[R-sig-ME] likelihood-ratio tests in conflict with coefficiants in maximal random effect model

[Emilia Ellsiepen]

Dear list members,

in analyzing a data set using lmers with maximal random effect
structure and subsequent likelihood-ratio tests (LRTs) following Barr
et al. 2013, I ran into the following problem: In some of the LRTs, it
turned out that the simpler model (only main effects) has a higher
likelihood than the more complicated model (including interaction),
resulting in Chi=0. If I simplify the models by taking out the
interactions in the two random effect terms, the LRT for the
interaction has a highly significant result.

Now, I figured this might either be a strong case for Barr et al., or
something is going wrong, as the data do suggest an interaction, and
the t-value for the interaction coefficiant in the model summary of
the maximal random effect model is 1.69 - which I would have expected
to be a (close to) marginal effect. Also, a lot of researchers who do
use maximal random effect models rather interpret the t-values
directly instead of running LRTs, which then might lead to different
interpretations of the same data.

My questions are:
1) Is the LRT reported below reliable, indicating there is no
interaction, or does the non-expected difference in logLik suggest
that something went wrong?
2) Is it possible that the control parameter that increases the number
of evaluations has something to do with it?


Here are some details:
The design is 2x2 within subjects and items, the factors are sum-coded.
I used REML=F to straightforwardly perform the LRTs afterwards and
increased the number of evaluations for the model to converge

m1 = lmer(score ~ Order*Voice +
(Order*Voice|subject)+(Order*Voice|sentence) ,REML=F,
control=lmerControl(optCtrl=list(maxfun=50000)),rawdata)
mi = lmer(score ~ Order+Voice +
(Order*Voice|subject)+(Order*Voice|sentence) ,REML=F,
control=lmerControl(optCtrl=list(maxfun=50000)),rawdata)

anova(m1,mi)

Models:
mi: score ~ Order + Voice + (Order * Voice | subject) + (Order *
mi:     Voice | sentence)
m1: score ~ Order * Voice + (Order * Voice | subject) + (Order *
m1:     Voice | sentence)
   Df    AIC    BIC  logLik deviance Chisq Chi Df Pr(>Chisq)
mi 24 1633.0 1742.9 -792.48   1585.0
m1 25 1664.1 1778.5 -807.03   1614.1     0      1          1


summary(m1)

Linear mixed model fit by maximum likelihood ['lmerMod']
Formula: score ~ Order * Voice + (Order * Voice | subject) + (Order *
    Voice | sentence)

      AIC       BIC    logLik  deviance
1664.0644 1778.5457 -807.0322 1614.0644

Random effects:
 Groups   Name          Variance  Std.Dev. Corr
 subject  (Intercept)   0.0387850 0.19694
          Order1        0.0005166 0.02273  0.65
          Voice1        0.0326954 0.18082  0.71 0.55
          Order1:Voice1 0.0266763 0.16333  0.34 0.76 0.57
 sentence (Intercept)   0.0683897 0.26151
          Order1        0.0779307 0.27916  1.00
          Voice1        0.0096621 0.09830  0.61 0.60
          Order1:Voice1 0.1013066 0.31829  0.55 0.55 0.34
 Residual               0.4272769 0.65366
Number of obs: 720, groups: subject, 36; sentence, 20

Fixed effects:
              Estimate Std. Error t value
(Intercept)    0.26184    0.07135   3.670
Order1        -0.12645    0.06711  -1.884
Voice1        -0.10761    0.04455  -2.415
Order1:Voice1  0.13562    0.08000   1.695

Correlation of Fixed Effects:
            (Intr) Order1 Voice1
Order1      0.776
Voice1      0.469  0.294
Order1:Voc1 0.458  0.468  0.282

----------------------------------------------------
Emilia Ellsiepen
Institut für Linguistik
Goethe-Universität Frankfurt