[R] continuous independent variable in lme

[Prof Brian Ripley]

Your anova call is a sequential anova, which you are misinterpreting.
You can't conclude terms are significant or not if later terms are.
You need to use type="marginal" to interpret things the way you do (except 
that I hope that does not drop the main effect and keep the interaction).

You also seem to be interpreting main effects in the presence of 
interactions incorrectly.  In your first model the coefs for `line' are
intercepts at 0 temp (probably uninteresting) whereas in the second they 
are at intercepts at temp=21.5 (probably also uninteresting).  It makes 
perfect sense to have lines of different slopes with similar intercepts at 
0 but different ones at 21.5.

Perhaps it is `temp' you want to think hard about how to code?

On Sun, 27 Jul 2003, Federico Calboli wrote:

> I am writing to ask a clarification on what R, and in particular lme, is
> doing.

Actually, it is the user who tells R what to do, and it does as it is
told.  What you are asking is what the language you used means.

> I have an experiment where fly wing area was measured in 4 selection lines,
> measured at 18 and 25 degrees. I am using a lme model because I have three
> replicated per line (coded 1:12 so I need not use getGroups to creat an
> orederd factor).
> 
> The lines are called: "18"; "25"; "l"; "s".  My data looks like:
> 
>   temp line replicate   area  
> 1   25    l    3  92693 
> 2   25    l    3 100092 
> 3   25    l    3 100039 
> 4   25    l    3  97558 
> 5   25    l    3  95603 
> 6   25    l    3 100482 
> .....
> 
> "18" and "25" are controls for the two other lines so I have set the
> following contrasts for lines:
> 
>    [,1] [,2] [,3]
> 18    1    0    1
> 25   -1    0    1
> l     0    1   -1
> s     0   -1   -1
> 
> If I do the following:
> 
> mod1<-lme(area ~ line * temp, random = ~1|replicate/temp, mydata)
> anova(mod1)
> 
> I get:
> 
>             numDF denDF  F-value p-value
> (Intercept)     1   336 41817.83  <.0001
> line            3     8    14.38  0.0014
> temp            1     8   338.21  <.0001
> line:temp       3     8     0.62  0.6211
> 
> 
> I have a significant effect of selection line. Eyeballing the
> interction.plot, it is clear the the line called "25" is smaller at both
> temperatures than the other lines.
> 
> but when I check the contrasts with summary(mod1) I get:
> 
> Fixed effects: area ~ line * temp 
>                 Value Std.Error  DF   t-value p-value
> (Intercept) 165417.32  3102.751 336  53.31312  <.0001
> line1         2631.71  4387.952   8   0.59976  0.5653
> line2        -2603.27  4387.952   8  -0.59328  0.5694
> line3        -4667.61  3102.751   8  -1.50435  0.1709
> temp         -2614.39   142.160   8 -18.39045  <.0001
> line1:temp      96.39   201.045   8   0.47946  0.6444
> line2:temp      95.74   201.045   8   0.47623  0.6466
> line3:temp     168.55   142.160   8   1.18561  0.2698
> 
> There seems to be no difference in my lines, according to the contrasts I set!
> 
> I tried to do the same analysis using temperature as an orderd factor:
> 
> mod2<-lme(area ~ line * ordered(temp), random = ~1|replicate/ordered(temp),
> mydata)
> anova(mod2)
> 
>                    numDF denDF  F-value p-value
> (Intercept)            1   336 41817.83  <.0001
> line                   3     8    14.38  0.0014
> ordered(temp)          1     8   338.21  <.0001
> line:ordered(temp)     3     8     0.62  0.6211
>  
> the same anova, but the contrasts are :
> 
> Fixed effects: area ~ line * ordered(temp) 
>                           Value Std.Error  DF   t-value p-value
> (Intercept)           109207.89  534.0393 336 204.49409  <.0001
> line1                   4704.14  755.2457   8   6.22862  0.0003
> line2                   -544.76  755.2457   8  -0.72130  0.4913
> line3                  -1043.87  534.0393   8  -1.95467  0.0864
> ordered(temp).L       -12940.58  703.6576   8 -18.39045  <.0001
> line1:ordered(temp).L    477.12  995.1221   8   0.47946  0.6444
> line2:ordered(temp).L    473.91  995.1221   8   0.47623  0.6466
> line3:ordered(temp).L    834.26  703.6576   8   1.18561  0.2698
> 
> way different from the previous model. This time the "18" and "25" lines
> are different!

Yes, as the interpretation is different.

> As I do not want to specify a model thinking I am doing something when I am
> not, I would like to ask you why the difference in the results? 
> 
> the fact that my continuous variable, temperature, is rapresented by two
> integers, 18 or 25, can cause the difference? assuming I were interested in
> the interaction between my contrasts and temperature, to asses differences
> in the slope between treatments, what should I do?

Code treatment sensibly, as a factor.  What is sensible depends on your 
subject's context.

> Again, I ask this in order to properly understand what lme is doing so I
> can go back to work and specify the model I want rather than something else
> altogether.

Almost nothing to do with lme, only with linear-model coding.  Please
read thoroughly e.g. the appropriate chapters of MASS so you understand 
coding.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595