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I have a linear mixed model in R for predicting the numeric value invested by participants in a Trust Game (it's an experimental paradigm) with the factors "group" (intervention group and control group) and "time" (every participant played the game twice, with a year interval between both times), the interaction factors timeXgroup and a random intercept (the random intercept was the participants).

I've consulted some already answered questions here in this site, but I want to be sure I'm doing this right. Here, here and here.

Is my interpretation of the summary of my model correct?

m_inv_td_30 <- lmer(investment ~ (1|id) + time*group,
                      data = data_cond, REML=FALSE) 
Fixed effects:
                   Estimate   Std. Error        df    t value     Pr(>|t|)    
(Intercept)          5.1900     0.2343       83.8743   22.152     < 2e-16 ***
time2               -0.2342     0.1115     5779.3286   -2.101     0.035698 *  
groupINTERV         -1.1750     0.3313       83.8743   -3.546     0.000642 ***
time2:groupINTERV    0.4754     0.2066     5753.1353    2.301     0.021414 *

Interpretations: a) The intercept of my model is the control group and time 1.

b) The control group invests 0.2342 less in time 2 than this same group in time 1.

c) In time 1, the INTERV (intervention) group invests 1.1750 less than control group.

d) The INTERV group invests 0.4754-0.2342= 0.2412 more in the time 2 than this same group in time 1.

e) All of this is significant.

f) From the interaction plot, I can say there is an interaction between group and time.

interaction.plot(x.factor = plot_media_f1$tempo, #x-axis variable
                 trace.factor = plot_media_f1$grupo, #variable for lines
                 response = plot_media_f1$media_investimento, #y-axis variable
                 fun = median, #metric to plot
                 ylab = "Investment",
                 xlab = "Time",
                 col = c("pink", "blue"),
                 lty = 1, #line type
                 lwd = 2, #line width
                 trace.label = "Groups")

Interaction plot

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  • $\begingroup$ There are a number of R packages that make it quite easy to calculate marginal predictions from the model and graph them. Those include ggeffects, marginalefffects, and emmeans. E.g., in ggeffects: int<- ggpredict(m_inv_td_30, terms = c("time2", "groupINTER")) ggplot(int, aes(x, predicted, colour = group)) + geom_line(). See strengejacke.github.io/ggeffects/articles/ggeffects.html $\endgroup$
    – Erik Ruzek
    Commented Jan 5 at 20:04
  • $\begingroup$ Thank you so much for this! $\endgroup$
    – statslily
    Commented Jan 26 at 0:35

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By looking at your plot, a) b) and c) seem OK, but for d), the value you calculated for INTERV group between time 1 and time 2 is not consistent with what the plot shows. The difference between the 2 time points should be much larger.

estimate of time2:groupINTERV - estimate of time 2 will not give you the magnitude of the difference between time 1 and time 2 for the group INTERV

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  • $\begingroup$ You're right! I think I've done something wrong with the plot, I've used some other data... I'm gonna see here what I've done with this plot and come back here. But thank you for your answer! $\endgroup$
    – statslily
    Commented Jan 4 at 23:14
  • $\begingroup$ I've used now the same data I've used in the model, and the same problem occurs... Do you have any idea of what could have happened? Although with no access to my data, I'm not sure you could help me with this one... $\endgroup$
    – statslily
    Commented Jan 4 at 23:26
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    $\begingroup$ No it is just the calculation that is wrong, time2:groupINTERV - time 2 will not give you the magnitude of the difference between time 1 and time 2 for the group INTERV $\endgroup$
    – CaroZ
    Commented Jan 4 at 23:50
  • $\begingroup$ Oh, I got it now! Do you know how could I interpret this interaction (time2:groupINTERV)? Can I say that time influences more group INTERV than group CONTROL? $\endgroup$
    – statslily
    Commented Jan 5 at 0:06

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