I am trying to predict response time (transformed in Log) from Group (a factor with two levels: NS and NNS), and Time of Testing (a factor with three levels: Pretest, Posttest, Delayed-test), using linear mixed effect model. The slope coefficient for Group was (-0.455006) suggesting that NNS (the reference level) had larger RT than NS. The slop coefficient for Time of Testing was: -.25 for from Pretest to Posttest, and -.35 from Pretest to Delayedtest. Both coefficient for Group and Time of testing were signifiant. There was also signifiant interaction. The model output is posted below:

Fixed effects:                           Estimate     Pr(>|t|)    
(Intercept)                              8.033121  < 0.0000 ***              
GroupNS:                                -0.455006    0.00195 ***   
Time_of_TestingPosttest:                -0.252902    0.00 ***  
Time_of_TestingDelayedtest:             -0.393049    0.000 ***  
Item_TypeAr:                             0.027541    0.459570                                    
Item_TypeCong:                          -0.057590    0.202765    
Item_TypeEng :                          -0.056005    0.097206 .  
scale(Length) :                          0.056470    0.00000189729 ***   
scale(Prof_Voc):                        -0.199754    0.000234 ***   
scale(AssocFor):                         0.007124    0.624079                                      
scale(PhraseChoice_Norming_NNS):        -0.030128    0.029637 *                     
scale(For_Comp_Norming_NNS_PERC):       -0.045862    0.019740 *  
scale(Back_Comp_Norming_NNS_PERC):      -0.027450    0.088654 .            
GroupNS:Time_of_TestingPosttest:         0.125559    0.00***                       
GroupNS:Time_of_TestingDelayedtest :     0.128348    0.00 ***                     
GroupNS:Item_TypeAr :                    0.152143    0.00***                  
GroupNS:Item_TypeCong:                   0.067548    0.00 **                  
GroupNS:Item_TypeEng:                   -0.125478    0.000 ***                 
Time_of_TestingPosttest:Item_TypeAr:    -0.118301    0.00 ***                             
Time_of_TestingDelayedtest:Item_TypeAr: -0.007223    0.80                    
Time_of_TestingPosttest:Item_TypeCong:  -0.057250    0.03 *                    
Time_of_TestingDelayedtest:Item_TypeCong 0.015867    0.56      
Time_of_TestingPosttest:Item_TypeEng    -0.066561    0.017 *  
Time_of_TestingDelayedtest:Item_TypeEng  0.018056    0.51  
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

1.) My first question, what does the positive sign in the interaction indicate? How can the positive + or negative - be used to understand the interaction effect relationship?

I had difficulty understating what the slope coefficient mean, so I plotted the graph below.

enter image description here

  1. ) However, I still don't see any interaction effect in the sense that Group depends on Time, or vice versa. I would really appreciate your kind assistance in interpreting the interaction coefficient based on the plot
  • $\begingroup$ Can you post your model output in its entirety in your original question? $\endgroup$ Commented May 14, 2019 at 20:16

1 Answer 1


What the interaction is saying is that the two lines are not parallel - and they are not. In particular, the difference between pre and post is larger for NNS than for NS.

An interaction is not "that group depends on time" it is that the effect of time is different in the different groups and the effect of group is different at different times.

One point is that the difference between groups is largest at the pretest. Were the subjects assigned at random? Did you use a multilevel model?

  • 1
    $\begingroup$ Thanks a lot Peter for your kind reply and clarification. To answer your question, I have used a multilevel modeling allowing the intercepts of subjects and items to vary. I think the large difference in the Pretest (Pre-treatment) between groups is due to the fact that NS are English native speakers and NNS are non-native speakers, and they are being testing on their response times when they read English words. Just a quick follow up question on your explanation for the interaction, how can we explain the interaction relationship if the slope sign was negative? Thanks again for your help. $\endgroup$ Commented May 14, 2019 at 22:51
  • $\begingroup$ The slope was negative because the scores are going down. But one group is going down less. $\endgroup$
    – Peter Flom
    Commented May 14, 2019 at 23:16
  • $\begingroup$ Thanks again Peter for your kind reply, and thanks for your patience. Your kind comment about the negative slope in the interaction captures the trend in the plot clearly, however, the coefficient I got for the interaction was not negative, it was a positive +0.125559 for Posttest and a positive +0.128348 for the delayed. Does the symbol (+) or (-) really matter in understating the direction of interaction? Thanks a lot for your assistance and I do really apologize for the many questions. $\endgroup$ Commented May 15, 2019 at 0:19
  • $\begingroup$ Yes. The + or - indicates which group was slower or faster in decline $\endgroup$
    – Peter Flom
    Commented May 15, 2019 at 1:00

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