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r - How do I plot mixed-effects linear regression?

I'm trying to make a boxplot to visualize this regression model

library(lme4)
lmer(dv1 ~ intervention + (1|id/area),
            data=data,
            REML=T)

In this experiment, the control and treatment intervention are both applied to a subject within discrete areas.

Here's the data I'm using

data <- data.frame("id" = 1:2, 
           "intervention" = c(rep("a",27),rep("b", 27)),
           "area" = 1:3,
           "dv1" = rnorm(54),
           "dv2" = rnorm(54),
           "dv3" = rnorm(54))
data$area <- as.factor(data$area)
data$id <- as.factor(data$id)

Here's what I've tried

library(ggplot2)
ggplot(data,aes(x=area,y=dv1,col=intervention)) +
  geom_point() +
  geom_boxplot(alpha=0.2) + 
  facet_wrap(~id) + 
  ggtitle("DV1") +
  xlab("Intervention") +
  ylab("DV1")

enter image description here

Instead of the red points overlaying the red boxplot, they're all over the place. How do I fix this?

Edit: I used the jitter options that u/eipi10 suggested and this is what I have now.

ggplot(data,aes(x=area,y=dv1,col=intervention)) +
  geom_point(position=position_jitterdodge(dodge.width=0.75, jitter.height=0, jitter.width=0.25), alpha=0.6) +
  geom_boxplot(alpha=0.2, size=0.3) + 
  facet_wrap(~id) + 
  ggtitle("DV1") +
  xlab("Area") +
  ylab("DV1")

enter image description here

question from:https://stackoverflow.com/questions/65946477/how-do-i-plot-mixed-effects-linear-regression

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