How to simulate data for an interaction? I'd like to simulate data for an interaction / moderation with a continuous exposure and outcome and binary moderator. For example, for the association between X and Y to be 0.1 when moderator = 0 and 0.2 when moderator = 1. This seems very simple but for some reason I'm struggling to do this in R.
Any help would be much appreciated.

I see it as a question of how to generate data from a (linear?) model with interaction. See below for the R code where y is the response, x is the covariate and z is the binary moderator.
set.seed(12)

n <-  1000
# simulate a covariate
x <- rnorm(n)

# simualte a binary moderator
z <- sample(c(0,1),size = n, replace = T)
beta0 <- 1
beta1 <- 2
sigma0 <- 1

# mu
mu <- beta0 + beta1*z + 0.1*x*z + 0.1*x

y <- rnorm(n, mu, sigma0)
dd <- data.frame(y=y, x=x, z=z)
summary(lm(y~x*z, data = dd))
Call:
lm(formula = y ~ x * z, data = dd)

Residuals:
     Min       1Q   Median       3Q      Max 
-3.11036 -0.63836 -0.00177  0.64706  3.00070 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.98525    0.04612  21.364  < 2e-16 ***
x            0.15460    0.04985   3.101  0.00198 ** 
z            2.02830    0.06320  32.092  < 2e-16 ***
x:z          0.04727    0.06632   0.713  0.47615    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9966 on 996 degrees of freedom
Multiple R-squared:  0.5137,    Adjusted R-squared:  0.5123 
F-statistic: 350.7 on 3 and 996 DF,  p-value: < 2.2e-16

