I have a model in R that looks like this
mdl.CL <- lmer(Y.CL ~ 1 + TL*PL*GO + (1|SUBJ), data = data.CL)
in which TL
has 3 levels, PL
6 levels, and GO
2 levels only.
Now, I'd like to test the effect of GO
. However, if I use both anova
and summary
, I obtain results that I am not sure on how to interpret. In particular, this is the (truncated) output of summary
:
> summary(mdl.CL)
Linear mixed model fit by REML ['lmerMod']
Formula: Y.CL ~ 1 + TL * PL * GO + (1 | SUBJ)
Data: data.CL
REML criterion at convergence: -1021.4
Scaled residuals:
Min 1Q Median 3Q Max
-3.2480 -0.6655 0.1448 0.7411 2.4780
Random effects:
Groups Name Variance Std.Dev.
SUBJ (Intercept) 0.007723 0.08788
Residual 0.050555 0.22485
Number of obs: 9134, groups: SUBJ, 23
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.620697 0.018724 33.15
TL.L 0.004658 0.005998 0.78
TL.Q 0.021164 0.007135 2.97
PL.L 0.001186 0.010432 0.11
PL.Q -0.027180 0.009702 -2.80
PL.C 0.010089 0.009453 1.07
PL^4 -0.001677 0.008922 -0.19
PL^5 -0.007471 0.007921 -0.94
GO.L 0.011405 0.005588 2.04
...
while this is the output of anova
:
> anova(mdl.CL)
Analysis of Variance Table
Df Sum Sq Mean Sq F value
TL 2 0.05962 0.029810 0.5896
PL 5 1.33398 0.266796 5.2773
GO 1 0.00210 0.002104 0.0416
...
As you can see, the t value from summary
is 2.04 and the F value from anova
is 0.0416. Now, since GO
has two levels only, I'd expect the t and the F values to be closely related, but this is not the case (at least, I could not find any obvious mapping between t and F, also with other models).
Does anybody know why?
anova()
computes type II sum of squares, whereas what you get fromsummary()
corresponds to type III sum of squares, so this might explain the difference. See here stats.stackexchange.com/questions/20452 about what type I/II/III means in ANOVA. $\endgroup$lmerTest::anova()
, whereas you seem to be usinglme4::anova()
. $\endgroup$