# R lmerTest step() function returns significant random effect without equivalent significant fixed effect

I do have a 2 level data set with 3 observations nested in one person. I am fitting a mixed model including 71 predictors and 28 random slopes in the following manner:

model = lmer(var1 ~ a + b + c + (1|PersID) + (0+a|PersID) + (0+b|PersID) + (0+c|PersID)


I am using the step() function of the lmerTest package to do backwards elimination of random and fixed effects of the model and get the following model:

Linear mixed model fit by REML
t-tests use  Satterthwaite approximations to degrees of freedom ['merModLmerTest']
Formula: Fufaksc1 ~ MusZ + HauZ + ArbZ + SpoZ + AusZ + TraZ + AAYYZ +
AMYZ + AMSZ + TNAZ + AuZ + MusM + HauM + EmoM + SpoM + TraM +
AMNM + WSM + AuM + SAE + Ex + RE + So + UC + (1 | PersID) +
(0 + HauZ | PersID) + (0 + SpoZ | PersID) + (0 + VaZ | PersID) + (0 + AuZ | PersID) Data: Sitsort2

REML criterion at convergence: 2703.1

Scaled residuals:
Min      1Q  Median      3Q     Max
-3.6274 -0.4721  0.0070  0.4884  4.1122

Random effects:
Groups   Name        Variance Std.Dev.
PersID   (Intercept) 0.259072 0.50899
PersID.1 HauZ        0.088366 0.29726
PersID.2 SpoZ        0.285073 0.53392
PersID.3 VaZ         0.008581 0.09263
PersID.4 AuZ         0.008177 0.09043
Residual             0.209756 0.45799
Number of obs: 1300, groups:  PersID, 555

Fixed effects:
Estimate Std. Error        df t value Pr(>|t|)
(Intercept)  -1.00698    0.19540 515.50000  -5.154 3.65e-07 ***
MusZ          0.55662    0.07930 627.30000   7.019 5.80e-12 ***
HauZ         -0.26976    0.06780 456.30000  -3.979 8.06e-05 ***
ArbZ          0.30543    0.07223 704.20000   4.229 2.66e-05 ***
SpoZ         -0.45474    0.09816 130.70000  -4.633 8.62e-06 ***
AusZ          0.17835    0.08102 653.20000   2.201 0.028067 *
TraZ         -0.10944    0.05563 648.90000  -1.967 0.049574 *
AAYYZ        -0.20878    0.05301 769.00000  -3.939 8.93e-05 ***
AMYZ          0.10063    0.04699 767.70000   2.141 0.032550 *
AMSZ          0.80907    0.16299 501.90000   4.964 9.49e-07 ***
TNAZ         -0.09069    0.04457 719.90000  -2.035 0.042261 *
AuZ           0.06479    0.01266 455.80000   5.118 4.57e-07 ***
MusM          0.49393    0.18577 522.40000   2.659 0.008082 **
HauM         -0.47557    0.14806 517.50000  -3.212 0.001401 **
EmoM         -0.63551    0.30854 490.60000  -2.060 0.039950 *
SpoM         -0.88607    0.20915 519.20000  -4.236 2.69e-05 ***
TraM         -0.35308    0.14697 513.00000  -2.402 0.016645 *
AMNM         -0.41692    0.20316 530.50000  -2.052 0.040644 *
WSM           0.04994    0.01685 530.80000   2.964 0.003172 **
AuM           0.09425    0.02577 527.50000   3.657 0.000281 ***
SAE           0.15065    0.02430 515.10000   6.198 1.17e-09 ***
Ex           -0.05206    0.02576 519.20000  -2.021 0.043836 *
RE            0.07022    0.02686 514.70000   2.614 0.009201 **
So            0.09297    0.02611 523.20000   3.561 0.000404 ***
UC           -0.11635    0.02710 510.80000  -4.293 2.11e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The model contains 5 significant random effects including the intercept. The only thing I do not understand is why there is a significant random effect for VaZ but no significant fixed effect for VaZ included in the model. As far as I understand this it would only make sense if the fixed effect would be exact 0 (which is realisticly impossible). From my point of view it does not make sense to include a random effect without an equivalent fixed effect. Can anyone explain this to me or is it a bug in the step() function?