# Interpretation of interaction and main effect in a mixed model when one is significant and the other is not [duplicate]

I have repeated (x4) measurements on 90 subjects. The outcome is zero inflated.

The model output gives these estimates:

Coefficients:
Estimate Std. Error z value   Pr(>|z|)
(Intercept)               -2.2151     1.6998   -1.30    0.193
time                       0.5283     0.2167    2.44    0.015
X                          0.0791     0.3267    0.24    0.811
time:X                    -0.1525     0.0611   -2.49    0.013
Y                          1.0348     0.4488    2.31    0.021
time:Y                    -0.0037     0.0583   -0.06    0.950

Number of observations: total=342, Subject=90
Random effect variance(s):
Group=Subject
Variance StdDev
(Intercept)    6.302   2.51
Negative binomial dispersion parameter: 3.9265 (std. err.: 0.69723)
Zero-inflation: 0.13169  (std. err.:  0.027756 )


X and Y both vary at the subject-level only, not at the time-level.

As you see, here the main effect of X is not significant, while the time:X interaction is significant. On the other hand, the main effect of Y is significant, while the time:Y interaction is not.

I believe that in the case of Y, this means that subjects with higher values of Y have higher trajectories of the outcome. Is this correct ?

However, how is the time:X interaction to be interpreted ?

• As discussed here, there are a lot of difficulties and various problems that can arise in interpreting the interaction between two continuous variables. – Randel Aug 27 '13 at 16:01
• – kjetil b halvorsen Oct 8 '19 at 8:36