Moderated regression and separate models give slightly different results When I run a regression with an interaction term (composed of one continuous variable and one binary variable) and several covariates, I get an interaction term value of -6.52. However, when I run two separate regressions for each value of the binary variable, the coefficients of the predictors are not -6.52 apart. This only occurs when I include the covariates in the model, does anyone know why? 
 A: Separate regressions is equivalent to the interaction of all of your covariates and the binary variable.  From your description, it sounds like you only fitted the interaction of one of the covariates and the binary variable.  See the simulated data below.
set.seed(20180216)
sim_data   <- data.frame(matrix(c(rnorm(500), rbinom(100,1,.5) ) , 100,6) )
sim_data$Y <- with( sim_data, X1 + X2 + X3 + X4 + X5 + 2 * X1 * X6 ) + rnorm(  100, 0, 2 )

model1 <- lm( Y ~ X6 * X1 + X2 + X3 + X4 + X5 ,  data = sim_data  )
model2 <- lm( Y ~ X6 * (X1 + X2 + X3 + X4 + X5) ,  data = sim_data  )
model3 <- lm( Y ~ X1 + X2 + X3 + X4 + X5 ,  data = sim_data , subset = sim_data$X6==0 )
model4 <- lm( Y ~ X1 + X2 + X3 + X4 + X5 ,  data = sim_data , subset = sim_data$X6==1 )

library(stargazer)
stargazer(model1,model2, model3, model4, type="text")


Model 1 in the image is the model you fitted which shows the interaction of X1 and the binary X6.  Model 2 fits the model with the interaction of X6 and all 5 of the other covariates.  Models 3 and 4 fit the separate regressions by group 0 and 1 respectively.
Immediately you will notice that the coefficients for model 3 are the same as those for the main effects of X1-X5 in model 2.
The coefficients for model 4 are the sum of the model 2 coefficients:


*

*X1 + X1 * X6

*X2 + X2 * X6

*...

*X5 + X5 * X6


The term for X6 in model 2 is the difference in the slopes in models 3 & 4.
