How to write a linear model formula with 100 variables in R

Question

Is there an easy way in R to create a linear regression over a model with 100 parameters in R? Let's say we have a vector Y with 10 values and a dataframe X with 10 columns and 100 rows In mathematical notation I would write Y = X[[1]] + X[[2]] + ... + X[[100]]. How do I write something similar in R syntax?

Answer 1

Try this

df<-data.frame(y=rnorm(10),x1=rnorm(10),x2=rnorm(10))
lm(y~.,df)

Answer 2

Great answers!

I would add that by default, calling formula on a data.frame creates an additive formula to regress the first column onto the others.

So in the case of the answer of @danas.zuokas you can even do

lm(df)

which is interpreted correctly.

Answer 3

If each row is an observation and each column is a predictor so that $Y$ is an $n$-length vector and $X$ is an $n \times p$ matrix ($p=100$ in this case), then you can do this with

Z = as.data.frame(cbind(Y,X))
lm(Y ~ .,data=Z)

If there are other columns you did not want to include as predictors, you would have to remove them from X before using this trick, or using - in the model formula to exclude them. For example, if you wanted to exclude the 67th predictor (that has the corresponding name x67), then you could write

lm(Y ~ .-x67,data=Z)

Also, if you want to include interactions, etc.. you will need to add them manually as (for example)

lm(Y ~ .+X[,1]*X[,2],data=Z)

or make sure they are entered as columns of X.

Answer 4

You can also use a combination of the formula and paste functions.

Setup data: Let's imagine we have a data.frame that contains the predictor variables x1 to x100 and our dependent variable y, but that there is also a nuisance variable asdfasdf. Also the predictor variables are arranged in an order such that they are not all contiguous in the data.frame.

Data <- data.frame(matrix(rnorm(102 * 200), ncol=102))
names(Data) <- c(paste("x", 1:50, sep=""), 
    "asdfasdf", "y", paste("x", 51:100, sep=""))

Imagine also that you have a string containing the names of the predictor variables. In this case, this can easily be created using the paste function, but in other situations, grep or some other approach might be used to get this string.

PredictorVariables <- paste("x", 1:100, sep="")

Apply approach: We can then construct a formula as follows:

Formula <- formula(paste("y ~ ", 
     paste(PredictorVariables, collapse=" + ")))
lm(Formula, Data)

• the collapse argument inserts + between the predictor variables
• formula converts the string into an object of class formula suitable for the lm function.

More generally, I use the following function quite regularly when I want to supply a the predictor variables as vector of variable names.

regression <- function(dv, ivs, data) {
    # run a linear model with text arguments for dv and ivs
    iv_string <- paste(ivs, collapse=" + ")
    regression_formula <- as.formula(paste(dv, iv_string, sep=" ~ "))
    lm(regression_formula, data)

}

E.g.,

regression("y", PredictorVariables, Data)