# glmer model in r, negative slope for a predictor, data seems to have positive slope

I fitted a glmer model to my data in r (with package lme4), one of significant fixed effects (order, which is continuous) has a negative estimate. But when I graph the averaged data, it seems to have a positive slope. what is going on here?

My response variable is binary. Here is my model:

g2amin = glmer (response ~ WMC + order + distance + DomSide + BlockType + (1 | pno) + WMC:order + WMC:distance + WMC:DomSide + order:DomSide + distance:DomSide + WMC:BlockType + distance:BlockType + DomSide:BlockType + order:BlockType, data = StudyDataN[StudyDataN$group == "Depressed",], family = binomial(link = "logit"))  And here is the summary of a results:  > summary(g2amin) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod] Family: binomial ( logit ) Formula: response ~ WMC + order + distance + DomSide + (1 | pno) + BlockType + WMC:order + WMC:distance + WMC:DomSide + order:DomSide + distance:DomSide + WMC:BlockType + distance:BlockType + DomSide:BlockType + order:BlockType Data: StudyDataN[StudyDataN$group == "Depressed", ]

AIC      BIC   logLik deviance df.resid
1667.7   1809.7   -809.9   1619.7     2716

Scaled residuals:
Min      1Q  Median      3Q     Max
-9.0582  0.1218  0.1916  0.3408  1.4150

Random effects:
Groups Name        Variance Std.Dev.
pno    (Intercept) 1.533    1.238
Number of obs: 2740, groups:  pno, 35

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                         0.1868731  0.8957168   0.209  0.83474
WMC                                 0.4359188  0.1643682   2.652  0.00800 **
order                              -0.0552924  0.1989800  -0.278  0.78111
distance2                          -0.0764481  0.4146961  -0.184  0.85374
distance3                           0.6319618  0.4773702   1.324  0.18556
distance4                           0.3508307  0.6401691   0.548  0.58367
DomSideRightDominant               -0.3313894  0.5686869  -0.583  0.56008
BlockTypeEasy                      -0.5018924  0.5723332  -0.877  0.38053
WMC:order                          -0.0003284  0.0360465  -0.009  0.99273
WMC:distance2                      -0.0011375  0.0751027  -0.015  0.98792
WMC:distance3                      -0.0112596  0.0861449  -0.131  0.89601
WMC:distance4                      -0.0105631  0.1175462  -0.090  0.92840
WMC:DomSideRightDominant           -0.0339368  0.0626720  -0.541  0.58816
order:DomSideRightDominant          0.1314148  0.1486902   0.884  0.37680
distance2:DomSideRightDominant      0.2820502  0.3102362   0.909  0.36327
distance3:DomSideRightDominant     -0.1464505  0.3594309  -0.407  0.68368
distance4:DomSideRightDominant     -0.0905467  0.4886552  -0.185  0.85300
WMC:BlockTypeEasy                  -0.0997565  0.0652019  -1.530  0.12603
distance2:BlockTypeEasy             0.2922394  0.3161517   0.924  0.35530
distance3:BlockTypeEasy            -0.4349740  0.3613730  -1.204  0.22872
distance4:BlockTypeEasy             0.4364490  0.5110543   0.854  0.39310
DomSideRightDominant:BlockTypeEasy  0.1938680  0.2662980   0.728  0.46661
order:BlockTypeEasy                 0.5382489  0.1523153   3.534  0.00041 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 23 > 12.
Use print(x, correlation=TRUE)  or
vcov(x)     if you need it

convergence code: 0
Model failed to converge with max|grad| = 0.00838529 (tol = 0.001, component 1)


I checked chi-square statistic to see which fixed effects are significant (using package car)

 > Anova(g2amin)
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: response
Chisq Df Pr(>Chisq)
WMC                10.8837  1  0.0009701 ***
order               9.0390  1  0.0026427 **
distance            4.6383  3  0.2002791
DomSide             0.0630  1  0.8017518
BlockType          28.4340  1  9.695e-08 ***
WMC:order           0.0001  1  0.9927304
WMC:distance        0.0230  3  0.9990761
WMC:DomSide         0.2932  1  0.5881645
order:DomSide       0.7811  1  0.3767953
distance:DomSide    1.5261  3  0.6762667
WMC:BlockType       2.3408  1  0.1260258
distance:BlockType  4.3078  3  0.2300926
DomSide:BlockType   0.5300  1  0.4666066
order:BlockType    12.4876  1  0.0004097 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


and variable order is significant in my model. Here is a graph of averaged data over the other variables (BlockType, distance, ...): order's slope in graph is obviously positive, but why it's negative in my model? Is the whole point of graphing for binomial data wrong??

• because order:BlockTypeEasy 0.5382489 >0. – user158565 Dec 3 '18 at 5:00

You have interaction terms of order with WMC, DomSide, and BlockType. This means that the coefficient you obtained for the main effect of order denotes the effect of this variable for WMC equal to zero, and DomSide and BlockType fixed at their reference level, which does not correspond to the marginal relationship you see in the plot.
• You could indeed use an effect plot to depict what is going on with order and BlockType. – Dimitris Rizopoulos Dec 3 '18 at 11:06