[R] Strange p-level for the fixed effect with lme function

[Prof Brian Ripley]

What code did you actually run to get what you labelled as 'ANOVA'?

If this was anova[.lme], the default type is "sequential", whereas the 
t-values (from summary[.lme], I presume) are from marginal tests.

Whether sequential and marginal tests are similar or even the same is a 
question of balance in the design (for linear models as well).

On Thu, 23 Feb 2006, Petar Milin wrote:

> Hello,
> I ran two lme analyses and got expected results. However, I saw
> something suspicious regarding p-level for fixed effect. Models are the
> same, only experimental designs differ and, of course, subjects. I am
> aware that I could done nesting Subjects within Experiments, but it is
> expected to have much slower RT (reaction time) in the second
> experiment, since the task is more complex, so it would not make much
> sense. That is why I kept analyses separated:
>
> (A) lme(RT ~ F2 + MI, random =~ 1 | Subject, data = exp1)
>
> ANOVA:
>            numDF denDF   F-value p-value
> (Intercept)     1  1379 243012.61  <.0001
> F2              1  1379     47.55  <.0001
> MI              1  1379      4.69  0.0305
>
> Fixed effects: RT ~ F2 + MI
>                Value  Std.Error   DF   t-value p-value
> (Intercept)  6.430962 0.03843484 1379 167.32118  0.0000
> F2          -0.028028 0.00445667 1379  -6.28896  0.0000
> MI          -0.004058 0.00187358 1379  -2.16612  0.0305
>
> ===========================================================
>
> (B) lme(RT ~ F2 + MI, random =~ 1 | Subject, data = exp2)
>
> ANOVA:
>            numDF denDF   F-value p-value
> (Intercept)     1   659 150170.71  <.0001
> F2              1   659     17.28  <.0001
> MI              1   659     13.43   3e-04
>
> Fixed effects: RT ~ F2 + MI
>                Value  Std.Error  DF   t-value p-value
> (Intercept)  6.608252 0.05100954 659 129.54935  0.0000
> F2          -0.008679 0.00616191 659  -1.40855  0.1594
> MI           0.009476 0.00258605 659   3.66420  0.0003
>
> As you can see, in exp1 p-levels for the model and for the fixed effects
> are the same, as thay should be, as far as I know. Yet, in exp2 there is
> significant p for F2 in the model, but insignificant regarding F2 as
> fixed factor. How is it possible? I have ran many linear models and
> those two values correspond (or are the same). Anyway, how can it be to
> have insignificant effect that is significant in the model? Some strange
> property of that factor, like distribution? Multicolinearity? Please,
> help me on that.

-- 
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