# 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 ! 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.