I want to analyse the distance covered by players per minute (TD_min) among player role and playing phase (possession, non possession). Main question is: does possession phase influence distance covered by players in different role? IE, does distance covered by DC differs according to phase? The same for CC etc

I have the following mixed model with interaction, but I am not sure how to interpret it

TD_min ~ Fase * Ruolo + (1 | Partita) + (1 | Giocatore)

Ruolo is categorical (DC, FB, CC, ES, AT) and Fase is categorical (P, NP). Results are compared against DC and NP.

Results are the following

Formula: TD_min ~ Fase * Ruolo + (1 | Partita) + (1 | Giocatore)
   Data: data

     AIC      BIC   logLik deviance df.resid 
  3994.6   4050.3  -1984.3   3968.6      525 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.4758 -0.6044 -0.0646  0.6251  3.9107 

Random effects:
 Groups    Name        Variance Std.Dev.
 Partita   (Intercept) 56.75    7.533   
 Giocatore (Intercept) 29.22    5.405   
 Residual              73.21    8.556   
Number of obs: 538, groups:  Partita, 34; Giocatore, 21

Fixed effects:
              Estimate Std. Error t value
(Intercept)   140.7730     2.9531  47.670
FaseP         -20.7943     1.4674 -14.171
RuoloFB         5.1787     4.2384   1.222
RuoloCC        24.0475     3.4692   6.932
RuoloES         5.4434     4.3090   1.263
RuoloAT         0.1933     5.1367   0.038
FaseP:RuoloFB   0.5874     2.1074   0.279
FaseP:RuoloCC   2.2702     1.9180   1.184
FaseP:RuoloES  14.8159     2.8730   5.157
FaseP:RuoloAT  18.6357     3.2812   5.679

Correlation of Fixed Effects:
            (Intr) FaseP  RuolFB RuolCC RuolES RuolAT FP:RFB FP:RCC FP:RES
FaseP       -0.248                                                        
RuoloFB     -0.563  0.173                                                 
RuoloCC     -0.688  0.211  0.479                                          
RuoloES     -0.553  0.170  0.385  0.470                                   
RuoloAT     -0.465  0.143  0.324  0.396  0.324                            
FaseP:RulFB  0.173 -0.696 -0.249 -0.147 -0.119 -0.099                     
FaseP:RulCC  0.190 -0.765 -0.132 -0.276 -0.130 -0.109  0.533              
FaseP:RulES  0.127 -0.511 -0.088 -0.108 -0.333 -0.073  0.356  0.391       
FaseP:RulAT  0.111 -0.447 -0.077 -0.095 -0.076 -0.319  0.311  0.342  0.228

I am ok with interpreting the fixed models without interaction (ie from FaseP to RuoloAT), but am not sure how I can interpret the others? Also I don't know what the correlation of fixed effects means.

I found other similar questions but it's still unclear. Thanks


1 Answer 1


If you don't know how to interpret the interaction terms that it is likely that you also do not know how to interpret the main effects, since this is not the same as with a model without the interaction. The main point is that when a model includes an interaction term - which simply allows the "effect" of one variable to differ at different levels of the other variable - the main effect of one variable is conditional on the variable that it is interacted with being zero (or at it's reference level in the case of a categotorical variable. So:

  • The intercept is the expected value of TD_min when Fase is zero and Ruolo is at it's reference level.

  • The main effect for Fase is the slope of Fase when Ruolo is at it's reference level. The individual main effects for the categories of Ruolo are the estimated differences between TD_min at the reference level, and each estimated level, when Fase is zero. For example, the diference between TD_min when Ruolo is at it's reference level and when Ruolo is at FB is 5.1787 when Fase is kept at zero.

  • The interaction terms are the differences in the slope for Fase for each level of Ruolo, compared to the reference level of Ruolo

There are many many similar questions with answers on this site. It is not relevant that this is a mixed model. Just look for any question on the interpretation of models with an interaction between a continuous and categorical variable. For example:
interaction of categorical and continuous variables
How should I implement this interaction between a continuous and categorical predictor?
Interaction Terms (Categorical * Continuous)

  • $\begingroup$ Thank you, very clear. Howevei I still have one doubt. I want to evaluate the difference of TD_min for each level of Ruolo according to Fase. For example, I want to compare TD_min of subjects with the same Ruolo when Fase is at its reference value vs TD_min of subjects with the same Ruolo when Fase is NOT at its reference value. I can't understand how to do that $\endgroup$
    – FrAiello
    May 17, 2021 at 10:20
  • $\begingroup$ Fase doesn't have a reference level. It's continuous, so you should think in terms of it's slope. $\endgroup$ May 17, 2021 at 14:38
  • $\begingroup$ Does this answer your question ? If so then please consider marking it as a the accepted answer and (if you haven't already) upvoting it. If not, please could you let us know why so that it can be improved $\endgroup$ Jun 4, 2021 at 14:51

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