20250204 - orthogonalizing

Author: isaactpetersen

sem.Rmd

@@ -1147,19 +1147,39 @@ names(states)[which(names(states) == "HS Grad")] <- "HS.Grad"
 states$Income_rescaled <- states$Income/100
 ```
 
-## Mean Center Predictors
+## Preparing the Predictors
 
 Make sure to mean-center or orthogonalize predictors before computing the interaction term.
 
+### Mean Center Predictors
+
 ```{r}
 states$Illiteracy_centered <- scale(states$Illiteracy, scale = FALSE)
 states$Murder_centered <- scale(states$Murder, scale = FALSE)
 ```
 
+### Orthogonalized Predictors
+
+Orthogonalizing is residual centering.
+
+```{r}
+states$interaction_notCentered <- states$Illiteracy * states$Murder
+
+states$Illiteracy_orthogonalized <- resid(lm(
+  data = states,
+  interaction_notCentered ~ Illiteracy
+))
+
+states$Murder_orthogonalized <- resid(lm(
+  data = states,
+  interaction_notCentered ~ Murder
+))
+```
+
 ## Compute Interaction Term
 
 ```{r}
-states$interaction <- states$Illiteracy_centered * states$Murder_centered
+states$interaction <- states$Illiteracy_centered * states$Murder_centered # or: states$Illiteracy_orthogonalized * states$Murder_orthogonalized
 ```
 
 ## Model Syntax