moderation model orthogonalizing in lavaan in r

Moderation describes the relationship between two variables which is conditional on a third variable. Orthogonalizing a predictor can simplify modeling with moderations, by removing covariation with other predictors. With the lavaan package in R, you can create a moderation model with orthogonalized predictors by following these steps:

1. Load the lavaan package and your data:

   main.r
   library(lavaan)
   mydata <- read.csv("mydata.csv")
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2. Center and standardize your predictors:

   main.r
   mydata$centered_predictor <- scale(mydata$predictor, center = TRUE, scale = TRUE)
   mydata$centered_moderator <- scale(mydata$moderator, center = TRUE, scale = TRUE)
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3. Create a model with the orthogonalized predictor as a mediator of the relationship between the original predictor and the outcome:

   main.r
   model <- "
             outcome ~ c(predictor) + c(moderator) + c(predictor.centered) + b*predictor.centered + b2*moderator
             predictor.centered ~ c(predictor) + c(moderator) + b3*moderator
            "
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4. Fit the model using the lavaan sem() function:

   main.r
   model_fit <- sem(model, data = mydata)
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5. Inspect the results using the summary() function:

   main.r
   summary(model_fit)
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By orthogonalizing one predictor, you can model conditional effects of that predictor while removing covariation with other predictors. This can lead to a more parsimonious and interpretable model.