# Help: Interpretation of Interaction Effect using a Linear regression in R

Im applying a regression to test the association between maternal postpardum depression score (maternal_postpardum_score) and functional connectivity changes (FC) in the brain - both continuous. I applied a moderator, adversity (ADV), which has two levels 0 for no adversity and 1 for adversity - a categorical variable. A moderator effect was included to test if there are any significant interaction effects.

As shown below:

compmem1<- lm(FC ~ maternal_postpardum_score*ADV, data=mat_adv)
summary(compmem1)

Call:

Residuals:
Min       1Q   Median       3Q      Max
-0.14579 -0.05758 -0.02837  0.08501  0.13421

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)                                           0.04506    0.03700   1.218   0.2513
maternal_postpardum_score                            -0.03524    0.01698  -2.076   0.0647 .
ADVyes                                                0.17281    0.05644   3.062   0.0120 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.104 on 10 degrees of freedom
Multiple R-squared:  0.6177,    Adjusted R-squared:  0.5031
F-statistic: 5.387 on 3 and 10 DF,  p-value: 0.01823


However, there were no statistically significant main effects nor interaction effects.. ADVyes was significant. What can be said about this? Can I say that there is no interaction effect but the moderator is significant? I'm trying to interpret this relationship.

• Can I interpret it in this way: Maternal adversity score has a smaller impact on Functional connectivity when ADV is 0 Mar 17, 2021 at 22:44
• Looking at the p-value of maternal_postpardum_score 0.0647 normally cries out for checking the sample size, if it is possible to increase sample size, it is possible that this one could get significant when some heavily wants to rely on the p < .5 threshold. Although some staticians say that these thresholds are a little flexible, so on a p < .10 level it could be seen as significant, depends on your subject. Have you tried to divide your sample and calc. two separate models one for each group, or is the sample size not large enough ? Mar 18, 2021 at 17:27
• From the output of your model it appears that your sample size is 14. With such a small sample size, I would highly recommend paying very little attention to p values. I assume that you did not do a sample size calculation prior to collecting the data ? Mar 18, 2021 at 17:43

You have to be very careful when trying to interpret the individual coefficients when there is an interaction. Something as simple as centering a continuous predictor can change the apparent "significance" of the coefficients of variables interacting with that predictor, raising questions about practical versus statistical significance.

The coefficient reported for the ADV predictor in this interaction model represents the association of ADV with outcome when the maternal_postpardum_score is exactly 0. Is the maternal_postpardum_score ever as low as 0? If not, that "statistical significance" might have no practical significance.

The coefficient reported for the maternal_postpardum_score is its association with outcome when ADV = 0, a situation that clearly holds in your data.

The coefficient reported for the interaction term is how much each of those associations changes per unit change in the other predictor: for example, the coefficient for maternal_postpardum_score when ADV = 1 would be estimated as $$-0.03524 + 0.02385 = -0.01139$$.

So, if these changes were statistically significant, then you could say something like "Maternal postpardum score has a more negative association with Functional connectivity when ADV is 0 versus 1." In your case, however, the interaction term is far from significant, with a p-value of 0.27. There is no evidence that the association of maternal_postpardum_score with the FC outcome differs with the value of ADV at all (or vice-versa).

In this case it might make sense to use a model that includes maternal_postpardum_score and ADV as separate predictors, without the interaction term. As you only seem to have 14 cases, your attempt to use 3 predictors (maternal_postpardum_score, ADV, and their interaction) was already at severe risk of overfitting. The usual rule of thumb is 1 predictor per 10-20 cases for a linear regression, so even a 2-predictor model is pushing things. As comments on the question indicate, you really need more data if you want to include both as predictors.