For R beginners, the first operator they use is probably the assignment operator <-. Google's R Style Guide suggests the usage of <- rather than = even though the equal sign is also allowed in R to do exactly the same thing when we assign a value to a variable. However, you might feel inconvenient because you need to type two characters to represent one symbol, which is different from many other programming languages.

As a result, many users ask Why we should use <- as the assignment operator?

Here I provide a simple explanation to the subtle difference between <- and = in R.

First, let's look at an example.

x <- rnorm(100)
y <- 2*x + rnorm(100)
lm(formula=y~x)

The above code uses both <- and = symbols, but the work they do are different. <- in the first two lines are used as assignment operator while = in the third line does not serves as assignment operator but an operator that specifies a named parameter formula for lm function.

In other words, <- evaluates the the expression on its right side (rnorm(100)) and assign the evaluated value to the symbol (variable) on the left side (x) in the current environment. = evaluates the expression on its right side (y~x) and set the evaluated value to the parameter of the name specified on the left side (formula) for a certain function.

We know that <- and = are perfectly equivalent when they are used as assignment operators.

Therefore, the above code is equivalent to the following code:

x = rnorm(100)
y = 2*x + rnorm(100)
lm(formula=y~x)

Here, we only use = but for two different purposes: in the first and second lines we use = as assignment operator and in the third line we use = as a specifier of named parameter.

Now let's see what happens if we change all = symbols to <-.

x <- rnorm(100)
y <- 2*x + rnorm(100)
lm(formula <- y~x)

If you run this code, you will find that the output are similar. But if you inspect the environment, you will observe the difference: a new variable formula is defined in the environment whose value is y~x. So what happens?

Actually, in the third line, two things happened: First, we introduce a new symbol (variable) formula to the environment and assign it a formula-typed value y~x. Then, the value of formula is provided to the first paramter of function lm rather than, accurately speaking, to the parameter named formula, although this time they mean the identical parameter of the function.

To test it, we conduct an experiment. This time we first prepare the data.

x <- rnorm(100)
y <- 2*x+rnorm(100)
z <- 3*x+rnorm(100)
data <- data.frame(z,x,y)
rm(x,y,z)

Basically, we just did similar things as before except that we store all vectors in a data frame and clear those numeric vectors from the environment. We know that lm function accepts a data frame as the data source when a formula is specified.

Standard usage:

lm(formula=z~x+y,data=data)

Working alternative where two named parameters are reordered:

lm(data=data,formula=z~x+y)

Working alternative with side effects that two new variable are defined:

lm(formula <- z~x+y, data <- data)

Nonworking example:

lm(data <- data, formula <- z~x+y)

The reason is exactly what I mentioned previously. We reassign data to data and give its value to the first argument (formula) of lm which only accepts a formula-typed value. We also try to assign z~x+y to a new variable formula and give it to the second argument (data) of lm which only accepts a data frame-typed value. Both types of the parameter we provide to lm are wrong, so we receive the message:

Error in as.data.frame.default(data) : 
    cannot coerce class ""formula"" to a data.frame

From the above examples and experiments, the bottom line gets clear: to reduce ambiguity, we should use either <- or = as assignment operator, and only use = as named-parameter specifier for functions.

In conclusion, for better readability of R code, I suggest that we only use <- for assignment and = for specifying named parameters.