# Discrepancy in the results of LMER and BayesFactor (R)

I have a within-subject dataset with 3 two-level factors and 1 numeric predictor. I was using LMER with a random-intercept model (a full random-effect model yield the same results though throws convergence warnings)

Crucially, one of the hypothesized interactions comp*corr is far from being significant with t = 0.6. The contrasts are set to contr.sum and with type 3 Anova test I will get p = 0.53 for that interaction.

summary(lmer_fit2<-lmer(awaren ~ (comp+corr+distance+eccentr)^4+(1|date), data = awaren_bs))
...

Fixed effects:
Estimate Std. Error t value
(Intercept)                   0.105062   0.015198    6.91
comp1                         0.004870   0.009879    0.49
corr                          0.898071   0.013970   64.28
distance1                    -0.021856   0.009879   -2.21
eccentr                       0.030428   0.002744   11.09
comp1:corr                   -0.008639   0.013970   -0.62
comp1:distance1               0.008253   0.009879    0.84
comp1:eccentr                 0.005976   0.002744    2.18
corr:distance1                0.037073   0.013970    2.65
corr:eccentr                 -0.045072   0.003878  -11.62
distance1:eccentr             0.022817   0.002744    8.31
comp1:corr:distance1         -0.008255   0.013970   -0.59
comp1:corr:eccentr           -0.006192   0.003878   -1.60
comp1:distance1:eccentr      -0.002895   0.002744   -1.05
corr:distance1:eccentr       -0.034998   0.003878   -9.03
comp1:corr:distance1:eccentr  0.003038   0.003878    0.78


However, when I'm doing the same analysis with bayesFactor, I get a totally different result:

> anova_res_1<-generalTestBF(awaren~(comp+corr+distance+eccentr)^4+date, awaren_bs, whichRandom = 'date', neverExclude=c('date'),whichModels = 'top')
|======================================================================================================================================| 100%
> anova_res_1
Bayes factor top-down analysis
--------------
When effect is omitted from comp + corr + distance + eccentr + comp:corr + comp:distance + comp:eccentr + corr:distance + corr:eccentr + distance:eccentr +     comp:corr:distance + comp:corr:eccentr + comp:distance:eccentr +     corr:distance:eccentr + comp:corr:distance:eccentr + date , BF is...
[1] Omit comp:corr:distance:eccentr : 9.096641      ±42.71%
[2] Omit corr:distance:eccentr      : 1.895645e-16  ±45.61%
[3] Omit comp:distance:eccentr      : 10.74473      ±42.71%
[4] Omit comp:corr:eccentr          : 6.881117      ±42.79%
[5] Omit comp:corr:distance         : 17.17485      ±43.47%
[6] Omit distance:eccentr           : 0.4269731     ±46.48%
[7] Omit corr:eccentr               : 8.269684e-27  ±42.86%
[8] Omit corr:distance              : 2.288794e-15  ±42.82%
[9] Omit comp:eccentr               : 4.673529      ±42.43%
[10] Omit comp:distance              : 6.021156      ±42.74%
[11] Omit comp:corr                  : 0.02781902    ±42.67%
[12] Omit eccentr                    : 0.005301817   ±45.12%
[13] Omit distance                   : 0.04890581    ±42.77%
[14] Omit corr                       : 6.956763e-431 ±40.56%
[15] Omit comp                       : 0.5002814     ±44.02%


The removal of comp*corr interaction leads to a worse model meaning that it is "significant".

I have several questions:

1) Do I translate LMER model to BayesFactor model correctly?

2) Do I understand correctly that type 3 ANOVA and generalTestBF with whichModels = "top" should give more or less the same results?

3) Why might I get such a discrepancy between the results?

I've uploaded the data, the output, and the minimal working example here: https://drive.google.com/open?id=0ByJtKXU-AjqmVHNQTHN5eEQ2elE

Long story: Turns out that if I use LMER with only main effects and two-factor interactions, the effect of comp*corr is also significant there. It disappears when a third-order interaction of comp1:corr:eccentr is added. So apparently this is a case when interaction "wipes out" the main effect (this question helps to understand how it can happen) despite the sum-to-zero contrasts. An sum-to-zero contrasts obviously have no effect on numerical predictors so that the effects not including numerical predictor (eccentr) are the effects at eccentr=0. So they are not "main effects" in a sense of the "an effect of the variable controlling for everything else" but simply contrasts at the baseline level.