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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?

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  • $\begingroup$ Actually, that question suggests that anova() computes type II sum of squares, whereas what you get from summary() 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. $\endgroup$
    – amoeba
    Commented Mar 1, 2017 at 10:26
  • $\begingroup$ Or maybe not - the unanswered Q linked above is about lmerTest::anova(), whereas you seem to be using lme4::anova(). $\endgroup$
    – amoeba
    Commented Mar 1, 2017 at 10:31
  • $\begingroup$ I'll try to have a look at the questions you posted, thanks. I'll post here again if I find a solution. $\endgroup$
    – ariadello
    Commented Mar 1, 2017 at 12:45

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