One-hot encoding using model.matrix

user_4653482 0
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There is something I do not understand in model.matrix. When I enter a single binary variable without an intercept it returns two levels. 

> temp.data <- data.frame('x' = sample(c('A', 'B'), 1000, replace = TRUE))
> temp.data.table <- model.matrix( ~ 0 + x, data = temp.data)
> head(temp.data.table)
  xA xB
1  1  0
2  0  1
3  0  1
4  0  1
5  1  0
6  0  1

However, when I enter another binary level, it creates only 3 columns. Why is that? What makes the behavior of the function suddenly different? and how can I avoid it? 

> temp.data <- data.frame('x' = sample(c('A', 'B'), 1000, replace = TRUE),
+                         'y' = sample(c('J', 'D'), 1000, replace = TRUE))
> temp.data.table <- model.matrix( ~ 0 + x + y, data = temp.data)
> head(temp.data.table)
  xA xB yJ
1  0  1  0
2  0  1  1
3  0  1  1
4  0  1  0
5  1  0  1
6  0  1  0
one-hot-encoding r
2 Answers

You need to work with factors and set the contrasts to FALSE. Try this:

n <- 10
temp.data <- data.frame('x'=sample(c('A', 'B'), n, replace=TRUE),
                        'y'=factor(sample(c('J', 'D'), n, replace=TRUE)))
model.matrix( ~ 0 + x + y, data=temp.data,
              contrasts=list(y=contrasts(temp.data$y, contrasts=FALSE)))

#    xA xB yD yJ
# 1   0  1  1  0
# 2   1  0  0  1
# 3   0  1  1  0
# 4   1  0  0  1
# 5   0  1  0  1
# 6   1  0  1  0
# 7   1  0  1  0
# 8   0  1  1  0
# 9   0  1  0  1
# 10  0  1  1  0
# attr(,"assign")
# [1] 1 1 2 2
# attr(,"contrasts")
# attr(,"contrasts")$x
# [1] "contr.treatment"
# 
# attr(,"contrasts")$y
#   D J
# D 1 0
# J 0 1

To understand why this happens, try:

contrasts(temp.data$y)
#   J
# D 0
# J 1

contrasts(temp.data$y, contrasts=F)
#   D J
# D 1 0
# J 0 1

With your x variable this happens automatically by setting 0 + to remove the intercept. (Actually x also should be coded as factor).

The reason is, that in linear regression the levels of factor variables are usually compared to a reference level (which you could change using relevel). In your model matrix, with 0 + you remove the intercept for your first variable but not to the following (try model.matrix( ~ 0 + y + x, data=temp.data) where you get only one x but to y). This is determined in the standard contrasts setting using treatment contrasts by default.

You may want to read a relevant post of Rose Maier (2015) explaining this in great detail:

user_65740380

You need to reset the contrasts of the factor variables. See this post.

temp.data <- data.frame('x' = sample(c('A', 'B'), 1000, replace = TRUE),
+                         'y' = sample(c('J', 'D'), 1000, replace = TRUE))

dat = model.matrix(~ -1 +., data=temp.data, contrasts.arg = lapply(temp.data[,1:2], contrasts, contrasts=FALSE))
head(dat)

  xA xB yD yJ
1  0  1  0  1
2  1  0  0  1
3  1  0  0  1
4  1  0  0  1
5  0  1  1  0
6  0  1  0  1
user_95244240
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