[R] reporting interactions of factors in linear mixed effects models

Wed Oct 29 19:21:31 CET 2008

Hi,

I have a question about how I should report the results for a linear
mixed effects model where the model includes as predictors three
factors (facA, facB and facC), one of which (facA) interacts with the
other two. facA and facB have two levels and facC has 3 levels. There
are also several other continuous predictors (e.g. varA, varB, varC).
My mixed model is specified with the following formula:

model <- lmer(RT~ facA*facB*facC - facA:facB:facC - facB:facC
+                    + varA + varB + varC + ... + (1|subject) +  (1|
item), data=alldata)

Here are the estimates of the fixed effects:

Estimate Std.Err t.value    pMCMC
(Intercept)                0.896   0.038  23.346    0.000
facA2                     -0.011   0.054  -0.204    0.811
facB2                     -0.024   0.007  -3.656    0.000
facC2                      0.099   0.012   8.040    0.000
facC3                      0.160   0.011  14.428    0.000
var1                       0.025   0.004   5.950    0.000
var2                       0.022   0.004   5.170    0.000
var3                      -0.010   0.004  -2.446    0.014
...
facA2:facB2                0.018   0.008   2.163    0.031
facA2:facC2                0.035   0.011   3.268    0.001
facA2:facC3                0.045   0.010   4.708    0.000

And here is the analysis of variance table, obtained with aovlmer.fnc
in the languageR package:

Df    Sum Sq   Mean Sq  F value        F    Df2
p
facA          1 1.469e-02 1.469e-02   0.3841   0.3841 9225.0
0.5
facB          1       0.7       0.7  18.1221  18.1221 9225.0
2.092e-05
facC          2      14.4       7.2 188.8753 188.8753 9225.0
0.0
varA          1       1.4       1.4  36.7171  36.7171 9225.0
1.419e-09
varB          1       1.1       1.1  28.5398  28.5398 9225.0
9.398e-08
varC          1       0.2       0.2   5.2951   5.2951 9225.0
2.141e-02
...
facA:facB     1       0.1       0.1   3.8429   3.8429 9225.0
4.552e-15
facA:facC     2       0.9       0.4  11.5971  11.5971 9225.0
1.419e-09

For simpler models with no interactions and one 2-level factor, I am
only reporting the estimates, t-values and p-values. However, since in
this model there are two coefficients associated with the facA x facC
interaction, I believe I should report the F-statistic in this case as
this tells us whether the interaction overall is significant (e.g. as
in Section 7.2.2 in Baayen's textbook). However, since the anova table
is calculated stepwise, how do I decide whether facB should appear
before facC in the model specification (the F values depends on the
order)? Also, the contrast coefficients for facA, facB and facC in the
model above are dependent on what the reference levels of those
factors are. Is it meaningful to explore the simple effects of the
factors by using relevel() to change the reference level of the
factors? Finally, why does aovlmer.fnc only give p-vales with one
significant digit in some cases (e.g. the p-value for facA is 0.5)?

Thanks in advance for any advice you can give me, it will be
appreciated greatly.

Barry.