# [R-sig-ME] What to do when a factor term has several p values?

Toby Marthews toby.marthews at ouce.ox.ac.uk
Thu Jan 20 17:45:19 CET 2011

```Dear Very-patient Mixed-modelling list,

Thank you very much for your replies to my nesting question earlier today. EXTREMEly helpful! It seems I'm tripping over a lot of basic misconceptions with this LME application.

I am running an lme fit with two categorical fixed effects (in this case roostsitu which is roosting situation of some birds - nestbox, tree, inside or other - and mnth=Jan,Nov) and I am trying to simplify the model, i.e. considering whether there is a significant interaction between mnth and roostsitu when measuring the mass of these birds. According to the Fixed effects table of the summary.lme I have 3 p-values (0.1802, 0.3683 and 0.5474) so there's no significant interaction for any of the levels of roostsitu (readout below).

I have tried and failed to create an example to show this, but say there were another factor FF in the LME model and I were trying to follow a model simplification process based on these p-values. Further suppose that the p-value of roostsitu:FF were 0.400. There's a question here whether I would remove roostsitu:FF or roostsitu:mnth from the model first during my model simplification process.

(1) If I'm always supposed to consider the maximum p-value across all levels of a factor, then roostsitu:mnth scores 0.5474 which is >0.400 and it goes out first
(2) If I'm always supposed to take the mean p-value then roostsitu:mnth will score mean(c(0.1802,0.3683,0.5474))=0.3653 which is <0.400 so roostsitu:FF will go out first.
(3) Or some other calculation?

Is there a basic principle or rule I'm missing here regarding what to do in the case of multi-level factors? I would really appreciate someone telling me which option is the right one. I have just spent >1 hour searching a large number of websites and leafed through Pinheiro & Bates again but can't find an answer to this. Lots of websites say to use p-values (referencing Crawley generally) but I need a bit more detail than is in Crawley, it seems.

Thanks very much!
Toby Marthews

> lmeres=lme(fixed=stmass~mnth*roostsitu,random=~1|subject,na.action=na.exclude)

> summary(lmeres)
Linear mixed-effects model fit by REML
Data: NULL
AIC      BIC    logLik
449.6082 472.3749 -214.8041

Random effects:
Formula: ~1 | subject
(Intercept) Residual
StdDev:   0.5868961 4.165333

Fixed effects: stmass ~ mnth * roostsitu
Value Std.Error DF  t-value p-value
(Intercept)                83.6  1.330205 36 62.84747  0.0000
mnthJan                     7.2  1.862793 36  3.86516  0.0004
roostsitunest-box          -4.2  1.881193 36 -2.23263  0.0319
roostsituinside            -5.0  1.881193 36 -2.65789  0.0117
roostsituother             -8.2  1.881193 36 -4.35893  0.0001
mnthJan:roostsitunest-box   3.6  2.634388 36  1.36654  0.1802
mnthJan:roostsituinside     2.4  2.634388 36  0.91103  0.3683
mnthJan:roostsituother      1.6  2.634388 36  0.60735  0.5474
Correlation:
(Intr) mnthJn rstst- rststn rststt mntJ:- mnthJn:rststn
mnthJan                   -0.700
roostsitunest-box         -0.707  0.495
roostsituinside           -0.707  0.495  0.500
roostsituother            -0.707  0.495  0.500  0.500
mnthJan:roostsitunest-box  0.495 -0.707 -0.700 -0.350 -0.350
mnthJan:roostsituinside    0.495 -0.707 -0.350 -0.700 -0.350  0.500
mnthJan:roostsituother     0.495 -0.707 -0.350 -0.350 -0.700  0.500  0.500

Standardized Within-Group Residuals:
Min          Q1         Med          Q3         Max
-1.75548143 -0.76870435 -0.08640394  0.70218233  2.16928300

Number of Observations: 80
Number of Groups: 40

> anova(lmeres)
numDF denDF   F-value p-value
(Intercept)        1    36 31143.554  <.0001
mnth               1    36    95.458  <.0001
roostsitu          3    36    10.614  <.0001
mnth:roostsitu     3    36     0.657  0.5838
>

```