in the sampling:dist interaction terms.

> The results seem to say that there are no significantly different slopes for any of the pair-wise comparisons of factor levels:
> 
>  Simultaneous Tests for General Linear Hypotheses
> 
> Multiple Comparisons of Means: Tukey Contrasts
> 
> 
> Fit: aov(formula = h ~ sampling * dist, data = data)
> 
> Linear Hypotheses:
>             Estimate Std. Error z value Pr(>|z|)
> sp - au == 0  0.06696    0.04562   1.468    0.457
> su - au == 0 -0.02238    0.04562  -0.491    0.961
> wi - au == 0  0.01203    0.04562   0.264    0.994
> su - sp == 0 -0.08934    0.04562  -1.958    0.204
> wi - sp == 0 -0.05493    0.04562  -1.204    0.624
> wi - su == 0  0.03441    0.04562   0.754    0.875
> (Adjusted p values reported -- single-step method)
> 

We don't have coefficients for your model, so it is a bit hard to tell what the parameter functions are, but I would expect those NOT to be the slope differences.

> Warning message:
> In mcp2matrix(model, linfct = linfct) :
>  covariate interactions found -- default contrast might be inappropriate
> 
> 
> 
> My questions are:
> 
> - Did I make a mistake somewhere? (I probably did!)

You need to figure out how to get glht to look at the appropriate linear hypothesis (and mcp(sampling=...) is not right). I'd do a straight lm() analysis so that I'd know exactly what the parameters mean -- aov() can be a little too good at hiding technical details from the user! 

> - Could I do pairwise ANCOVAs and thus have just two factor levels (=two regression slopes) to compare each time?

Possibly, but you'd lose the multiple comparison features of glht.

> What does the warning message "covariate interactions found -- default contrast might be inappropriate" mean?
> 

That you likely don't want to look at intercepts (or whatever the "sampling" parameters represent --- I'm not familiar with that ancova() function) in the presence of interactions... 

> Thank you!
> Athanasios Evagelopoulos
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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