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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, ...): proportion correct as a function of order

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??

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  • $\begingroup$ because order:BlockTypeEasy 0.5382489 >0. $\endgroup$
    – user158565
    Commented Dec 3, 2018 at 5:00

1 Answer 1

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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.

Moreover, note that you have done the plot on the probability scale whereas the coefficients are on the log odds scale.

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  • $\begingroup$ Thanks Dimitris. So, if the plot is not useful, how could I interpret the interaction effect of order * BlockType? I used a plot for that effect too! $\endgroup$
    – Zahra Arjmandi
    Commented Dec 3, 2018 at 5:40
  • $\begingroup$ You could indeed use an effect plot to depict what is going on with order and BlockType. $\endgroup$
    – Dimitris Rizopoulos
    Commented Dec 3, 2018 at 11:06
  • $\begingroup$ Many thanks :) Package effects was a good help to prepare data for plotting fitted values: quantdev.ssri.psu.edu/tutorials/… $\endgroup$
    – Zahra Arjmandi
    Commented Dec 3, 2018 at 11:54
  • $\begingroup$ I've got another question. for variable order beta = -.06. so for every unit increase in order, odd ratio change is exp(-.06) - 1= .94 - 1 = -.06. If odd's ration decrease -> my response variable's probability decreases. but when I plot fitted value by order, it's still increasing! I can't get what's the problem! $\endgroup$
    – Zahra Arjmandi
    Commented Dec 3, 2018 at 12:57
  • $\begingroup$ I used this line of code to plot fitted value against order: ggplot(as.data.frame(effect("order", mod = g2amin)), aes(x = order, y = fit)+ geom_point() @DimitrisR $\endgroup$
    – Zahra Arjmandi
    Commented Dec 3, 2018 at 13:07

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