# interaction term in a linear mixed-effects model

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula:
Frontal_Med_Lt ~ 1 + SUVmax_VAT + FU_Period + SUVmax_VAT * FU_Period +
(1 + FU_Period | pNo)
Data: brain

REML criterion at convergence: -164.5

Scaled residuals:
Min      1Q  Median      3Q     Max
-3.1931 -0.3939  0.0999  0.5484  2.2075

Random effects:
Groups   Name        Variance  Std.Dev. Corr
pNo      (Intercept) 1.869e-02 0.136722
FU_Period   2.429e-05 0.004928 0.22
Residual             2.153e-02 0.146743
Number of obs: 355, groups:  pNo, 150

Fixed effects:
Estimate Std. Error        df t value Pr(>|t|)
(Intercept)            1.00790    0.06486 244.64322  15.539  < 2e-16 ***
SUVmax_VAT             0.08089    0.12188 244.70962   0.664  0.50752
FU_Period              0.02476    0.01272  91.09228   1.946  0.05471 .
SUVmax_VAT:FU_Period  -0.08331    0.02662 104.47484  -3.130  0.00227 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) SUVm_VAT FU_Prd
SUVmax_VAT  -0.971
FU_Period   -0.548  0.553
SUV_VAT:FU_  0.465 -0.493   -0.969

This is the result of the LMM I fitted. As you can see, the interaction term is significant while the fixed effects are not. Can I say that SUVmax_VAT has an effect on the dependent variable? How do I interpret this result?

• I don't know who has voted to close this, but it is clearly on topic ! Commented Aug 20, 2021 at 12:18

There are a few things to consider. Based on the model fitted you can say that there is strong evidence that SUVmax_VAT is indeed associated with the dependent variable, however the association is dependent on the value of FU_Period. There is very little evidence that SUVmax_VAT is associated with the DV, when FU_Period is zero. There is some evidence that FU_Period is associated with the DV when SUVmax_VAT is zero.

As you will realise from the above, the interpretation of the main effects are conditional on the other variable being zero (or at it's reference level in the case of a categorical variable, but it looks like your variables are continuous, so they are conditional on them being zero). If zero is not meaningful for either of these variables, then it would be a good idea to centre it at it's mean, and then the interpretation will be conditional on the other variable being at it's mean instead.

Lastly, try to avoid causal language such as "has an effect on". We cannot infer anything about causation from this model, so we should instead talk about an "association". It may be consistent with a causal effect, but that is all we can say.