# Main effects and interaction effects - direction?

just a quick question regarding main effects and interaction effects:

For example, in a LME model like

lme_model <- lmer(outcome ~ Group*Time + var1 + (1|Sub), data=datatable


In the analysis there would be main effects of group, time (and var1), correct? Group x Time (or Group:Time , does it matter how I write it btw?) would then be called an interaction effect, if I am not mistaken? Someone told me that main effects are without direction. Is that correct? I am pretty sure I am getting I direction shown in the output of summary(lme_model). The interaction effect also has a direction effect, hasn't it?

Maybe the other person used anova(lme_model) to get to that opinion, which instead of summary(lme_model) doesn't produce estimates and a direction for main and interaction effects?

Edit: with direction I meant positive or negative, e.g. there is a negative groupXtime interaction effect

• I think it really depends on what you mean by direction here. Point estimates from regression coefficients usually give an idea of how a predictor decreases or increases a conditional mean value, which is your outcome variable. Interaction coefficients do the same thing really as far as I know. Aug 20, 2022 at 0:32

I assume by "direction" you mean "sign" (positive or negative). Then yes, all coefficients — the main effects and the interaction — have a sign.

The sign of the main effect for a variable that interacts with other variables might not be particularly easy to interpret on its own. Same goes for the interaction.

Say the model is $$\operatorname{E}\{Y\} = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_1x_2$$. When $$x_2$$ changes by one unit, $$\operatorname{E}\{Y\}$$ changes by $$\beta_2 + \beta_3x_1$$. The expected change in the response depends on the coefficients $$\beta_2$$ and $$\beta_3$$ (and their signs) as well as on the (fixed) value of $$x_1$$.

There is an easier way to visualize and understand the effects of a predictor that works equally well in models with and without interactions: partial effect plots.

Here is how to create a partial effect plot in R using the ggeffects package.

library("ggeffects")

set.seed(1234)

n <- 100

# Generate data with an interaction between x1 (categorical) and x2 (continuous)
data <-
data.frame(
x1 = sample(c("A", "B"), n, replace = TRUE),
x2 = rnorm(n)
)
data$$y <- ifelse(data$$x1 == "A", 1 + data$$x2, 2 - data$$x2 / 3) + rnorm(n)

# Fit the model
model <- lm(y ~ x1 * x2, data = data)

# Make a partial effect plot for the continuous variable, x2,
# at each level of the categorical variable, x1
plot(
ggpredict(model, terms = c("x2", "x1"))
)