Gene-specific Regularized Ordinary Least Squares fit statistics for supervised PCA

Model statistics for Ordinary Least Squares (OLS) regression by gene.

olsTrain_fun(x, y, s0.perc = NULL)

Arguments

x

An \(p \times n\) predictor matrix.
y

A response vector.
s0.perc

Percentile of the standard error of the slope estimate to be used for regularization. The Default value of NULL will use the median of this distribution.

Value

A list of OLS model statistics:

  • tt : The Student's \(t\) test statistic the slopes (\(\beta\)).

  • numer : The estimate of \(\beta\).

  • sd : The standard error of the estimates for \(\beta\) (the standard error divided by the square root of Sxx).

  • fudge : A regularization parameter. See Details for description.

Details

This function calculates the Sxx, Syy, and Sxy sums from the gene- specific OLS models, then calculates estimates of the regression slopes for each gene and their corresponding regularized test statistics, $$t = \hat{\beta} / (sd + e),$$ where \(e\) is a regularization parameter.

If s0.perc is NULL, then \(e\) is median of the sd values. Otherwise, \(e\) is set equal to quantile(sd, s0.perc).

Examples

  # DO NOT CALL THIS FUNCTION DIRECTLY.
  # Use SuperPCA_pVals() instead

if (FALSE) {
  p <- 500
  n <- 50

  x_mat <- matrix(rnorm(n * p), nrow = p, ncol = n)
  time_int <- rpois(n, lambda = 365 * 2)

  olsTrain_fun(
    x = x_mat,
    y = time_int
  )
}