Rfast (version 1.2)

Many univariate simple linear regressions: Many univariate simple linear regressions

Description

It performs very many univariate simple linear regressions with or without categorical variables.

Usage

regression(x, y)

Arguments

x

A data.frame with the data, where the rows denote the samples (and the two groups) and the columns are the variables. Currently only continuous variables are allowed. A data frame is expected if you have categorical predictor variables. If you only have continuous predictor variables you should the function allbetas instead as it is faster.

y

The dependent variable; a numerical vector.

Value

A matrix with two rows. The first row is the F statistic and the second row is the degrees of freedom of the numerator in the F test. That is the number of estimated parameters. For example if some variables are continuous, the number of parameters is 1. In the case of a categorical variable with D distinct values (or levels) the number of parameters is D-1.

Details

The function is written in C++ and this is why it is very fast. It can accept thousands of predictor variables. It is usefull for univariate screening. We provide no p-value correction (such as fdr or q-values); this is up to the user. The user must take the F test statistics along with the numertor degrees and calculate the relevant p-values. We provide the degrees of freedom of the numerator in the F test. The degrees of freedom in the denominator are always n - df of the numerator.

References

Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.

McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition, 1989.

See Also

allbetas, correls, univglms, mvbetas

Examples

## 500 variables, hence 500 univariate regressions are to be fitted
x = matrix( rnorm(100 * 500), ncol = 500 )
x = as.data.frame(x)


## 100 observations in total
y = rnorm(100)   ## binary logistic regression
system.time( regression(x, y) )


a1 = regression(x, y)