[R-lang] lmer: Significant fixed effect only when random slope is included

[Jorrig Vogels]

Dear R users,

I have a logit mixed model with two categorical predictors (two types of salience measures) and a categorical dependent variable (pronoun used Y/N). One predictor has 2 levels, and the other has 3. I centered the 2-level predictor, and transformed the 3-level predictor into two binary predictors using contrast (sum) coding. I determined the random-effects structure by starting from a full model, and eliminating step by step all terms without a significant contribution to the model.

In the final model, I end up with random intercepts for subjects and items, and a by-subject random slope for my 2-level predictor. In this model, I get significant interactions between the fixed factors, which I had not expected to be significant by just looking at the data. Removing the random slope from the model completely eliminates these interactions, but model comparison suggests the random slope should be included. I have attached the two model summaries below.

Now my question is: is it normal to find such a large influence of random effects on the fixed effects structure? How do I know the interaction effects are not spurious? And what exactly do these findings mean? Participants varied greatly in their reaction to predictor B, but when this variation is accounted for, predictor B affects pronoun use, but differently for each level of predictor A?


Jorrig Vogels
PhD candidate
Tilburg Univ., Netherlands

================================================================

Model with random slope: 

Generalized linear mixed model fit by the Laplace approximation
Formula: PRO ~ cAGTOP * cAGVIS + (1 + cAGVIS | SUBJ) + (1 | ITEM)
   Data: vislingag
   AIC   BIC logLik deviance
318.4 361.4 -149.2    298.4
Random effects:
Groups Name        Variance Std.Dev. Corr
SUBJ   (Intercept) 49.6457  7.0460
        cAGVIS      21.8342  4.6727   0.663
ITEM   (Intercept)  1.3205  1.1491
Number of obs: 544, groups: SUBJ, 48; ITEM, 12

Fixed effects:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)      -2.578      1.217  -2.117  0.03422 *
cAGTOP1          -6.627      0.913  -7.259 3.90e-13 ***
cAGTOP2           9.868      1.502   6.569 5.05e-11 ***
cAGVIS           -1.699      1.008  -1.685  0.09207 .
cAGTOP1:cAGVIS   -3.223      1.170  -2.755  0.00587 **
cAGTOP2:cAGVIS    3.120      1.371   2.275  0.02289 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) cAGTOP1 cAGTOP2 cAGVIS cAGTOP1:
cAGTOP1      0.075
cAGTOP2     -0.041 -0.867
cAGVIS       0.535  0.108  -0.059
cAGTOP1:AGV  0.074  0.562  -0.346   0.128
cAGTOP2:AGV -0.049 -0.480   0.528  -0.054 -0.668


Model without random slope:

Generalized linear mixed model fit by the Laplace approximation
Formula: PRO ~ cAGTOP * cAGVIS + (1 | SUBJ) + (1 | ITEM)
   Data: vislingag
   AIC   BIC logLik deviance
324.3 358.7 -154.2    308.3
Random effects:
Groups Name        Variance Std.Dev.
SUBJ   (Intercept) 21.63217 4.65104
ITEM   (Intercept)  0.61539 0.78447
Number of obs: 544, groups: SUBJ, 48; ITEM, 12

Fixed effects:
               Estimate Std. Error z value Pr(>|z|)
(Intercept)    -1.41142    0.77639  -1.818   0.0691 .
cAGTOP1        -4.59707    0.52139  -8.817   <2e-16 ***
cAGTOP2         7.13115    0.84489   8.440   <2e-16 ***
cAGVIS         -0.35538    0.40416  -0.879   0.3792
cAGTOP1:cAGVIS -0.59940    0.58255  -1.029   0.3035
cAGTOP2:cAGVIS -0.08268    0.56682  -0.146   0.8840
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) cAGTOP1 cAGTOP2 cAGVIS cAGTOP1:
cAGTOP1      0.070
cAGTOP2     -0.040 -0.867
cAGVIS       0.000  0.061  -0.036
cAGTOP1:AGV  0.038  0.082  -0.012   0.102
cAGTOP2:AGV -0.020  0.008  -0.037   0.037 -0.575
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