[R-sig-ME] (stupid) results interpretation question

[Ben Bolker]

CL Pressland wrote:
> I have a seemingly stupid but fundamental question I need answering.
> 
> I've had some strange plots and am now seriously questioning my 
> interpretation of the lmer output: if I have a fixed effects results table 
> that looks like this, can someone please check I'm interpreting it 
> correctly?
> 
> ---------
> Fixed effects:
>             Estimate Std. Error t value
> 1	(Intercept) -1.58481    0.18585   -8.53
> 2	GM1          0.02400    0.20472    0.12
> 3	GM2          0.17941    0.15916    1.13
> 4	Morph1      -1.54068    0.02202  -69.97
> 5	GM1:Morph1  -0.21681    0.04701   -4.61
> 6	GM2:Morph1  -0.12910    0.03321   -3.89
> ---------
> 
> 1. Intercept is GM0 and Morph0
> In my understanding the estimates given are the differences from the 
> intercept alone so would give mean values for each category of:
> 1	-1.58481
> 2	-1.5601
> 3	-1.4054
> 4	-3.12549
> 5	-1.80162
> 6	-1.71391
> 

  If z <- fixef(fit) then the last two should be
z[1]+z[2]+z[4]+z[5]=-3.32, z[1]+z[3]+z[4]+z[6]=-3.076
(i.e. "intercept plus difference from baseline in GM (if any)
plus difference difference from baseline in Morph (if any) plus
interaction").  You may be able to get more interpretable parameters
by using -1 (drop intercept) judiciously in your model statement,
although it will make tests of effects harder.

  You can also try to use predict() to see if you've understood
the parameterization correctly.

> I don't want to plough through thinking I've understood this when I may not 
> have! I've tried looking in Pinheiro and Bates etc but they all just say 
> the "estimate is the difference in the means" - I want to make sure I'm 
> interpreting it correctly.