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I am trying to use mixed-effects modelling for my data in R. I have two independent variables and both of them have three levels. Is it necessary that I have to code my variables? If so, can I use dummy/treatment coding? I also have some other predictor variables. I am attaching the model with this,

model1 <- lmer(rt ~ emotion + trial + emotion*trial + age + emotion*trial*age + (1|participant)

The results obtained are as follows:

Fixed effects:
                                                            Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)                                                 295.9898    21.9655    59.9409  13.475   <2e-16 ***
EmotionNegative                                              12.9354    10.3385 17076.8218   1.251   0.2109    
EmotionNeutral                                               13.2439    10.2729 17076.4637   1.289   0.1973    
trial_typeincongruent                                        20.6828    10.6194 17077.0115   1.948   0.0515 .  
trial_typeneutral                                            23.0839    10.4112 17076.4873   2.217   0.0266 *  
Age                                                          -0.2310     4.0893    60.0862  -0.056   0.9551    
EmotionNegative:trial_typeincongruent                        -5.9407    15.2334 17076.6471  -0.390   0.6966    
EmotionNeutral:trial_typeincongruent                          4.0637    15.1272 17076.5003   0.269   0.7882    
EmotionNegative:trial_typeneutral                            11.5807    14.8398 17076.5762   0.780   0.4352    
EmotionNeutral:trial_typeneutral                              8.1210    14.8446 17076.3594   0.547   0.5843    
EmotionNegative:Age                                           0.4182     1.9479 17076.9098   0.215   0.8300    
EmotionNeutral:Age                                           -2.0714     1.9280 17076.4446  -1.074   0.2827    
trial_typeincongruent:Age                                    -2.6537     1.9935 17077.2263  -1.331   0.1831    
trial_typeneutral:Age                                        -0.2855     1.9518 17076.5935  -0.146   0.8837    
EmotionNegative:trial_typeincongruent:Age                     3.3124     2.8751 17076.6068   1.152   0.2493    
EmotionNeutral:trial_typeincongruent:Age                      1.6189     2.8473 17076.4467   0.569   0.5696    
EmotionNegative:trial_typeneutral:Age                        -1.3162     2.7958 17076.6643  -0.471   0.6378    
EmotionNeutral:trial_typeneutral:Age                         -1.7054     2.7918 17076.2931  -0.611   0.5413

How should I interpret this data? Do I need to mention the variable coding and if so, why is it important?

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Is it necessary that I have to code my variables? If so, can I use dummy/treatment coding?

R will use treatment coding by default.

How should I interpret this data?

The interpretation of the fixed effects is the same as with a linear model:

Do I need to mention the variable coding and if so, why is it important?

It doesn't hurt to mention what coding you use, but I say that unless you are using something other than teatment coding, or perpahs if another coding scheme was generally used in your field, it is not necessary.

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  • $\begingroup$ I understood the logic of interpretation. However, when you are citing the results in a scientific journal, how do you explain or interpret the results? To be specific, how do you write the two-way and three-way interactions? $\endgroup$
    – Christina
    Commented Oct 21, 2020 at 3:09
  • $\begingroup$ First, it depends on the context (what each variable represents in the study) and what yiur research questions are. Then it depends on what type of variables are involved in the interactions: numeric or categorical. If categorical.it depends on how many levels it has. If numeric it depends on whether it is centred or not. There are so many possibilities that you have to consider each separately. That's why I linked to the other questions. $\endgroup$
    – Robert Long
    Commented Oct 21, 2020 at 6:31
  • $\begingroup$ Yes. I went through the links but couldn't find what I was looking for. It would be great if you could help me with one example. Here, emotion and trial type are categorical variables with three levels. I have kept positive emotion and congruent trial type as reference level. How do I explain the EmotionNegative:trial_typeincongruent interaction? Similarly, how do I explain EmotionNeutral:trial_typeneutral:Age ? $\endgroup$
    – Christina
    Commented Oct 22, 2020 at 3:15
  • $\begingroup$ The first one EmotionNegative:trial_typeincongruent is a two-way interaction between categorical variables which is explained very well here and which I linked to in my answer. Simply put it is the additional contribution to the outcome when Emotion is Negative and when trial_type is incongruent to when either one of them takes those values. For the 2nd one: EmotionNeutral:trial_typeneutral:Age this is an interaction between the two-way interaction EmotionNeutral:trial_typeneutral and the continuous variable Age <cont> $\endgroup$
    – Robert Long
    Commented Oct 22, 2020 at 11:20
  • $\begingroup$ ...Two way interaction is interpreted in the same way as just described. Then the 3-way interaction is the change in the two-way interaction for a unit increase in Age. $\endgroup$
    – Robert Long
    Commented Oct 22, 2020 at 11:21

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