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The process of transforming a multi-categorical wide format data to long format using R involves the following steps:

1. Load the necessary packages: The dplyr package and tidyr package for data manipulation.

2. Load the dataset: Load the wide format dataset into R using the read.csv function.

3. Reshape the data: Use the gather function from the tidyr package to reshape the columns into rows. The function will take in the dataset, the names of the columns to gather, and the name of the new column.

4. Rename variables: Use the rename function from the dplyr package to give the new variables more meaningful names.

5. Reorder variables: Use the select function from the dplyr package to reorder the variables in the desired order.

6. Save the data: Use the write.csv function to save the long format data to a file.

Example:

Assuming we have a dataset with multiple variables - race, gender, age, and location - and our goal is to transform it from wide format to long format, we can apply the following steps in R:

# Load necessary packages
library(dplyr)
library(tidyr)

# Load dataset
wide_data <- read.csv("wide_data.csv")

# Reshape into long format
long_data <- wide_data %>% gather(key = "variable", value = "value", -race, -gender, -age, -location)

# Rename variables
long_data <- long_data %>% rename("category" = "variable")

# Reorder variables
long_data <- long_data %>% select(race, gender, age, location, category, value)

# Save data
write.csv(long_data, "long_data.csv", row.names = FALSE)