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